begin
theorem
for
h,
x being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) holds
(cD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= ((fD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,(h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) )) : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) . x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
- ((fD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,(- (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) )) : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) . x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
h,
x being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) holds
(fD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,(- (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= - ((bD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,(h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) )) : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) . x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
h,
x being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) holds
(cD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= ((bD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,(h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) )) : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) . x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
- ((bD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,(- (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) )) : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) . x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
n being ( ( ) (
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
for
r,
h,
x being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f1,
f2 being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) holds
((fdif (((r : ( ( ) ( V11() V12() ext-real ) Real) (#) f1 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) + f2 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . (n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (r : ( ( ) ( V11() V12() ext-real ) Real) * (((fdif (f1 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . (n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) . x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
+ (((fdif (f2 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . (n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) . x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
n being ( ( ) (
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
for
r,
h,
x being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f1,
f2 being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) holds
((fdif ((f1 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + (r : ( ( ) ( V11() V12() ext-real ) Real) (#) f2 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . (n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (((fdif (f1 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . (n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) . x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
+ (r : ( ( ) ( V11() V12() ext-real ) Real) * (((fdif (f2 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . (n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) . x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
n being ( ( ) (
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
for
r1,
r2,
h,
x being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f1,
f2 being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) holds
((fdif (((r1 : ( ( ) ( V11() V12() ext-real ) Real) (#) f1 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) - (r2 : ( ( ) ( V11() V12() ext-real ) Real) (#) f2 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . (n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (r1 : ( ( ) ( V11() V12() ext-real ) Real) * (((fdif (f1 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . (n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) . x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
- (r2 : ( ( ) ( V11() V12() ext-real ) Real) * (((fdif (f2 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . (n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) . x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
h being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) holds
(fdif (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18()
V27(
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ,
K69(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) ( )
set ) ) ) (
V13()
V16(
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
V17(
K69(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) ( )
set ) )
V18()
V27(
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ,
K69(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) ( )
set ) ) )
Element of
bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( )
set ) : ( ( ) ( )
set ) )
. 1 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real positive V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
= fD (
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ,
h : ( ( ) (
V11()
V12()
ext-real )
Real) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) ;
theorem
for
n being ( ( ) (
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
for
r,
h,
x being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f1,
f2 being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) holds
((bdif (((r : ( ( ) ( V11() V12() ext-real ) Real) (#) f1 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) + f2 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . (n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (r : ( ( ) ( V11() V12() ext-real ) Real) * (((bdif (f1 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . (n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) . x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
+ (((bdif (f2 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . (n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) . x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
n being ( ( ) (
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
for
r,
h,
x being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f1,
f2 being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) holds
((bdif ((f1 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + (r : ( ( ) ( V11() V12() ext-real ) Real) (#) f2 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . (n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (((bdif (f1 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . (n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) . x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
+ (r : ( ( ) ( V11() V12() ext-real ) Real) * (((bdif (f2 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . (n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) . x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
n being ( ( ) (
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
for
r1,
r2,
h,
x being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f1,
f2 being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) holds
((bdif (((r1 : ( ( ) ( V11() V12() ext-real ) Real) (#) f1 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) - (r2 : ( ( ) ( V11() V12() ext-real ) Real) (#) f2 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . (n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (r1 : ( ( ) ( V11() V12() ext-real ) Real) * (((bdif (f1 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . (n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) . x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
- (r2 : ( ( ) ( V11() V12() ext-real ) Real) * (((bdif (f2 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . (n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) . x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
h being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) holds
(bdif (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18()
V27(
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ,
K69(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) ( )
set ) ) ) (
V13()
V16(
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
V17(
K69(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) ( )
set ) )
V18()
V27(
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ,
K69(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) ( )
set ) ) )
Element of
bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( )
set ) : ( ( ) ( )
set ) )
. 1 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real positive V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
= bD (
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ,
h : ( ( ) (
V11()
V12()
ext-real )
Real) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) ;
theorem
for
m,
n being ( ( ) (
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
for
h,
x being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) holds
((bdif (((bdif (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . m : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= ((bdif (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . (m : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) + n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
n being ( ( ) (
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
for
r,
h,
x being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f1,
f2 being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) holds
((cdif (((r : ( ( ) ( V11() V12() ext-real ) Real) (#) f1 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) + f2 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . (n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (r : ( ( ) ( V11() V12() ext-real ) Real) * (((cdif (f1 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . (n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) . x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
+ (((cdif (f2 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . (n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) . x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
n being ( ( ) (
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
for
r,
h,
x being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f1,
f2 being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) holds
((cdif ((f1 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + (r : ( ( ) ( V11() V12() ext-real ) Real) (#) f2 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . (n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (((cdif (f1 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . (n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) . x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
+ (r : ( ( ) ( V11() V12() ext-real ) Real) * (((cdif (f2 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . (n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) . x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
n being ( ( ) (
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
for
r1,
r2,
h,
x being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f1,
f2 being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) holds
((cdif (((r1 : ( ( ) ( V11() V12() ext-real ) Real) (#) f1 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) - (r2 : ( ( ) ( V11() V12() ext-real ) Real) (#) f2 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . (n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (r1 : ( ( ) ( V11() V12() ext-real ) Real) * (((cdif (f1 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . (n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) . x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
- (r2 : ( ( ) ( V11() V12() ext-real ) Real) * (((cdif (f2 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . (n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) . x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
h being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) holds
(cdif (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18()
V27(
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ,
K69(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) ( )
set ) ) ) (
V13()
V16(
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
V17(
K69(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) ( )
set ) )
V18()
V27(
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ,
K69(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) ( )
set ) ) )
Element of
bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( )
set ) : ( ( ) ( )
set ) )
. 1 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real positive V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
= cD (
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ,
h : ( ( ) (
V11()
V12()
ext-real )
Real) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) ;
theorem
for
m,
n being ( ( ) (
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
for
h,
x being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) holds
((cdif (((cdif (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . m : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= ((cdif (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . (m : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) + n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
n being ( ( ) (
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
for
h,
x being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st
((fdif (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= ((cdif (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. (x : ( ( ) ( V11() V12() ext-real ) Real) + ((n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) holds
((bdif (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= ((cdif (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. (x : ( ( ) ( V11() V12() ext-real ) Real) - ((n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
n being ( ( ) (
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
for
h,
x being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st
((fdif (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= ((cdif (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. ((x : ( ( ) ( V11() V12() ext-real ) Real) + (((n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) - 1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) holds
((bdif (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= ((cdif (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. ((x : ( ( ) ( V11() V12() ext-real ) Real) - (((n : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) - 1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x,
h being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) holds
[!f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,x : ( ( ) ( V11() V12() ext-real ) Real) ,(x : ( ( ) ( V11() V12() ext-real ) Real) + h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) !] : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= ((fD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) . x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
/ h : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x,
h being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) holds
[!f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,(x : ( ( ) ( V11() V12() ext-real ) Real) - h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,x : ( ( ) ( V11() V12() ext-real ) Real) !] : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= ((bD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) . x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
/ h : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x,
h being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) holds
[!f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,(x : ( ( ) ( V11() V12() ext-real ) Real) - (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,(x : ( ( ) ( V11() V12() ext-real ) Real) + (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) !] : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= ((cD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) . x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
/ h : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x,
h being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) holds
[!f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,(x : ( ( ) ( V11() V12() ext-real ) Real) - (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,(x : ( ( ) ( V11() V12() ext-real ) Real) + (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) !] : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (((cdif (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . 1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) . x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
/ h : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
h,
x being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st
h : ( ( ) (
V11()
V12()
ext-real )
Real)
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) holds
[!f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,(x : ( ( ) ( V11() V12() ext-real ) Real) - h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,x : ( ( ) ( V11() V12() ext-real ) Real) ,(x : ( ( ) ( V11() V12() ext-real ) Real) + h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) !] : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (((cdif (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) . x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
/ ((2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x0,
x1 being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f1,
f2 being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) holds
[!(f1 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - f2 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ,x0 : ( ( ) ( V11() V12() ext-real ) Real) ,x1 : ( ( ) ( V11() V12() ext-real ) Real) !] : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= [!f1 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,x0 : ( ( ) ( V11() V12() ext-real ) Real) ,x1 : ( ( ) ( V11() V12() ext-real ) Real) !] : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
- [!f2 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,x0 : ( ( ) ( V11() V12() ext-real ) Real) ,x1 : ( ( ) ( V11() V12() ext-real ) Real) !] : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
r,
x0,
x1 being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f1,
f2 being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) holds
[!((r : ( ( ) ( V11() V12() ext-real ) Real) (#) f1 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) + f2 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ,x0 : ( ( ) ( V11() V12() ext-real ) Real) ,x1 : ( ( ) ( V11() V12() ext-real ) Real) !] : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (r : ( ( ) ( V11() V12() ext-real ) Real) * [!f1 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,x0 : ( ( ) ( V11() V12() ext-real ) Real) ,x1 : ( ( ) ( V11() V12() ext-real ) Real) !] : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
+ [!f2 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,x0 : ( ( ) ( V11() V12() ext-real ) Real) ,x1 : ( ( ) ( V11() V12() ext-real ) Real) !] : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
r,
x0,
x1 being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f1,
f2 being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) holds
[!((r : ( ( ) ( V11() V12() ext-real ) Real) (#) f1 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) - f2 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ,x0 : ( ( ) ( V11() V12() ext-real ) Real) ,x1 : ( ( ) ( V11() V12() ext-real ) Real) !] : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (r : ( ( ) ( V11() V12() ext-real ) Real) * [!f1 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,x0 : ( ( ) ( V11() V12() ext-real ) Real) ,x1 : ( ( ) ( V11() V12() ext-real ) Real) !] : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
- [!f2 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,x0 : ( ( ) ( V11() V12() ext-real ) Real) ,x1 : ( ( ) ( V11() V12() ext-real ) Real) !] : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
r,
x0,
x1 being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f1,
f2 being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) holds
[!(f1 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + (r : ( ( ) ( V11() V12() ext-real ) Real) (#) f2 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ,x0 : ( ( ) ( V11() V12() ext-real ) Real) ,x1 : ( ( ) ( V11() V12() ext-real ) Real) !] : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= [!f1 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,x0 : ( ( ) ( V11() V12() ext-real ) Real) ,x1 : ( ( ) ( V11() V12() ext-real ) Real) !] : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
+ (r : ( ( ) ( V11() V12() ext-real ) Real) * [!f2 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,x0 : ( ( ) ( V11() V12() ext-real ) Real) ,x1 : ( ( ) ( V11() V12() ext-real ) Real) !] : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
r,
x0,
x1 being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f1,
f2 being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) holds
[!(f1 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - (r : ( ( ) ( V11() V12() ext-real ) Real) (#) f2 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ,x0 : ( ( ) ( V11() V12() ext-real ) Real) ,x1 : ( ( ) ( V11() V12() ext-real ) Real) !] : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= [!f1 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,x0 : ( ( ) ( V11() V12() ext-real ) Real) ,x1 : ( ( ) ( V11() V12() ext-real ) Real) !] : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
- (r : ( ( ) ( V11() V12() ext-real ) Real) * [!f2 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,x0 : ( ( ) ( V11() V12() ext-real ) Real) ,x1 : ( ( ) ( V11() V12() ext-real ) Real) !] : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
r1,
r2,
x0,
x1 being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f1,
f2 being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) holds
[!((r1 : ( ( ) ( V11() V12() ext-real ) Real) (#) f1 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) - (r2 : ( ( ) ( V11() V12() ext-real ) Real) (#) f2 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ,x0 : ( ( ) ( V11() V12() ext-real ) Real) ,x1 : ( ( ) ( V11() V12() ext-real ) Real) !] : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (r1 : ( ( ) ( V11() V12() ext-real ) Real) * [!f1 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,x0 : ( ( ) ( V11() V12() ext-real ) Real) ,x1 : ( ( ) ( V11() V12() ext-real ) Real) !] : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
- (r2 : ( ( ) ( V11() V12() ext-real ) Real) * [!f2 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,x0 : ( ( ) ( V11() V12() ext-real ) Real) ,x1 : ( ( ) ( V11() V12() ext-real ) Real) !] : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
h,
x being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f1,
f2 being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) holds
((bdif ((f1 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) (#) f2 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . 1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= ((f1 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) . x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (((bdif (f2 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . 1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) . x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
+ ((f2 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) . (x : ( ( ) ( V11() V12() ext-real ) Real) - h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (((bdif (f1 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . 1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) . x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x0,
x1,
x2 being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st
x0 : ( ( ) (
V11()
V12()
ext-real )
Real) ,
x1 : ( ( ) (
V11()
V12()
ext-real )
Real) ,
x2 : ( ( ) (
V11()
V12()
ext-real )
Real)
are_mutually_different holds
[!f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,x0 : ( ( ) ( V11() V12() ext-real ) Real) ,x1 : ( ( ) ( V11() V12() ext-real ) Real) ,x2 : ( ( ) ( V11() V12() ext-real ) Real) !] : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= [!f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,x0 : ( ( ) ( V11() V12() ext-real ) Real) ,x2 : ( ( ) ( V11() V12() ext-real ) Real) ,x1 : ( ( ) ( V11() V12() ext-real ) Real) !] : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
h,
x being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f1,
f2 being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
for
S being ( (
V18()
V27(
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ,
K69(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) ( )
set ) )
Sequence-yielding ) (
V13()
V16(
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
V17(
K69(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) ( )
set ) )
V18()
V27(
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ,
K69(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) ( )
set ) )
Sequence-yielding )
Seq_Sequence) st ( for
n,
i being ( (
V10() ) (
V10()
V11()
V12()
ext-real )
Nat) st
i : ( (
V10() ) (
V10()
V11()
V12()
ext-real )
Nat)
<= n : ( (
V10() ) (
V10()
V11()
V12()
ext-real )
Nat) holds
(S : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) Sequence-yielding ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) Sequence-yielding ) Seq_Sequence) . n : ( ( V10() ) ( V10() V11() V12() ext-real ) Nat) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. i : ( (
V10() ) (
V10()
V11()
V12()
ext-real )
Nat) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= ((n : ( ( V10() ) ( V10() V11() V12() ext-real ) Nat) choose i : ( ( V10() ) ( V10() V11() V12() ext-real ) Nat) ) : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * (((bdif (f1 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . i : ( ( V10() ) ( V10() V11() V12() ext-real ) Nat) ) : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) . x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
* (((bdif (f2 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . (n : ( ( V10() ) ( V10() V11() V12() ext-real ) Nat) -' i : ( ( V10() ) ( V10() V11() V12() ext-real ) Nat) ) : ( ( ) ( V10() V11() V12() ext-real non negative V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) . (x : ( ( ) ( V11() V12() ext-real ) Real) - (i : ( ( V10() ) ( V10() V11() V12() ext-real ) Nat) * h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) holds
(
((bdif ((f1 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) (#) f2 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . 1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= Sum (
(S : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) Sequence-yielding ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) Sequence-yielding ) Seq_Sequence) . 1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( (
V18()
V27(
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V13()
V16(
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
V27(
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Element of
bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) ,1 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real positive V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) &
((bdif ((f1 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) (#) f2 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= Sum (
(S : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) Sequence-yielding ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) Sequence-yielding ) Seq_Sequence) . 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( (
V18()
V27(
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V13()
V16(
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
V27(
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Element of
bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) ,2 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real positive V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) ;
theorem
for
h,
x being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f1,
f2 being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) holds
((cdif ((f1 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) (#) f2 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . 1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= ((f1 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) . (x : ( ( ) ( V11() V12() ext-real ) Real) + (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (((cdif (f2 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . 1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) . x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
+ ((f2 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) . (x : ( ( ) ( V11() V12() ext-real ) Real) - (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (((cdif (f1 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . 1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) . x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
h,
x being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f1,
f2 being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
for
S being ( (
V18()
V27(
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ,
K69(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) ( )
set ) )
Sequence-yielding ) (
V13()
V16(
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
V17(
K69(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) ( )
set ) )
V18()
V27(
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ,
K69(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) ( )
set ) )
Sequence-yielding )
Seq_Sequence) st ( for
n,
i being ( (
V10() ) (
V10()
V11()
V12()
ext-real )
Nat) st
i : ( (
V10() ) (
V10()
V11()
V12()
ext-real )
Nat)
<= n : ( (
V10() ) (
V10()
V11()
V12()
ext-real )
Nat) holds
(S : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) Sequence-yielding ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) Sequence-yielding ) Seq_Sequence) . n : ( ( V10() ) ( V10() V11() V12() ext-real ) Nat) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. i : ( (
V10() ) (
V10()
V11()
V12()
ext-real )
Nat) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= ((n : ( ( V10() ) ( V10() V11() V12() ext-real ) Nat) choose i : ( ( V10() ) ( V10() V11() V12() ext-real ) Nat) ) : ( ( ) ( V10() V11() V12() ext-real V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * (((cdif (f1 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . i : ( ( V10() ) ( V10() V11() V12() ext-real ) Nat) ) : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) . (x : ( ( ) ( V11() V12() ext-real ) Real) + ((n : ( ( V10() ) ( V10() V11() V12() ext-real ) Nat) -' i : ( ( V10() ) ( V10() V11() V12() ext-real ) Nat) ) : ( ( ) ( V10() V11() V12() ext-real non negative V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
* (((cdif (f2 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . (n : ( ( V10() ) ( V10() V11() V12() ext-real ) Nat) -' i : ( ( V10() ) ( V10() V11() V12() ext-real ) Nat) ) : ( ( ) ( V10() V11() V12() ext-real non negative V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) . (x : ( ( ) ( V11() V12() ext-real ) Real) - (i : ( ( V10() ) ( V10() V11() V12() ext-real ) Nat) * (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) holds
(
((cdif ((f1 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) (#) f2 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . 1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= Sum (
(S : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) Sequence-yielding ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) Sequence-yielding ) Seq_Sequence) . 1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( (
V18()
V27(
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V13()
V16(
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
V27(
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Element of
bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) ,1 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real positive V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) &
((cdif ((f1 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) (#) f2 : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) ) Element of bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= Sum (
(S : ( ( V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) Sequence-yielding ) ( V13() V16( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) V17(K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) V18() V27( NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,K69(REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) : ( ( ) ( ) set ) ) Sequence-yielding ) Seq_Sequence) . 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( (
V18()
V27(
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V13()
V16(
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
V27(
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Element of
bool [:NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) ,2 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real positive V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) ;
theorem
for
x0,
x1 being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= sqrt x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
x0 : ( ( ) (
V11()
V12()
ext-real )
Real)
<> x1 : ( ( ) (
V11()
V12()
ext-real )
Real) &
x0 : ( ( ) (
V11()
V12()
ext-real )
Real)
> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) &
x1 : ( ( ) (
V11()
V12()
ext-real )
Real)
> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) holds
[!f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,x0 : ( ( ) ( V11() V12() ext-real ) Real) ,x1 : ( ( ) ( V11() V12() ext-real ) Real) !] : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= 1 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real positive V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
/ ((sqrt x0 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + (sqrt x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x0,
x1,
x2 being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= sqrt x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
x0 : ( ( ) (
V11()
V12()
ext-real )
Real) ,
x1 : ( ( ) (
V11()
V12()
ext-real )
Real) ,
x2 : ( ( ) (
V11()
V12()
ext-real )
Real)
are_mutually_different &
x0 : ( ( ) (
V11()
V12()
ext-real )
Real)
> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) &
x1 : ( ( ) (
V11()
V12()
ext-real )
Real)
> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) &
x2 : ( ( ) (
V11()
V12()
ext-real )
Real)
> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) holds
[!f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,x0 : ( ( ) ( V11() V12() ext-real ) Real) ,x1 : ( ( ) ( V11() V12() ext-real ) Real) ,x2 : ( ( ) ( V11() V12() ext-real ) Real) !] : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= - (1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) / ((((sqrt x0 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + (sqrt x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * ((sqrt x0 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + (sqrt x2 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * ((sqrt x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + (sqrt x2 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x0,
x1,
x2,
x3 being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= sqrt x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
x0 : ( ( ) (
V11()
V12()
ext-real )
Real) ,
x1 : ( ( ) (
V11()
V12()
ext-real )
Real) ,
x2 : ( ( ) (
V11()
V12()
ext-real )
Real) ,
x3 : ( ( ) (
V11()
V12()
ext-real )
Real)
are_mutually_different &
x0 : ( ( ) (
V11()
V12()
ext-real )
Real)
> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) &
x1 : ( ( ) (
V11()
V12()
ext-real )
Real)
> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) &
x2 : ( ( ) (
V11()
V12()
ext-real )
Real)
> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) &
x3 : ( ( ) (
V11()
V12()
ext-real )
Real)
> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) holds
[!f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,x0 : ( ( ) ( V11() V12() ext-real ) Real) ,x1 : ( ( ) ( V11() V12() ext-real ) Real) ,x2 : ( ( ) ( V11() V12() ext-real ) Real) ,x3 : ( ( ) ( V11() V12() ext-real ) Real) !] : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= ((((sqrt x0 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + (sqrt x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + (sqrt x2 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + (sqrt x3 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
/ (((((((sqrt x0 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + (sqrt x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * ((sqrt x0 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + (sqrt x2 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * ((sqrt x0 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + (sqrt x3 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * ((sqrt x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + (sqrt x2 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * ((sqrt x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + (sqrt x3 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * ((sqrt x2 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + (sqrt x3 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x,
h being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= sqrt x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
x : ( ( ) (
V11()
V12()
ext-real )
Real)
> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) &
x : ( ( ) (
V11()
V12()
ext-real )
Real)
+ h : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) holds
(fD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (sqrt (x : ( ( ) ( V11() V12() ext-real ) Real) + h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
- (sqrt x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x,
h being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= sqrt x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
x : ( ( ) (
V11()
V12()
ext-real )
Real)
> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) &
x : ( ( ) (
V11()
V12()
ext-real )
Real)
- h : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) holds
(bD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (sqrt x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
- (sqrt (x : ( ( ) ( V11() V12() ext-real ) Real) - h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x,
h being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= sqrt x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
x : ( ( ) (
V11()
V12()
ext-real )
Real)
+ (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) &
x : ( ( ) (
V11()
V12()
ext-real )
Real)
- (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) holds
(cD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (sqrt (x : ( ( ) ( V11() V12() ext-real ) Real) + (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
- (sqrt (x : ( ( ) ( V11() V12() ext-real ) Real) - (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x0,
x1 being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= x : ( ( ) (
V11()
V12()
ext-real )
Real)
^2 : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
x0 : ( ( ) (
V11()
V12()
ext-real )
Real)
<> x1 : ( ( ) (
V11()
V12()
ext-real )
Real) holds
[!f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,x0 : ( ( ) ( V11() V12() ext-real ) Real) ,x1 : ( ( ) ( V11() V12() ext-real ) Real) !] : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= x0 : ( ( ) (
V11()
V12()
ext-real )
Real)
+ x1 : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x0,
x1,
x2 being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= x : ( ( ) (
V11()
V12()
ext-real )
Real)
^2 : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
x0 : ( ( ) (
V11()
V12()
ext-real )
Real) ,
x1 : ( ( ) (
V11()
V12()
ext-real )
Real) ,
x2 : ( ( ) (
V11()
V12()
ext-real )
Real)
are_mutually_different holds
[!f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,x0 : ( ( ) ( V11() V12() ext-real ) Real) ,x1 : ( ( ) ( V11() V12() ext-real ) Real) ,x2 : ( ( ) ( V11() V12() ext-real ) Real) !] : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= 1 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real positive V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) ;
theorem
for
x0,
x1,
x2,
x3 being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= x : ( ( ) (
V11()
V12()
ext-real )
Real)
^2 : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
x0 : ( ( ) (
V11()
V12()
ext-real )
Real) ,
x1 : ( ( ) (
V11()
V12()
ext-real )
Real) ,
x2 : ( ( ) (
V11()
V12()
ext-real )
Real) ,
x3 : ( ( ) (
V11()
V12()
ext-real )
Real)
are_mutually_different holds
[!f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,x0 : ( ( ) ( V11() V12() ext-real ) Real) ,x1 : ( ( ) ( V11() V12() ext-real ) Real) ,x2 : ( ( ) ( V11() V12() ext-real ) Real) ,x3 : ( ( ) ( V11() V12() ext-real ) Real) !] : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) ;
theorem
for
h,
x being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= x : ( ( ) (
V11()
V12()
ext-real )
Real)
^2 : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) holds
(fD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= ((2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
+ (h : ( ( ) ( V11() V12() ext-real ) Real) ^2) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
h,
x being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= x : ( ( ) (
V11()
V12()
ext-real )
Real)
^2 : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) holds
(bD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= h : ( ( ) (
V11()
V12()
ext-real )
Real)
* ((2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
h,
x being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= x : ( ( ) (
V11()
V12()
ext-real )
Real)
^2 : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) holds
(cD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
* x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
k,
x0,
x1 being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= k : ( ( ) (
V11()
V12()
ext-real )
Real)
/ (x : ( ( ) ( V11() V12() ext-real ) Real) ^2) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
x0 : ( ( ) (
V11()
V12()
ext-real )
Real)
<> x1 : ( ( ) (
V11()
V12()
ext-real )
Real) &
x0 : ( ( ) (
V11()
V12()
ext-real )
Real)
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) &
x1 : ( ( ) (
V11()
V12()
ext-real )
Real)
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) holds
[!f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,x0 : ( ( ) ( V11() V12() ext-real ) Real) ,x1 : ( ( ) ( V11() V12() ext-real ) Real) !] : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= - ((k : ( ( ) ( V11() V12() ext-real ) Real) / (x0 : ( ( ) ( V11() V12() ext-real ) Real) * x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * ((1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) / x0 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + (1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) / x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
k,
x0,
x1,
x2 being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= k : ( ( ) (
V11()
V12()
ext-real )
Real)
/ (x : ( ( ) ( V11() V12() ext-real ) Real) ^2) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
x0 : ( ( ) (
V11()
V12()
ext-real )
Real)
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) &
x1 : ( ( ) (
V11()
V12()
ext-real )
Real)
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) &
x2 : ( ( ) (
V11()
V12()
ext-real )
Real)
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) &
x0 : ( ( ) (
V11()
V12()
ext-real )
Real) ,
x1 : ( ( ) (
V11()
V12()
ext-real )
Real) ,
x2 : ( ( ) (
V11()
V12()
ext-real )
Real)
are_mutually_different holds
[!f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,x0 : ( ( ) ( V11() V12() ext-real ) Real) ,x1 : ( ( ) ( V11() V12() ext-real ) Real) ,x2 : ( ( ) ( V11() V12() ext-real ) Real) !] : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (k : ( ( ) ( V11() V12() ext-real ) Real) / ((x0 : ( ( ) ( V11() V12() ext-real ) Real) * x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * x2 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
* (((1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) / x0 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + (1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) / x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + (1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) / x2 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
k,
x,
h being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= k : ( ( ) (
V11()
V12()
ext-real )
Real)
/ (x : ( ( ) ( V11() V12() ext-real ) Real) ^2) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
x : ( ( ) (
V11()
V12()
ext-real )
Real)
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) &
x : ( ( ) (
V11()
V12()
ext-real )
Real)
+ h : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) holds
(fD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (((- k : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * ((2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
/ (((x : ( ( ) ( V11() V12() ext-real ) Real) ^2) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + (h : ( ( ) ( V11() V12() ext-real ) Real) * x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ^2) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
k,
x,
h being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= k : ( ( ) (
V11()
V12()
ext-real )
Real)
/ (x : ( ( ) ( V11() V12() ext-real ) Real) ^2) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
x : ( ( ) (
V11()
V12()
ext-real )
Real)
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) &
x : ( ( ) (
V11()
V12()
ext-real )
Real)
- h : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) holds
(bD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (((- k : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * ((2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
/ (((x : ( ( ) ( V11() V12() ext-real ) Real) ^2) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - (x : ( ( ) ( V11() V12() ext-real ) Real) * h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ^2) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
k,
x,
h being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= k : ( ( ) (
V11()
V12()
ext-real )
Real)
/ (x : ( ( ) ( V11() V12() ext-real ) Real) ^2) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
x : ( ( ) (
V11()
V12()
ext-real )
Real)
+ (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) &
x : ( ( ) (
V11()
V12()
ext-real )
Real)
- (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) holds
(cD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (- (((2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * k : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
/ (((x : ( ( ) ( V11() V12() ext-real ) Real) ^2) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - ((h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ^2) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ^2) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x0,
x1 being ( ( ) (
V11()
V12()
ext-real )
Real) holds
[!((sin : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) (#) sin : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) (#) sin : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ,x0 : ( ( ) ( V11() V12() ext-real ) Real) ,x1 : ( ( ) ( V11() V12() ext-real ) Real) !] : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= ((1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V1() V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (((3 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * (cos ((x0 : ( ( ) ( V11() V12() ext-real ) Real) + x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (sin ((x0 : ( ( ) ( V11() V12() ext-real ) Real) - x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - ((cos ((3 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * (x0 : ( ( ) ( V11() V12() ext-real ) Real) + x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (sin ((3 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * (x0 : ( ( ) ( V11() V12() ext-real ) Real) - x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
/ (x0 : ( ( ) ( V11() V12() ext-real ) Real) - x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
h,
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
(fD (((sin : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) (#) sin : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) (#) sin : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V1()
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
* (((3 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * (cos (((2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (sin (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - ((cos ((3 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * ((2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (sin ((3 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
h,
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
(bD (((sin : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) (#) sin : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) (#) sin : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V1()
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
* (((3 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * (cos (((2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (sin (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - ((cos ((3 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * ((2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (sin ((3 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
h,
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
(cD (((sin : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) (#) sin : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) (#) sin : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V1()
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
* (((3 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * (cos x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (sin (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - ((cos (3 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (sin ((3 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x0,
x1 being ( ( ) (
V11()
V12()
ext-real )
Real) holds
[!((cos : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) (#) cos : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) (#) cos : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ,x0 : ( ( ) ( V11() V12() ext-real ) Real) ,x1 : ( ( ) ( V11() V12() ext-real ) Real) !] : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= - (((1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V1() V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (((3 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * (sin ((x0 : ( ( ) ( V11() V12() ext-real ) Real) + x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (sin ((x0 : ( ( ) ( V11() V12() ext-real ) Real) - x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + ((sin (((3 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * x0 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + (3 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (sin (((3 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * x0 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - (3 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / (x0 : ( ( ) ( V11() V12() ext-real ) Real) - x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
h,
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
(fD (((cos : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) (#) cos : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) (#) cos : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= - ((1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V1() V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (((3 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * (sin (((2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (sin (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + ((sin ((3 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * ((2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (sin ((3 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
h,
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
(bD (((cos : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) (#) cos : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) (#) cos : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= - ((1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V1() V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (((3 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * (sin (((2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (sin (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + ((sin ((3 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * ((2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (sin ((3 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
h,
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
(cD (((cos : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) (#) cos : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) (#) cos : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( ( V18() ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= - ((1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V1() V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (((3 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * (sin x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (sin (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + ((sin (3 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (sin ((3 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x0,
x1 being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= 1 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real positive V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
/ (sin x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
sin x0 : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) &
sin x1 : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) holds
[!f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,x0 : ( ( ) ( V11() V12() ext-real ) Real) ,x1 : ( ( ) ( V11() V12() ext-real ) Real) !] : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= - (((2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * ((sin x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - (sin x0 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / ((cos (x0 : ( ( ) ( V11() V12() ext-real ) Real) + x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - (cos (x0 : ( ( ) ( V11() V12() ext-real ) Real) - x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / (x0 : ( ( ) ( V11() V12() ext-real ) Real) - x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x,
h being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= 1 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real positive V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
/ (sin x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
sin x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) &
sin (x : ( ( ) ( V11() V12() ext-real ) Real) + h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) holds
(fD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= - ((2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * ((sin x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - (sin (x : ( ( ) ( V11() V12() ext-real ) Real) + h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / ((cos ((2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - (cos h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x,
h being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= 1 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real positive V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
/ (sin x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
sin x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) &
sin (x : ( ( ) ( V11() V12() ext-real ) Real) - h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) holds
(bD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= ((- 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V1() V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * ((sin (x : ( ( ) ( V11() V12() ext-real ) Real) - h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - (sin x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
/ ((cos ((2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - (cos h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x,
h being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= 1 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real positive V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
/ (sin x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
sin (x : ( ( ) ( V11() V12() ext-real ) Real) + (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) &
sin (x : ( ( ) ( V11() V12() ext-real ) Real) - (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) holds
(cD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= - ((2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * ((sin (x : ( ( ) ( V11() V12() ext-real ) Real) - (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - (sin (x : ( ( ) ( V11() V12() ext-real ) Real) + (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / ((cos (2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - (cos h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x0,
x1 being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= 1 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real positive V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
/ (cos x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
x0 : ( ( ) (
V11()
V12()
ext-real )
Real)
<> x1 : ( ( ) (
V11()
V12()
ext-real )
Real) &
cos x0 : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) &
cos x1 : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) holds
[!f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,x0 : ( ( ) ( V11() V12() ext-real ) Real) ,x1 : ( ( ) ( V11() V12() ext-real ) Real) !] : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= ((2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * ((cos x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - (cos x0 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / ((cos (x0 : ( ( ) ( V11() V12() ext-real ) Real) + x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + (cos (x0 : ( ( ) ( V11() V12() ext-real ) Real) - x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
/ (x0 : ( ( ) ( V11() V12() ext-real ) Real) - x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x,
h being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= 1 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real positive V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
/ (cos x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
cos x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) &
cos (x : ( ( ) ( V11() V12() ext-real ) Real) + h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) holds
(fD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * ((cos x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - (cos (x : ( ( ) ( V11() V12() ext-real ) Real) + h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
/ ((cos ((2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + (cos h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x,
h being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= 1 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real positive V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
/ (cos x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
cos x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) &
cos (x : ( ( ) ( V11() V12() ext-real ) Real) - h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) holds
(bD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * ((cos (x : ( ( ) ( V11() V12() ext-real ) Real) - h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - (cos x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
/ ((cos ((2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + (cos h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x,
h being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= 1 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real positive V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
/ (cos x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
cos (x : ( ( ) ( V11() V12() ext-real ) Real) + (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) &
cos (x : ( ( ) ( V11() V12() ext-real ) Real) - (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) holds
(cD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * ((cos (x : ( ( ) ( V11() V12() ext-real ) Real) - (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - (cos (x : ( ( ) ( V11() V12() ext-real ) Real) + (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
/ ((cos (2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + (cos h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x0,
x1 being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= 1 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real positive V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
/ ((sin x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ^2) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
x0 : ( ( ) (
V11()
V12()
ext-real )
Real)
<> x1 : ( ( ) (
V11()
V12()
ext-real )
Real) &
sin x0 : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) &
sin x1 : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) holds
[!f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,x0 : ( ( ) ( V11() V12() ext-real ) Real) ,x1 : ( ( ) ( V11() V12() ext-real ) Real) !] : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= ((((16 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * (cos ((x1 : ( ( ) ( V11() V12() ext-real ) Real) + x0 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (sin ((x1 : ( ( ) ( V11() V12() ext-real ) Real) - x0 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (cos ((x1 : ( ( ) ( V11() V12() ext-real ) Real) - x0 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (sin ((x1 : ( ( ) ( V11() V12() ext-real ) Real) + x0 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
/ ((((cos (x0 : ( ( ) ( V11() V12() ext-real ) Real) + x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - (cos (x0 : ( ( ) ( V11() V12() ext-real ) Real) - x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ^2) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (x0 : ( ( ) ( V11() V12() ext-real ) Real) - x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x,
h being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= 1 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real positive V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
/ ((sin x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ^2) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
sin x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) &
sin (x : ( ( ) ( V11() V12() ext-real ) Real) + h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) holds
(fD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= ((((16 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * (cos (((2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (sin ((- h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (cos ((- h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (sin (((2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
/ (((cos ((2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - (cos h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ^2) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x,
h being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= 1 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real positive V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
/ ((sin x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ^2) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
sin x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) &
sin (x : ( ( ) ( V11() V12() ext-real ) Real) - h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) holds
(bD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= ((((16 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * (cos (((2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (sin ((- h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (cos ((- h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (sin (((2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
/ (((cos ((2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - (cos h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ^2) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x,
h being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= 1 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real positive V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
/ ((sin x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ^2) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
sin (x : ( ( ) ( V11() V12() ext-real ) Real) + (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) &
sin (x : ( ( ) ( V11() V12() ext-real ) Real) - (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) holds
(cD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= ((((16 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * (cos x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (sin ((- h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (cos ((- h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (sin x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
/ (((cos (2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - (cos h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ^2) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x0,
x1 being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= 1 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real positive V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
/ ((cos x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ^2) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
x0 : ( ( ) (
V11()
V12()
ext-real )
Real)
<> x1 : ( ( ) (
V11()
V12()
ext-real )
Real) &
cos x0 : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) &
cos x1 : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) holds
[!f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,x0 : ( ( ) ( V11() V12() ext-real ) Real) ,x1 : ( ( ) ( V11() V12() ext-real ) Real) !] : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= ((((((- 16 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V1() V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (sin ((x1 : ( ( ) ( V11() V12() ext-real ) Real) + x0 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (sin ((x1 : ( ( ) ( V11() V12() ext-real ) Real) - x0 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (cos ((x1 : ( ( ) ( V11() V12() ext-real ) Real) + x0 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (cos ((x1 : ( ( ) ( V11() V12() ext-real ) Real) - x0 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / (((cos (x0 : ( ( ) ( V11() V12() ext-real ) Real) + x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + (cos (x0 : ( ( ) ( V11() V12() ext-real ) Real) - x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ^2) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
/ (x0 : ( ( ) ( V11() V12() ext-real ) Real) - x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x,
h being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= 1 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real positive V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
/ ((cos x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ^2) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
cos x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) &
cos (x : ( ( ) ( V11() V12() ext-real ) Real) + h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) holds
(fD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (((((- 16 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V1() V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (sin (((2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (sin ((- h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (cos (((2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (cos ((- h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
/ (((cos ((2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + (cos h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ^2) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x,
h being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= 1 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real positive V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
/ ((cos x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ^2) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
cos x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) &
cos (x : ( ( ) ( V11() V12() ext-real ) Real) - h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) holds
(bD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (((((- 16 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V1() V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (sin (((2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (sin ((- h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (cos (((2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (cos ((- h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
/ (((cos ((2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + (cos h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ^2) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x,
h being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= 1 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real positive V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) )
/ ((cos x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ^2) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
cos (x : ( ( ) ( V11() V12() ext-real ) Real) + (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) &
cos (x : ( ( ) ( V11() V12() ext-real ) Real) - (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
<> 0 : ( ( ) (
V1()
V10()
V11()
V12()
ext-real V43()
V49()
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
NAT : ( ( ) (
V50()
V51()
V52()
V53()
V54()
V55()
V56() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) ) holds
(cD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (((((- 16 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V1() V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (sin x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (sin ((- h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (cos x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (cos ((- h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
/ (((cos (2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + (cos h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ^2) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x0,
x1 being ( ( ) (
V11()
V12()
ext-real )
Real) st
x0 : ( ( ) (
V11()
V12()
ext-real )
Real)
in dom tan : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) : ( ( ) (
V50()
V51()
V52() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) &
x1 : ( ( ) (
V11()
V12()
ext-real )
Real)
in dom tan : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) : ( ( ) (
V50()
V51()
V52() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) holds
[!(tan : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) (#) sin : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ,x0 : ( ( ) ( V11() V12() ext-real ) Real) ,x1 : ( ( ) ( V11() V12() ext-real ) Real) !] : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= ((((1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) / (cos x0 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - (cos x0 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - (1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) / (cos x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + (cos x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
/ (x0 : ( ( ) ( V11() V12() ext-real ) Real) - x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x,
h being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (tan : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) (#) sin : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
x : ( ( ) (
V11()
V12()
ext-real )
Real)
in dom tan : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) : ( ( ) (
V50()
V51()
V52() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) &
x : ( ( ) (
V11()
V12()
ext-real )
Real)
+ h : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
in dom tan : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) : ( ( ) (
V50()
V51()
V52() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) holds
(fD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (((1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) / (cos (x : ( ( ) ( V11() V12() ext-real ) Real) + h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - (cos (x : ( ( ) ( V11() V12() ext-real ) Real) + h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - (1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) / (cos x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
+ (cos x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x,
h being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (tan : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) (#) sin : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
x : ( ( ) (
V11()
V12()
ext-real )
Real)
in dom tan : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) : ( ( ) (
V50()
V51()
V52() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) &
x : ( ( ) (
V11()
V12()
ext-real )
Real)
- h : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
in dom tan : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) : ( ( ) (
V50()
V51()
V52() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) holds
(bD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (((1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) / (cos x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - (cos x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - (1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) / (cos (x : ( ( ) ( V11() V12() ext-real ) Real) - h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
+ (cos (x : ( ( ) ( V11() V12() ext-real ) Real) - h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x,
h being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (tan : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) (#) sin : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
x : ( ( ) (
V11()
V12()
ext-real )
Real)
+ (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
in dom tan : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) : ( ( ) (
V50()
V51()
V52() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) &
x : ( ( ) (
V11()
V12()
ext-real )
Real)
- (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
in dom tan : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) : ( ( ) (
V50()
V51()
V52() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) holds
(cD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (((1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) / (cos (x : ( ( ) ( V11() V12() ext-real ) Real) + (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - (cos (x : ( ( ) ( V11() V12() ext-real ) Real) + (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - (1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) / (cos (x : ( ( ) ( V11() V12() ext-real ) Real) - (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
+ (cos (x : ( ( ) ( V11() V12() ext-real ) Real) - (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x0,
x1 being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (tan : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) (#) cos : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
x0 : ( ( ) (
V11()
V12()
ext-real )
Real)
in dom tan : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) : ( ( ) (
V50()
V51()
V52() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) &
x1 : ( ( ) (
V11()
V12()
ext-real )
Real)
in dom tan : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) : ( ( ) (
V50()
V51()
V52() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) holds
[!f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,x0 : ( ( ) ( V11() V12() ext-real ) Real) ,x1 : ( ( ) ( V11() V12() ext-real ) Real) !] : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= ((sin x0 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - (sin x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
/ (x0 : ( ( ) ( V11() V12() ext-real ) Real) - x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x,
h being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (tan : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) (#) cos : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
x : ( ( ) (
V11()
V12()
ext-real )
Real)
in dom tan : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) : ( ( ) (
V50()
V51()
V52() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) &
x : ( ( ) (
V11()
V12()
ext-real )
Real)
+ h : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
in dom tan : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) : ( ( ) (
V50()
V51()
V52() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) holds
(fD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (sin (x : ( ( ) ( V11() V12() ext-real ) Real) + h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
- (sin x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x,
h being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (tan : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) (#) cos : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
x : ( ( ) (
V11()
V12()
ext-real )
Real)
in dom tan : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) : ( ( ) (
V50()
V51()
V52() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) &
x : ( ( ) (
V11()
V12()
ext-real )
Real)
- h : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
in dom tan : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) : ( ( ) (
V50()
V51()
V52() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) holds
(bD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (sin x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
- (sin (x : ( ( ) ( V11() V12() ext-real ) Real) - h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x,
h being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (tan : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) (#) cos : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
x : ( ( ) (
V11()
V12()
ext-real )
Real)
+ (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
in dom tan : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) : ( ( ) (
V50()
V51()
V52() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) &
x : ( ( ) (
V11()
V12()
ext-real )
Real)
- (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
in dom tan : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) : ( ( ) (
V50()
V51()
V52() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) holds
(cD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (sin (x : ( ( ) ( V11() V12() ext-real ) Real) + (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
- (sin (x : ( ( ) ( V11() V12() ext-real ) Real) - (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x0,
x1 being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (cot : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) (#) cos : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
x0 : ( ( ) (
V11()
V12()
ext-real )
Real)
in dom cot : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) : ( ( ) (
V50()
V51()
V52() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) &
x1 : ( ( ) (
V11()
V12()
ext-real )
Real)
in dom cot : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) : ( ( ) (
V50()
V51()
V52() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) holds
[!f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,x0 : ( ( ) ( V11() V12() ext-real ) Real) ,x1 : ( ( ) ( V11() V12() ext-real ) Real) !] : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= ((((1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) / (sin x0 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - (sin x0 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - (1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) / (sin x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) + (sin x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
/ (x0 : ( ( ) ( V11() V12() ext-real ) Real) - x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x,
h being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (cot : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) (#) cos : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
x : ( ( ) (
V11()
V12()
ext-real )
Real)
in dom cot : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) : ( ( ) (
V50()
V51()
V52() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) &
x : ( ( ) (
V11()
V12()
ext-real )
Real)
+ h : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
in dom cot : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) : ( ( ) (
V50()
V51()
V52() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) holds
(fD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (((1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) / (sin (x : ( ( ) ( V11() V12() ext-real ) Real) + h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - (sin (x : ( ( ) ( V11() V12() ext-real ) Real) + h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - (1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) / (sin x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
+ (sin x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x,
h being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (cot : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) (#) cos : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
x : ( ( ) (
V11()
V12()
ext-real )
Real)
in dom cot : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) : ( ( ) (
V50()
V51()
V52() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) &
x : ( ( ) (
V11()
V12()
ext-real )
Real)
- h : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
in dom cot : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) : ( ( ) (
V50()
V51()
V52() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) holds
(bD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (((1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) / (sin x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - (sin x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - (1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) / (sin (x : ( ( ) ( V11() V12() ext-real ) Real) - h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
+ (sin (x : ( ( ) ( V11() V12() ext-real ) Real) - h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x,
h being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (cot : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) (#) cos : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
x : ( ( ) (
V11()
V12()
ext-real )
Real)
+ (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
in dom cot : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) : ( ( ) (
V50()
V51()
V52() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) &
x : ( ( ) (
V11()
V12()
ext-real )
Real)
- (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
in dom cot : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) : ( ( ) (
V50()
V51()
V52() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) holds
(cD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (((1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) / (sin (x : ( ( ) ( V11() V12() ext-real ) Real) + (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - (sin (x : ( ( ) ( V11() V12() ext-real ) Real) + (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - (1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) / (sin (x : ( ( ) ( V11() V12() ext-real ) Real) - (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
+ (sin (x : ( ( ) ( V11() V12() ext-real ) Real) - (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x0,
x1 being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (cot : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) (#) sin : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
x0 : ( ( ) (
V11()
V12()
ext-real )
Real)
in dom cot : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) : ( ( ) (
V50()
V51()
V52() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) &
x1 : ( ( ) (
V11()
V12()
ext-real )
Real)
in dom cot : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) : ( ( ) (
V50()
V51()
V52() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) holds
[!f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,x0 : ( ( ) ( V11() V12() ext-real ) Real) ,x1 : ( ( ) ( V11() V12() ext-real ) Real) !] : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= ((cos x0 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - (cos x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
/ (x0 : ( ( ) ( V11() V12() ext-real ) Real) - x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x,
h being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (cot : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) (#) sin : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
x : ( ( ) (
V11()
V12()
ext-real )
Real)
in dom cot : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) : ( ( ) (
V50()
V51()
V52() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) &
x : ( ( ) (
V11()
V12()
ext-real )
Real)
+ h : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
in dom cot : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) : ( ( ) (
V50()
V51()
V52() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) holds
(fD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (cos (x : ( ( ) ( V11() V12() ext-real ) Real) + h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
- (cos x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x,
h being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (cot : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) (#) sin : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
x : ( ( ) (
V11()
V12()
ext-real )
Real)
in dom cot : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) : ( ( ) (
V50()
V51()
V52() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) &
x : ( ( ) (
V11()
V12()
ext-real )
Real)
- h : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
in dom cot : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) : ( ( ) (
V50()
V51()
V52() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) holds
(bD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (cos x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
- (cos (x : ( ( ) ( V11() V12() ext-real ) Real) - h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x,
h being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (cot : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) (#) sin : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
x : ( ( ) (
V11()
V12()
ext-real )
Real)
+ (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
in dom cot : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) : ( ( ) (
V50()
V51()
V52() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) &
x : ( ( ) (
V11()
V12()
ext-real )
Real)
- (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
in dom cot : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) : ( ( ) (
V50()
V51()
V52() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) holds
(cD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (cos (x : ( ( ) ( V11() V12() ext-real ) Real) + (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
- (cos (x : ( ( ) ( V11() V12() ext-real ) Real) - (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x0,
x1 being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (tan : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) (#) tan : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
x0 : ( ( ) (
V11()
V12()
ext-real )
Real)
in dom tan : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) : ( ( ) (
V50()
V51()
V52() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) &
x1 : ( ( ) (
V11()
V12()
ext-real )
Real)
in dom tan : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) : ( ( ) (
V50()
V51()
V52() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) holds
[!f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,x0 : ( ( ) ( V11() V12() ext-real ) Real) ,x1 : ( ( ) ( V11() V12() ext-real ) Real) !] : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (((cos x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ^2) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - ((cos x0 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ^2) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
/ ((((cos x0 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (cos x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ^2) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (x0 : ( ( ) ( V11() V12() ext-real ) Real) - x1 : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x,
h being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (tan : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) (#) tan : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
x : ( ( ) (
V11()
V12()
ext-real )
Real)
in dom tan : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) : ( ( ) (
V50()
V51()
V52() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) &
x : ( ( ) (
V11()
V12()
ext-real )
Real)
+ h : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
in dom tan : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) : ( ( ) (
V50()
V51()
V52() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) holds
(fD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= - (((1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V1() V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * ((cos (2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * (x : ( ( ) ( V11() V12() ext-real ) Real) + h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - (cos (2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / (((cos (x : ( ( ) ( V11() V12() ext-real ) Real) + h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (cos x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ^2) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x,
h being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (tan : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) (#) tan : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
x : ( ( ) (
V11()
V12()
ext-real )
Real)
in dom tan : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) : ( ( ) (
V50()
V51()
V52() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) &
x : ( ( ) (
V11()
V12()
ext-real )
Real)
- h : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
in dom tan : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) : ( ( ) (
V50()
V51()
V52() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) holds
(bD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= - (((1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V1() V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * ((cos (2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - (cos (2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * (h : ( ( ) ( V11() V12() ext-real ) Real) - x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / (((cos x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (cos (x : ( ( ) ( V11() V12() ext-real ) Real) - h : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ^2) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;
theorem
for
x,
h being ( ( ) (
V11()
V12()
ext-real )
Real)
for
f being ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) st ( for
x being ( ( ) (
V11()
V12()
ext-real )
Real) holds
f : ( (
V18()
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) (
V1()
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V23(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V27(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V33()
V34()
V35() )
Function of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ,
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= (tan : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) (#) tan : ( ( V18() ) ( V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V33() V34() V35() ) Element of bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) ( V33() V34() V35() ) set ) : ( ( ) ( ) set ) ) ) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ) &
x : ( ( ) (
V11()
V12()
ext-real )
Real)
+ (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
in dom tan : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) : ( ( ) (
V50()
V51()
V52() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) &
x : ( ( ) (
V11()
V12()
ext-real )
Real)
- (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
in dom tan : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) ) : ( ( ) (
V50()
V51()
V52() )
Element of
bool REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) : ( ( ) ( )
set ) ) holds
(cD (f : ( ( V18() V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) ( V1() V13() V16( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V17( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V18() V23( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V27( REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) V33() V34() V35() ) Function of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) , REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ,h : ( ( ) ( V11() V12() ext-real ) Real) )) : ( (
V18() ) (
V13()
V16(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V17(
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
V18()
V33()
V34()
V35() )
Element of
bool [:REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ,REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) :] : ( ( ) (
V33()
V34()
V35() )
set ) : ( ( ) ( )
set ) )
. x : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) )
= - (((1 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V1() V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * ((cos (h : ( ( ) ( V11() V12() ext-real ) Real) + (2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) - (cos (h : ( ( ) ( V11() V12() ext-real ) Real) - (2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) * x : ( ( ) ( V11() V12() ext-real ) Real) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) / (((cos (x : ( ( ) ( V11() V12() ext-real ) Real) + (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) * (cos (x : ( ( ) ( V11() V12() ext-real ) Real) - (h : ( ( ) ( V11() V12() ext-real ) Real) / 2 : ( ( ) ( V1() V10() V11() V12() ext-real positive V43() V49() V50() V51() V52() V53() V54() V55() ) Element of NAT : ( ( ) ( V50() V51() V52() V53() V54() V55() V56() ) Element of bool REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ^2) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( V1() V44() V50() V51() V52() V56() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) (
V1()
V44()
V50()
V51()
V52()
V56() )
set ) ) ;