begin
theorem
for
X being ( ( ) ( )
TopStruct )
for
S,
V being ( ( non
empty ) ( non
empty )
TopStruct )
for
B being ( ( non
empty ) ( non
empty )
Subset of )
for
f being ( (
Function-like quasi_total ) (
Relation-like the
carrier of
b1 : ( ( ) ( )
TopStruct ) : ( ( ) ( )
set )
-defined the
carrier of
(b2 : ( ( non empty ) ( non empty ) TopStruct ) | b4 : ( ( non empty ) ( non empty ) Subset of ) ) : ( (
strict ) ( non
empty strict )
SubSpace of
b2 : ( ( non
empty ) ( non
empty )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like V29( the
carrier of
b1 : ( ( ) ( )
TopStruct ) : ( ( ) ( )
set ) )
quasi_total )
Function of ( ( ) ( )
set ) , ( ( ) ( non
empty )
set ) )
for
g being ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
b2 : ( ( non
empty ) ( non
empty )
TopStruct ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
b3 : ( ( non
empty ) ( non
empty )
TopStruct ) : ( ( ) ( non
empty )
set )
-valued Function-like V29( the
carrier of
b2 : ( ( non
empty ) ( non
empty )
TopStruct ) : ( ( ) ( non
empty )
set ) )
quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( non
empty )
set ) )
for
h being ( (
Function-like quasi_total ) (
Relation-like the
carrier of
b1 : ( ( ) ( )
TopStruct ) : ( ( ) ( )
set )
-defined the
carrier of
b3 : ( ( non
empty ) ( non
empty )
TopStruct ) : ( ( ) ( non
empty )
set )
-valued Function-like V29( the
carrier of
b1 : ( ( ) ( )
TopStruct ) : ( ( ) ( )
set ) )
quasi_total )
Function of ( ( ) ( )
set ) , ( ( ) ( non
empty )
set ) ) st
h : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
b1 : ( ( ) ( )
TopStruct ) : ( ( ) ( )
set )
-defined the
carrier of
b3 : ( ( non
empty ) ( non
empty )
TopStruct ) : ( ( ) ( non
empty )
set )
-valued Function-like V29( the
carrier of
b1 : ( ( ) ( )
TopStruct ) : ( ( ) ( )
set ) )
quasi_total )
Function of ( ( ) ( )
set ) , ( ( ) ( non
empty )
set ) )
= g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
b2 : ( ( non
empty ) ( non
empty )
TopStruct ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
b3 : ( ( non
empty ) ( non
empty )
TopStruct ) : ( ( ) ( non
empty )
set )
-valued Function-like V29( the
carrier of
b2 : ( ( non
empty ) ( non
empty )
TopStruct ) : ( ( ) ( non
empty )
set ) )
quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( non
empty )
set ) )
* f : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
b1 : ( ( ) ( )
TopStruct ) : ( ( ) ( )
set )
-defined the
carrier of
(b2 : ( ( non empty ) ( non empty ) TopStruct ) | b4 : ( ( non empty ) ( non empty ) Subset of ) ) : ( (
strict ) ( non
empty strict )
SubSpace of
b2 : ( ( non
empty ) ( non
empty )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like V29( the
carrier of
b1 : ( ( ) ( )
TopStruct ) : ( ( ) ( )
set ) )
quasi_total )
Function of ( ( ) ( )
set ) , ( ( ) ( non
empty )
set ) ) : ( (
Function-like ) (
Relation-like the
carrier of
b1 : ( ( ) ( )
TopStruct ) : ( ( ) ( )
set )
-defined the
carrier of
b3 : ( ( non
empty ) ( non
empty )
TopStruct ) : ( ( ) ( non
empty )
set )
-valued Function-like )
Element of
K6(
K7( the
carrier of
b1 : ( ( ) ( )
TopStruct ) : ( ( ) ( )
set ) , the
carrier of
b3 : ( ( non
empty ) ( non
empty )
TopStruct ) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) &
f : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
b1 : ( ( ) ( )
TopStruct ) : ( ( ) ( )
set )
-defined the
carrier of
(b2 : ( ( non empty ) ( non empty ) TopStruct ) | b4 : ( ( non empty ) ( non empty ) Subset of ) ) : ( (
strict ) ( non
empty strict )
SubSpace of
b2 : ( ( non
empty ) ( non
empty )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like V29( the
carrier of
b1 : ( ( ) ( )
TopStruct ) : ( ( ) ( )
set ) )
quasi_total )
Function of ( ( ) ( )
set ) , ( ( ) ( non
empty )
set ) ) is
continuous &
g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
b2 : ( ( non
empty ) ( non
empty )
TopStruct ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
b3 : ( ( non
empty ) ( non
empty )
TopStruct ) : ( ( ) ( non
empty )
set )
-valued Function-like V29( the
carrier of
b2 : ( ( non
empty ) ( non
empty )
TopStruct ) : ( ( ) ( non
empty )
set ) )
quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( non
empty )
set ) ) is
continuous holds
h : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
b1 : ( ( ) ( )
TopStruct ) : ( ( ) ( )
set )
-defined the
carrier of
b3 : ( ( non
empty ) ( non
empty )
TopStruct ) : ( ( ) ( non
empty )
set )
-valued Function-like V29( the
carrier of
b1 : ( ( ) ( )
TopStruct ) : ( ( ) ( )
set ) )
quasi_total )
Function of ( ( ) ( )
set ) , ( ( ) ( non
empty )
set ) ) is
continuous ;
theorem
for
a,
b,
d,
e,
s1,
s2,
t1,
t2 being ( ( ) (
V11()
real ext-real )
Real)
for
h being ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(Closed-Interval-TSpace (b1 : ( ( ) ( V11() real ext-real ) Real) ,b2 : ( ( ) ( V11() real ext-real ) Real) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(Closed-Interval-TSpace (b3 : ( ( ) ( V11() real ext-real ) Real) ,b4 : ( ( ) ( V11() real ext-real ) Real) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-valued Function-like V29( the
carrier of
(Closed-Interval-TSpace (b1 : ( ( ) ( V11() real ext-real ) Real) ,b2 : ( ( ) ( V11() real ext-real ) Real) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty V142()
V143()
V144() )
set ) ) st
h : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(Closed-Interval-TSpace (b1 : ( ( ) ( V11() real ext-real ) Real) ,b2 : ( ( ) ( V11() real ext-real ) Real) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(Closed-Interval-TSpace (b3 : ( ( ) ( V11() real ext-real ) Real) ,b4 : ( ( ) ( V11() real ext-real ) Real) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-valued Function-like V29( the
carrier of
(Closed-Interval-TSpace (b1 : ( ( ) ( V11() real ext-real ) Real) ,b2 : ( ( ) ( V11() real ext-real ) Real) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty V142()
V143()
V144() )
set ) ) is
being_homeomorphism &
h : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(Closed-Interval-TSpace (b1 : ( ( ) ( V11() real ext-real ) Real) ,b2 : ( ( ) ( V11() real ext-real ) Real) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(Closed-Interval-TSpace (b3 : ( ( ) ( V11() real ext-real ) Real) ,b4 : ( ( ) ( V11() real ext-real ) Real) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-valued Function-like V29( the
carrier of
(Closed-Interval-TSpace (b1 : ( ( ) ( V11() real ext-real ) Real) ,b2 : ( ( ) ( V11() real ext-real ) Real) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
. s1 : ( ( ) (
V11()
real ext-real )
Real) : ( ( ) ( )
set )
= t1 : ( ( ) (
V11()
real ext-real )
Real) &
h : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(Closed-Interval-TSpace (b1 : ( ( ) ( V11() real ext-real ) Real) ,b2 : ( ( ) ( V11() real ext-real ) Real) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(Closed-Interval-TSpace (b3 : ( ( ) ( V11() real ext-real ) Real) ,b4 : ( ( ) ( V11() real ext-real ) Real) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-valued Function-like V29( the
carrier of
(Closed-Interval-TSpace (b1 : ( ( ) ( V11() real ext-real ) Real) ,b2 : ( ( ) ( V11() real ext-real ) Real) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
. s2 : ( ( ) (
V11()
real ext-real )
Real) : ( ( ) ( )
set )
= t2 : ( ( ) (
V11()
real ext-real )
Real) &
h : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(Closed-Interval-TSpace (b1 : ( ( ) ( V11() real ext-real ) Real) ,b2 : ( ( ) ( V11() real ext-real ) Real) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(Closed-Interval-TSpace (b3 : ( ( ) ( V11() real ext-real ) Real) ,b4 : ( ( ) ( V11() real ext-real ) Real) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-valued Function-like V29( the
carrier of
(Closed-Interval-TSpace (b1 : ( ( ) ( V11() real ext-real ) Real) ,b2 : ( ( ) ( V11() real ext-real ) Real) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
. b : ( ( ) (
V11()
real ext-real )
Real) : ( ( ) ( )
set )
= e : ( ( ) (
V11()
real ext-real )
Real) &
d : ( ( ) (
V11()
real ext-real )
Real)
<= e : ( ( ) (
V11()
real ext-real )
Real) &
t1 : ( ( ) (
V11()
real ext-real )
Real)
<= t2 : ( ( ) (
V11()
real ext-real )
Real) &
s1 : ( ( ) (
V11()
real ext-real )
Real)
in [.a : ( ( ) ( V11() real ext-real ) Real) ,b : ( ( ) ( V11() real ext-real ) Real) .] : ( ( ) (
V142()
V143()
V144()
V204() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) &
s2 : ( ( ) (
V11()
real ext-real )
Real)
in [.a : ( ( ) ( V11() real ext-real ) Real) ,b : ( ( ) ( V11() real ext-real ) Real) .] : ( ( ) (
V142()
V143()
V144()
V204() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) holds
s1 : ( ( ) (
V11()
real ext-real )
Real)
<= s2 : ( ( ) (
V11()
real ext-real )
Real) ;
theorem
for
a,
b,
d,
e,
s1,
s2,
t1,
t2 being ( ( ) (
V11()
real ext-real )
Real)
for
h being ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(Closed-Interval-TSpace (b1 : ( ( ) ( V11() real ext-real ) Real) ,b2 : ( ( ) ( V11() real ext-real ) Real) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(Closed-Interval-TSpace (b3 : ( ( ) ( V11() real ext-real ) Real) ,b4 : ( ( ) ( V11() real ext-real ) Real) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-valued Function-like V29( the
carrier of
(Closed-Interval-TSpace (b1 : ( ( ) ( V11() real ext-real ) Real) ,b2 : ( ( ) ( V11() real ext-real ) Real) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty V142()
V143()
V144() )
set ) ) st
h : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(Closed-Interval-TSpace (b1 : ( ( ) ( V11() real ext-real ) Real) ,b2 : ( ( ) ( V11() real ext-real ) Real) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(Closed-Interval-TSpace (b3 : ( ( ) ( V11() real ext-real ) Real) ,b4 : ( ( ) ( V11() real ext-real ) Real) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-valued Function-like V29( the
carrier of
(Closed-Interval-TSpace (b1 : ( ( ) ( V11() real ext-real ) Real) ,b2 : ( ( ) ( V11() real ext-real ) Real) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty V142()
V143()
V144() )
set ) ) is
being_homeomorphism &
h : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(Closed-Interval-TSpace (b1 : ( ( ) ( V11() real ext-real ) Real) ,b2 : ( ( ) ( V11() real ext-real ) Real) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(Closed-Interval-TSpace (b3 : ( ( ) ( V11() real ext-real ) Real) ,b4 : ( ( ) ( V11() real ext-real ) Real) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-valued Function-like V29( the
carrier of
(Closed-Interval-TSpace (b1 : ( ( ) ( V11() real ext-real ) Real) ,b2 : ( ( ) ( V11() real ext-real ) Real) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
. s1 : ( ( ) (
V11()
real ext-real )
Real) : ( ( ) ( )
set )
= t1 : ( ( ) (
V11()
real ext-real )
Real) &
h : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(Closed-Interval-TSpace (b1 : ( ( ) ( V11() real ext-real ) Real) ,b2 : ( ( ) ( V11() real ext-real ) Real) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(Closed-Interval-TSpace (b3 : ( ( ) ( V11() real ext-real ) Real) ,b4 : ( ( ) ( V11() real ext-real ) Real) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-valued Function-like V29( the
carrier of
(Closed-Interval-TSpace (b1 : ( ( ) ( V11() real ext-real ) Real) ,b2 : ( ( ) ( V11() real ext-real ) Real) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
. s2 : ( ( ) (
V11()
real ext-real )
Real) : ( ( ) ( )
set )
= t2 : ( ( ) (
V11()
real ext-real )
Real) &
h : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(Closed-Interval-TSpace (b1 : ( ( ) ( V11() real ext-real ) Real) ,b2 : ( ( ) ( V11() real ext-real ) Real) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(Closed-Interval-TSpace (b3 : ( ( ) ( V11() real ext-real ) Real) ,b4 : ( ( ) ( V11() real ext-real ) Real) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-valued Function-like V29( the
carrier of
(Closed-Interval-TSpace (b1 : ( ( ) ( V11() real ext-real ) Real) ,b2 : ( ( ) ( V11() real ext-real ) Real) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
. b : ( ( ) (
V11()
real ext-real )
Real) : ( ( ) ( )
set )
= d : ( ( ) (
V11()
real ext-real )
Real) &
e : ( ( ) (
V11()
real ext-real )
Real)
>= d : ( ( ) (
V11()
real ext-real )
Real) &
t1 : ( ( ) (
V11()
real ext-real )
Real)
>= t2 : ( ( ) (
V11()
real ext-real )
Real) &
s1 : ( ( ) (
V11()
real ext-real )
Real)
in [.a : ( ( ) ( V11() real ext-real ) Real) ,b : ( ( ) ( V11() real ext-real ) Real) .] : ( ( ) (
V142()
V143()
V144()
V204() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) &
s2 : ( ( ) (
V11()
real ext-real )
Real)
in [.a : ( ( ) ( V11() real ext-real ) Real) ,b : ( ( ) ( V11() real ext-real ) Real) .] : ( ( ) (
V142()
V143()
V144()
V204() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) holds
s1 : ( ( ) (
V11()
real ext-real )
Real)
<= s2 : ( ( ) (
V11()
real ext-real )
Real) ;
begin
theorem
for
f,
g being ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
for
a,
b,
c,
d being ( ( ) (
V11()
real ext-real )
Real)
for
O,
I being ( ( ) (
V11()
real ext-real )
Point of ( ( ) ( non
empty V142()
V143()
V144() )
set ) ) st
O : ( ( ) (
V11()
real ext-real )
Point of ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
= 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
I : ( ( ) (
V11()
real ext-real )
Point of ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
= 1 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
continuous &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
one-to-one &
g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
continuous &
g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
one-to-one &
a : ( ( ) (
V11()
real ext-real )
Real)
<> b : ( ( ) (
V11()
real ext-real )
Real) &
c : ( ( ) (
V11()
real ext-real )
Real)
<> d : ( ( ) (
V11()
real ext-real )
Real) &
(f : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) ) quasi_total ) Function of ( ( ) ( non empty V142() V143() V144() ) set ) , ( ( ) ( non empty functional ) set ) ) . O : ( ( ) ( V11() real ext-real ) Point of ( ( ) ( non empty V142() V143() V144() ) set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
= a : ( ( ) (
V11()
real ext-real )
Real) &
c : ( ( ) (
V11()
real ext-real )
Real)
<= (f : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) ) quasi_total ) Function of ( ( ) ( non empty V142() V143() V144() ) set ) , ( ( ) ( non empty functional ) set ) ) . O : ( ( ) ( V11() real ext-real ) Point of ( ( ) ( non empty V142() V143() V144() ) set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) &
(f : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) ) quasi_total ) Function of ( ( ) ( non empty V142() V143() V144() ) set ) , ( ( ) ( non empty functional ) set ) ) . O : ( ( ) ( V11() real ext-real ) Point of ( ( ) ( non empty V142() V143() V144() ) set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
<= d : ( ( ) (
V11()
real ext-real )
Real) &
(f : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) ) quasi_total ) Function of ( ( ) ( non empty V142() V143() V144() ) set ) , ( ( ) ( non empty functional ) set ) ) . I : ( ( ) ( V11() real ext-real ) Point of ( ( ) ( non empty V142() V143() V144() ) set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
= b : ( ( ) (
V11()
real ext-real )
Real) &
c : ( ( ) (
V11()
real ext-real )
Real)
<= (f : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) ) quasi_total ) Function of ( ( ) ( non empty V142() V143() V144() ) set ) , ( ( ) ( non empty functional ) set ) ) . I : ( ( ) ( V11() real ext-real ) Point of ( ( ) ( non empty V142() V143() V144() ) set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) &
(f : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) ) quasi_total ) Function of ( ( ) ( non empty V142() V143() V144() ) set ) , ( ( ) ( non empty functional ) set ) ) . I : ( ( ) ( V11() real ext-real ) Point of ( ( ) ( non empty V142() V143() V144() ) set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
<= d : ( ( ) (
V11()
real ext-real )
Real) &
(g : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) ) quasi_total ) Function of ( ( ) ( non empty V142() V143() V144() ) set ) , ( ( ) ( non empty functional ) set ) ) . O : ( ( ) ( V11() real ext-real ) Point of ( ( ) ( non empty V142() V143() V144() ) set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
= c : ( ( ) (
V11()
real ext-real )
Real) &
a : ( ( ) (
V11()
real ext-real )
Real)
<= (g : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) ) quasi_total ) Function of ( ( ) ( non empty V142() V143() V144() ) set ) , ( ( ) ( non empty functional ) set ) ) . O : ( ( ) ( V11() real ext-real ) Point of ( ( ) ( non empty V142() V143() V144() ) set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) &
(g : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) ) quasi_total ) Function of ( ( ) ( non empty V142() V143() V144() ) set ) , ( ( ) ( non empty functional ) set ) ) . O : ( ( ) ( V11() real ext-real ) Point of ( ( ) ( non empty V142() V143() V144() ) set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
<= b : ( ( ) (
V11()
real ext-real )
Real) &
(g : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) ) quasi_total ) Function of ( ( ) ( non empty V142() V143() V144() ) set ) , ( ( ) ( non empty functional ) set ) ) . I : ( ( ) ( V11() real ext-real ) Point of ( ( ) ( non empty V142() V143() V144() ) set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
= d : ( ( ) (
V11()
real ext-real )
Real) &
a : ( ( ) (
V11()
real ext-real )
Real)
<= (g : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) ) quasi_total ) Function of ( ( ) ( non empty V142() V143() V144() ) set ) , ( ( ) ( non empty functional ) set ) ) . I : ( ( ) ( V11() real ext-real ) Point of ( ( ) ( non empty V142() V143() V144() ) set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) &
(g : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) ) quasi_total ) Function of ( ( ) ( non empty V142() V143() V144() ) set ) , ( ( ) ( non empty functional ) set ) ) . I : ( ( ) ( V11() real ext-real ) Point of ( ( ) ( non empty V142() V143() V144() ) set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
<= b : ( ( ) (
V11()
real ext-real )
Real) & ( for
r being ( ( ) (
V11()
real ext-real )
Point of ( ( ) ( non
empty V142()
V143()
V144() )
set ) ) holds
( (
a : ( ( ) (
V11()
real ext-real )
Real)
>= (f : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) ) quasi_total ) Function of ( ( ) ( non empty V142() V143() V144() ) set ) , ( ( ) ( non empty functional ) set ) ) . r : ( ( ) ( V11() real ext-real ) Point of ( ( ) ( non empty V142() V143() V144() ) set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) or
(f : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) ) quasi_total ) Function of ( ( ) ( non empty V142() V143() V144() ) set ) , ( ( ) ( non empty functional ) set ) ) . r : ( ( ) ( V11() real ext-real ) Point of ( ( ) ( non empty V142() V143() V144() ) set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
>= b : ( ( ) (
V11()
real ext-real )
Real) or
c : ( ( ) (
V11()
real ext-real )
Real)
>= (f : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) ) quasi_total ) Function of ( ( ) ( non empty V142() V143() V144() ) set ) , ( ( ) ( non empty functional ) set ) ) . r : ( ( ) ( V11() real ext-real ) Point of ( ( ) ( non empty V142() V143() V144() ) set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) or
(f : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) ) quasi_total ) Function of ( ( ) ( non empty V142() V143() V144() ) set ) , ( ( ) ( non empty functional ) set ) ) . r : ( ( ) ( V11() real ext-real ) Point of ( ( ) ( non empty V142() V143() V144() ) set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
>= d : ( ( ) (
V11()
real ext-real )
Real) ) & (
a : ( ( ) (
V11()
real ext-real )
Real)
>= (g : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) ) quasi_total ) Function of ( ( ) ( non empty V142() V143() V144() ) set ) , ( ( ) ( non empty functional ) set ) ) . r : ( ( ) ( V11() real ext-real ) Point of ( ( ) ( non empty V142() V143() V144() ) set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) or
(g : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) ) quasi_total ) Function of ( ( ) ( non empty V142() V143() V144() ) set ) , ( ( ) ( non empty functional ) set ) ) . r : ( ( ) ( V11() real ext-real ) Point of ( ( ) ( non empty V142() V143() V144() ) set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
>= b : ( ( ) (
V11()
real ext-real )
Real) or
c : ( ( ) (
V11()
real ext-real )
Real)
>= (g : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) ) quasi_total ) Function of ( ( ) ( non empty V142() V143() V144() ) set ) , ( ( ) ( non empty functional ) set ) ) . r : ( ( ) ( V11() real ext-real ) Point of ( ( ) ( non empty V142() V143() V144() ) set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) or
(g : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) ) quasi_total ) Function of ( ( ) ( non empty V142() V143() V144() ) set ) , ( ( ) ( non empty functional ) set ) ) . r : ( ( ) ( V11() real ext-real ) Point of ( ( ) ( non empty V142() V143() V144() ) set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
>= d : ( ( ) (
V11()
real ext-real )
Real) ) ) ) holds
rng f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) )
meets rng g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) ;
theorem
for
f being ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) st
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
continuous &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
one-to-one holds
ex
f2 being ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) st
(
f2 : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set )
= f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. 1 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set ) &
f2 : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. 1 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set )
= f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set ) &
rng f2 : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) )
= rng f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) &
f2 : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
continuous &
f2 : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
one-to-one ) ;
theorem
for
f,
g being ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
for
C0,
KXP,
KXN,
KYP,
KYN being ( ( ) (
functional )
Subset of )
for
O,
I being ( ( ) (
V11()
real ext-real )
Point of ( ( ) ( non
empty V142()
V143()
V144() )
set ) ) st
O : ( ( ) (
V11()
real ext-real )
Point of ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
= 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
I : ( ( ) (
V11()
real ext-real )
Point of ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
= 1 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
continuous &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
one-to-one &
g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
continuous &
g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
one-to-one &
C0 : ( ( ) (
functional )
Subset of )
= { p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) where p is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) : |.p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) .| : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) <= 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) } &
KXP : ( ( ) (
functional )
Subset of )
= { q1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) where q1 is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) : ( |.q1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) .| : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) = 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) & q1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) <= q1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `1 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) & q1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) >= - (q1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `1) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ) } &
KXN : ( ( ) (
functional )
Subset of )
= { q2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) where q2 is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) : ( |.q2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) .| : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) = 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) & q2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) >= q2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `1 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) & q2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) <= - (q2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `1) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ) } &
KYP : ( ( ) (
functional )
Subset of )
= { q3 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) where q3 is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) : ( |.q3 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) .| : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) = 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) & q3 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) >= q3 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `1 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) & q3 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) >= - (q3 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `1) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ) } &
KYN : ( ( ) (
functional )
Subset of )
= { q4 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) where q4 is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) : ( |.q4 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) .| : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) = 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) & q4 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) <= q4 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `1 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) & q4 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) <= - (q4 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `1) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ) } &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. O : ( ( ) (
V11()
real ext-real )
Point of ( ( ) ( non
empty V142()
V143()
V144() )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
in KXN : ( ( ) (
functional )
Subset of ) &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. I : ( ( ) (
V11()
real ext-real )
Point of ( ( ) ( non
empty V142()
V143()
V144() )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
in KXP : ( ( ) (
functional )
Subset of ) &
g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. O : ( ( ) (
V11()
real ext-real )
Point of ( ( ) ( non
empty V142()
V143()
V144() )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
in KYP : ( ( ) (
functional )
Subset of ) &
g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. I : ( ( ) (
V11()
real ext-real )
Point of ( ( ) ( non
empty V142()
V143()
V144() )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
in KYN : ( ( ) (
functional )
Subset of ) &
rng f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) )
c= C0 : ( ( ) (
functional )
Subset of ) &
rng g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) )
c= C0 : ( ( ) (
functional )
Subset of ) holds
rng f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) )
meets rng g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) ;
theorem
for
f,
g being ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
for
C0,
KXP,
KXN,
KYP,
KYN being ( ( ) (
functional )
Subset of )
for
O,
I being ( ( ) (
V11()
real ext-real )
Point of ( ( ) ( non
empty V142()
V143()
V144() )
set ) ) st
O : ( ( ) (
V11()
real ext-real )
Point of ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
= 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
I : ( ( ) (
V11()
real ext-real )
Point of ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
= 1 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
continuous &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
one-to-one &
g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
continuous &
g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
one-to-one &
C0 : ( ( ) (
functional )
Subset of )
= { p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) where p is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) : |.p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) .| : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) >= 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) } &
KXP : ( ( ) (
functional )
Subset of )
= { q1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) where q1 is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) : ( |.q1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) .| : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) = 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) & q1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) <= q1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `1 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) & q1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) >= - (q1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `1) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ) } &
KXN : ( ( ) (
functional )
Subset of )
= { q2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) where q2 is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) : ( |.q2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) .| : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) = 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) & q2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) >= q2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `1 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) & q2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) <= - (q2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `1) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ) } &
KYP : ( ( ) (
functional )
Subset of )
= { q3 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) where q3 is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) : ( |.q3 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) .| : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) = 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) & q3 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) >= q3 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `1 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) & q3 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) >= - (q3 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `1) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ) } &
KYN : ( ( ) (
functional )
Subset of )
= { q4 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) where q4 is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) : ( |.q4 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) .| : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) = 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) & q4 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) <= q4 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `1 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) & q4 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) <= - (q4 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `1) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ) } &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. O : ( ( ) (
V11()
real ext-real )
Point of ( ( ) ( non
empty V142()
V143()
V144() )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
in KXN : ( ( ) (
functional )
Subset of ) &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. I : ( ( ) (
V11()
real ext-real )
Point of ( ( ) ( non
empty V142()
V143()
V144() )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
in KXP : ( ( ) (
functional )
Subset of ) &
g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. O : ( ( ) (
V11()
real ext-real )
Point of ( ( ) ( non
empty V142()
V143()
V144() )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
in KYN : ( ( ) (
functional )
Subset of ) &
g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. I : ( ( ) (
V11()
real ext-real )
Point of ( ( ) ( non
empty V142()
V143()
V144() )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
in KYP : ( ( ) (
functional )
Subset of ) &
rng f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) )
c= C0 : ( ( ) (
functional )
Subset of ) &
rng g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) )
c= C0 : ( ( ) (
functional )
Subset of ) holds
rng f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) )
meets rng g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) ;
theorem
for
f,
g being ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
for
C0,
KXP,
KXN,
KYP,
KYN being ( ( ) (
functional )
Subset of )
for
O,
I being ( ( ) (
V11()
real ext-real )
Point of ( ( ) ( non
empty V142()
V143()
V144() )
set ) ) st
O : ( ( ) (
V11()
real ext-real )
Point of ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
= 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
I : ( ( ) (
V11()
real ext-real )
Point of ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
= 1 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
continuous &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
one-to-one &
g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
continuous &
g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
one-to-one &
C0 : ( ( ) (
functional )
Subset of )
= { p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) where p is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) : |.p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) .| : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) >= 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) } &
KXP : ( ( ) (
functional )
Subset of )
= { q1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) where q1 is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) : ( |.q1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) .| : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) = 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) & q1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) <= q1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `1 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) & q1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) >= - (q1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `1) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ) } &
KXN : ( ( ) (
functional )
Subset of )
= { q2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) where q2 is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) : ( |.q2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) .| : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) = 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) & q2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) >= q2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `1 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) & q2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) <= - (q2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `1) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ) } &
KYP : ( ( ) (
functional )
Subset of )
= { q3 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) where q3 is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) : ( |.q3 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) .| : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) = 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) & q3 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) >= q3 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `1 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) & q3 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) >= - (q3 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `1) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ) } &
KYN : ( ( ) (
functional )
Subset of )
= { q4 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) where q4 is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) : ( |.q4 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) .| : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) = 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) & q4 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) <= q4 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `1 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) & q4 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) <= - (q4 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `1) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ) } &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. O : ( ( ) (
V11()
real ext-real )
Point of ( ( ) ( non
empty V142()
V143()
V144() )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
in KXN : ( ( ) (
functional )
Subset of ) &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. I : ( ( ) (
V11()
real ext-real )
Point of ( ( ) ( non
empty V142()
V143()
V144() )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
in KXP : ( ( ) (
functional )
Subset of ) &
g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. O : ( ( ) (
V11()
real ext-real )
Point of ( ( ) ( non
empty V142()
V143()
V144() )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
in KYP : ( ( ) (
functional )
Subset of ) &
g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. I : ( ( ) (
V11()
real ext-real )
Point of ( ( ) ( non
empty V142()
V143()
V144() )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
in KYN : ( ( ) (
functional )
Subset of ) &
rng f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) )
c= C0 : ( ( ) (
functional )
Subset of ) &
rng g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) )
c= C0 : ( ( ) (
functional )
Subset of ) holds
rng f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) )
meets rng g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) ;
theorem
for
f,
g being ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
for
C0 being ( ( ) (
functional )
Subset of ) st
C0 : ( ( ) (
functional )
Subset of )
= { q : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) where q is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) : |.q : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) .| : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) >= 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) } &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
continuous &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
one-to-one &
g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
continuous &
g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
one-to-one &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set )
= |[(- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative Function-like functional V79() V80() V142() V143() V144() V145() V146() V147() V148() V201() V204() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. 1 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set )
= |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative Function-like functional V79() V80() V142() V143() V144() V145() V146() V147() V148() V201() V204() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. 1 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set )
= |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative Function-like functional V79() V80() V142() V143() V144() V145() V146() V147() V148() V201() V204() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set )
= |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative Function-like functional V79() V80() V142() V143() V144() V145() V146() V147() V148() V201() V204() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ,(- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
rng f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) )
c= C0 : ( ( ) (
functional )
Subset of ) &
rng g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) )
c= C0 : ( ( ) (
functional )
Subset of ) holds
rng f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) )
meets rng g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) ;
theorem
for
p1,
p2,
p3,
p4 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
for
C0 being ( ( ) (
functional )
Subset of ) st
C0 : ( ( ) (
functional )
Subset of )
= { p : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) ) quasi_total ) Function of ( ( ) ( non empty V142() V143() V144() ) set ) , ( ( ) ( non empty functional ) set ) ) where p is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) : |.p : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) ) quasi_total ) Function of ( ( ) ( non empty V142() V143() V144() ) set ) , ( ( ) ( non empty functional ) set ) ) .| : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) >= 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) } &
|.p1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) .| : ( ( ) (
V11()
real ext-real non
negative )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
= 1 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
|.p2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) .| : ( ( ) (
V11()
real ext-real non
negative )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
= 1 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
|.p3 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) .| : ( ( ) (
V11()
real ext-real non
negative )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
= 1 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
|.p4 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) .| : ( ( ) (
V11()
real ext-real non
negative )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
= 1 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) & ex
h being ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) ) st
(
h : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
being_homeomorphism &
h : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
.: C0 : ( ( ) (
functional )
Subset of ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) )
c= C0 : ( ( ) (
functional )
Subset of ) &
h : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
= |[(- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative Function-like functional V79() V80() V142() V143() V144() V145() V146() V147() V148() V201() V204() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
h : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
= |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative Function-like functional V79() V80() V142() V143() V144() V145() V146() V147() V148() V201() V204() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
h : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
= |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative Function-like functional V79() V80() V142() V143() V144() V145() V146() V147() V148() V201() V204() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
h : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
= |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative Function-like functional V79() V80() V142() V143() V144() V145() V146() V147() V148() V201() V204() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ,(- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) ) holds
for
f,
g being ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) st
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
continuous &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
one-to-one &
g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
continuous &
g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
one-to-one &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set )
= p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. 1 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set )
= p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set )
= p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. 1 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set )
= p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
rng f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) )
c= C0 : ( ( ) (
functional )
Subset of ) &
rng g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) )
c= C0 : ( ( ) (
functional )
Subset of ) holds
rng f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) )
meets rng g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) ;
begin
begin
theorem
for
a,
b,
d,
e being ( ( ) (
V11()
real ext-real )
Real) st
a : ( ( ) (
V11()
real ext-real )
Real)
<= b : ( ( ) (
V11()
real ext-real )
Real) &
e : ( ( ) (
V11()
real ext-real )
Real)
> 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) holds
ex
f being ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(Closed-Interval-TSpace (b1 : ( ( ) ( V11() real ext-real ) Real) ,b2 : ( ( ) ( V11() real ext-real ) Real) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(Closed-Interval-TSpace (((b4 : ( ( ) ( V11() real ext-real ) Real) * b1 : ( ( ) ( V11() real ext-real ) Real) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) + b3 : ( ( ) ( V11() real ext-real ) Real) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,((b4 : ( ( ) ( V11() real ext-real ) Real) * b2 : ( ( ) ( V11() real ext-real ) Real) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) + b3 : ( ( ) ( V11() real ext-real ) Real) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-valued Function-like V29( the
carrier of
(Closed-Interval-TSpace (b1 : ( ( ) ( V11() real ext-real ) Real) ,b2 : ( ( ) ( V11() real ext-real ) Real) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty V142()
V143()
V144() )
set ) ) st
(
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(Closed-Interval-TSpace (b1 : ( ( ) ( V11() real ext-real ) Real) ,b2 : ( ( ) ( V11() real ext-real ) Real) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(Closed-Interval-TSpace (((b4 : ( ( ) ( V11() real ext-real ) Real) * b1 : ( ( ) ( V11() real ext-real ) Real) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) + b3 : ( ( ) ( V11() real ext-real ) Real) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,((b4 : ( ( ) ( V11() real ext-real ) Real) * b2 : ( ( ) ( V11() real ext-real ) Real) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) + b3 : ( ( ) ( V11() real ext-real ) Real) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-valued Function-like V29( the
carrier of
(Closed-Interval-TSpace (b1 : ( ( ) ( V11() real ext-real ) Real) ,b2 : ( ( ) ( V11() real ext-real ) Real) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty V142()
V143()
V144() )
set ) ) is
being_homeomorphism & ( for
r being ( ( ) (
V11()
real ext-real )
Real) st
r : ( ( ) (
V11()
real ext-real )
Real)
in [.a : ( ( ) ( V11() real ext-real ) Real) ,b : ( ( ) ( V11() real ext-real ) Real) .] : ( ( ) (
V142()
V143()
V144()
V204() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) holds
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(Closed-Interval-TSpace (b1 : ( ( ) ( V11() real ext-real ) Real) ,b2 : ( ( ) ( V11() real ext-real ) Real) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(Closed-Interval-TSpace (((b4 : ( ( ) ( V11() real ext-real ) Real) * b1 : ( ( ) ( V11() real ext-real ) Real) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) + b3 : ( ( ) ( V11() real ext-real ) Real) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,((b4 : ( ( ) ( V11() real ext-real ) Real) * b2 : ( ( ) ( V11() real ext-real ) Real) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) + b3 : ( ( ) ( V11() real ext-real ) Real) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-valued Function-like V29( the
carrier of
(Closed-Interval-TSpace (b1 : ( ( ) ( V11() real ext-real ) Real) ,b2 : ( ( ) ( V11() real ext-real ) Real) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
. r : ( ( ) (
V11()
real ext-real )
Real) : ( ( ) ( )
set )
= (e : ( ( ) ( V11() real ext-real ) Real) * r : ( ( ) ( V11() real ext-real ) Real) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
+ d : ( ( ) (
V11()
real ext-real )
Real) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) ) ) ;
theorem
for
a,
b,
d,
e being ( ( ) (
V11()
real ext-real )
Real) st
a : ( ( ) (
V11()
real ext-real )
Real)
<= b : ( ( ) (
V11()
real ext-real )
Real) &
e : ( ( ) (
V11()
real ext-real )
Real)
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) holds
ex
f being ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(Closed-Interval-TSpace (b1 : ( ( ) ( V11() real ext-real ) Real) ,b2 : ( ( ) ( V11() real ext-real ) Real) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(Closed-Interval-TSpace (((b4 : ( ( ) ( V11() real ext-real ) Real) * b2 : ( ( ) ( V11() real ext-real ) Real) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) + b3 : ( ( ) ( V11() real ext-real ) Real) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,((b4 : ( ( ) ( V11() real ext-real ) Real) * b1 : ( ( ) ( V11() real ext-real ) Real) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) + b3 : ( ( ) ( V11() real ext-real ) Real) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-valued Function-like V29( the
carrier of
(Closed-Interval-TSpace (b1 : ( ( ) ( V11() real ext-real ) Real) ,b2 : ( ( ) ( V11() real ext-real ) Real) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty V142()
V143()
V144() )
set ) ) st
(
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(Closed-Interval-TSpace (b1 : ( ( ) ( V11() real ext-real ) Real) ,b2 : ( ( ) ( V11() real ext-real ) Real) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(Closed-Interval-TSpace (((b4 : ( ( ) ( V11() real ext-real ) Real) * b2 : ( ( ) ( V11() real ext-real ) Real) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) + b3 : ( ( ) ( V11() real ext-real ) Real) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,((b4 : ( ( ) ( V11() real ext-real ) Real) * b1 : ( ( ) ( V11() real ext-real ) Real) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) + b3 : ( ( ) ( V11() real ext-real ) Real) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-valued Function-like V29( the
carrier of
(Closed-Interval-TSpace (b1 : ( ( ) ( V11() real ext-real ) Real) ,b2 : ( ( ) ( V11() real ext-real ) Real) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty V142()
V143()
V144() )
set ) ) is
being_homeomorphism & ( for
r being ( ( ) (
V11()
real ext-real )
Real) st
r : ( ( ) (
V11()
real ext-real )
Real)
in [.a : ( ( ) ( V11() real ext-real ) Real) ,b : ( ( ) ( V11() real ext-real ) Real) .] : ( ( ) (
V142()
V143()
V144()
V204() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) holds
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(Closed-Interval-TSpace (b1 : ( ( ) ( V11() real ext-real ) Real) ,b2 : ( ( ) ( V11() real ext-real ) Real) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(Closed-Interval-TSpace (((b4 : ( ( ) ( V11() real ext-real ) Real) * b2 : ( ( ) ( V11() real ext-real ) Real) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) + b3 : ( ( ) ( V11() real ext-real ) Real) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,((b4 : ( ( ) ( V11() real ext-real ) Real) * b1 : ( ( ) ( V11() real ext-real ) Real) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) + b3 : ( ( ) ( V11() real ext-real ) Real) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-valued Function-like V29( the
carrier of
(Closed-Interval-TSpace (b1 : ( ( ) ( V11() real ext-real ) Real) ,b2 : ( ( ) ( V11() real ext-real ) Real) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
. r : ( ( ) (
V11()
real ext-real )
Real) : ( ( ) ( )
set )
= (e : ( ( ) ( V11() real ext-real ) Real) * r : ( ( ) ( V11() real ext-real ) Real) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
+ d : ( ( ) (
V11()
real ext-real )
Real) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) ) ) ;
theorem
ex
f being ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(Closed-Interval-TSpace ((- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty V142()
V143()
V144() )
set ) ) st
(
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(Closed-Interval-TSpace ((- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty V142()
V143()
V144() )
set ) ) is
being_homeomorphism & ( for
r being ( ( ) (
V11()
real ext-real )
Real) st
r : ( ( ) (
V11()
real ext-real )
Real)
in [.0 : ( ( ) ( empty natural V11() real ext-real non positive non negative Function-like functional V79() V80() V142() V143() V144() V145() V146() V147() V148() V201() V204() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) .] : ( ( ) (
V142()
V143()
V144()
V204() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) holds
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(Closed-Interval-TSpace ((- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
. r : ( ( ) (
V11()
real ext-real )
Real) : ( ( ) ( )
set )
= ((- 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) * r : ( ( ) ( V11() real ext-real ) Real) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
+ 1 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) ) &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(Closed-Interval-TSpace ((- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
. 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
set )
= 1 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(Closed-Interval-TSpace ((- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
. 1 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
set )
= - 1 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V11()
real ext-real non
positive )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) ) ;
theorem
ex
f being ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(Closed-Interval-TSpace ((- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty V142()
V143()
V144() )
set ) ) st
(
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(Closed-Interval-TSpace ((- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty V142()
V143()
V144() )
set ) ) is
being_homeomorphism & ( for
r being ( ( ) (
V11()
real ext-real )
Real) st
r : ( ( ) (
V11()
real ext-real )
Real)
in [.0 : ( ( ) ( empty natural V11() real ext-real non positive non negative Function-like functional V79() V80() V142() V143() V144() V145() V146() V147() V148() V201() V204() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) .] : ( ( ) (
V142()
V143()
V144()
V204() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) holds
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(Closed-Interval-TSpace ((- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
. r : ( ( ) (
V11()
real ext-real )
Real) : ( ( ) ( )
set )
= (2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) * r : ( ( ) ( V11() real ext-real ) Real) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
- 1 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) ) &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(Closed-Interval-TSpace ((- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
. 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
set )
= - 1 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V11()
real ext-real non
positive )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(Closed-Interval-TSpace ((- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
. 1 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
set )
= 1 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) ) ;
theorem
for
P being ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) st
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of )
= { p : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of (Closed-Interval-TSpace ((- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty strict ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) -defined the carrier of ((TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | (Lower_Arc b1 : ( ( non empty compact ) ( non empty functional closed compact ) Subset of ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty strict TopSpace-like T_0 T_1 T_2 ) SubSpace of TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) ) : ( ( ) ( non empty ) set ) -valued Function-like V29( the carrier of (Closed-Interval-TSpace ((- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty strict ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) ) quasi_total ) Function of ( ( ) ( non empty V142() V143() V144() ) set ) , ( ( ) ( non empty ) set ) ) where p is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) : |.p : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of (Closed-Interval-TSpace ((- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty strict ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) -defined the carrier of ((TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | (Lower_Arc b1 : ( ( non empty compact ) ( non empty functional closed compact ) Subset of ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty strict TopSpace-like T_0 T_1 T_2 ) SubSpace of TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) ) : ( ( ) ( non empty ) set ) -valued Function-like V29( the carrier of (Closed-Interval-TSpace ((- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty strict ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) ) quasi_total ) Function of ( ( ) ( non empty V142() V143() V144() ) set ) , ( ( ) ( non empty ) set ) ) .| : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) = 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) } holds
ex
f being ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(Closed-Interval-TSpace ((- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | (Lower_Arc b1 : ( ( non empty compact ) ( non empty functional closed compact ) Subset of ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like V29( the
carrier of
(Closed-Interval-TSpace ((- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty )
set ) ) st
(
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(Closed-Interval-TSpace ((- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | (Lower_Arc b1 : ( ( non empty compact ) ( non empty functional closed compact ) Subset of ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like V29( the
carrier of
(Closed-Interval-TSpace ((- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty )
set ) ) is
being_homeomorphism & ( for
q being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) st
q : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
in Lower_Arc P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) : ( ( non
empty ) ( non
empty functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) holds
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(Closed-Interval-TSpace ((- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | (Lower_Arc b1 : ( ( non empty compact ) ( non empty functional closed compact ) Subset of ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like V29( the
carrier of
(Closed-Interval-TSpace ((- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty )
set ) )
. (q : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `1) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set )
= q : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ) &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(Closed-Interval-TSpace ((- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | (Lower_Arc b1 : ( ( non empty compact ) ( non empty functional closed compact ) Subset of ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like V29( the
carrier of
(Closed-Interval-TSpace ((- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty )
set ) )
. (- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V11()
real ext-real non
positive )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set )
= W-min P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(Closed-Interval-TSpace ((- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | (Lower_Arc b1 : ( ( non empty compact ) ( non empty functional closed compact ) Subset of ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like V29( the
carrier of
(Closed-Interval-TSpace ((- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty )
set ) )
. 1 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
set )
= E-max P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) ) ;
theorem
for
P being ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) st
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of )
= { p : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of (Closed-Interval-TSpace ((- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty strict ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) -defined the carrier of ((TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | (Upper_Arc b1 : ( ( non empty compact ) ( non empty functional closed compact ) Subset of ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty strict TopSpace-like T_0 T_1 T_2 ) SubSpace of TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) ) : ( ( ) ( non empty ) set ) -valued Function-like V29( the carrier of (Closed-Interval-TSpace ((- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty strict ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) ) quasi_total ) Function of ( ( ) ( non empty V142() V143() V144() ) set ) , ( ( ) ( non empty ) set ) ) where p is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) : |.p : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of (Closed-Interval-TSpace ((- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty strict ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) -defined the carrier of ((TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | (Upper_Arc b1 : ( ( non empty compact ) ( non empty functional closed compact ) Subset of ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty strict TopSpace-like T_0 T_1 T_2 ) SubSpace of TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) ) : ( ( ) ( non empty ) set ) -valued Function-like V29( the carrier of (Closed-Interval-TSpace ((- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty strict ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) ) quasi_total ) Function of ( ( ) ( non empty V142() V143() V144() ) set ) , ( ( ) ( non empty ) set ) ) .| : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) = 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) } holds
ex
f being ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(Closed-Interval-TSpace ((- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | (Upper_Arc b1 : ( ( non empty compact ) ( non empty functional closed compact ) Subset of ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like V29( the
carrier of
(Closed-Interval-TSpace ((- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty )
set ) ) st
(
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(Closed-Interval-TSpace ((- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | (Upper_Arc b1 : ( ( non empty compact ) ( non empty functional closed compact ) Subset of ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like V29( the
carrier of
(Closed-Interval-TSpace ((- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty )
set ) ) is
being_homeomorphism & ( for
q being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) st
q : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
in Upper_Arc P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) : ( ( non
empty ) ( non
empty functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) holds
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(Closed-Interval-TSpace ((- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | (Upper_Arc b1 : ( ( non empty compact ) ( non empty functional closed compact ) Subset of ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like V29( the
carrier of
(Closed-Interval-TSpace ((- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty )
set ) )
. (q : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) `1) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set )
= q : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ) &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(Closed-Interval-TSpace ((- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | (Upper_Arc b1 : ( ( non empty compact ) ( non empty functional closed compact ) Subset of ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like V29( the
carrier of
(Closed-Interval-TSpace ((- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty )
set ) )
. (- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V11()
real ext-real non
positive )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set )
= W-min P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(Closed-Interval-TSpace ((- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | (Upper_Arc b1 : ( ( non empty compact ) ( non empty functional closed compact ) Subset of ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like V29( the
carrier of
(Closed-Interval-TSpace ((- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non
empty strict ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty )
set ) )
. 1 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
set )
= E-max P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) ) ;
theorem
for
P being ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) st
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of )
= { p : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) -defined the carrier of ((TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | (Lower_Arc b1 : ( ( non empty compact ) ( non empty functional closed compact ) Subset of ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty strict TopSpace-like T_0 T_1 T_2 ) SubSpace of TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) ) : ( ( ) ( non empty ) set ) -valued Function-like V29( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) ) quasi_total ) Function of ( ( ) ( non empty V142() V143() V144() ) set ) , ( ( ) ( non empty ) set ) ) where p is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) : |.p : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) -defined the carrier of ((TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | (Lower_Arc b1 : ( ( non empty compact ) ( non empty functional closed compact ) Subset of ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty strict TopSpace-like T_0 T_1 T_2 ) SubSpace of TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) ) : ( ( ) ( non empty ) set ) -valued Function-like V29( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) ) quasi_total ) Function of ( ( ) ( non empty V142() V143() V144() ) set ) , ( ( ) ( non empty ) set ) ) .| : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) = 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) } holds
ex
f being ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | (Lower_Arc b1 : ( ( non empty compact ) ( non empty functional closed compact ) Subset of ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty )
set ) ) st
(
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | (Lower_Arc b1 : ( ( non empty compact ) ( non empty functional closed compact ) Subset of ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty )
set ) ) is
being_homeomorphism & ( for
q1,
q2 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
for
r1,
r2 being ( ( ) (
V11()
real ext-real )
Real) st
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | (Lower_Arc b1 : ( ( non empty compact ) ( non empty functional closed compact ) Subset of ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty )
set ) )
. r1 : ( ( ) (
V11()
real ext-real )
Real) : ( ( ) ( )
set )
= q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | (Lower_Arc b1 : ( ( non empty compact ) ( non empty functional closed compact ) Subset of ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty )
set ) )
. r2 : ( ( ) (
V11()
real ext-real )
Real) : ( ( ) ( )
set )
= q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
r1 : ( ( ) (
V11()
real ext-real )
Real)
in [.0 : ( ( ) ( empty natural V11() real ext-real non positive non negative Function-like functional V79() V80() V142() V143() V144() V145() V146() V147() V148() V201() V204() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) .] : ( ( ) (
V142()
V143()
V144()
V204() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) &
r2 : ( ( ) (
V11()
real ext-real )
Real)
in [.0 : ( ( ) ( empty natural V11() real ext-real non positive non negative Function-like functional V79() V80() V142() V143() V144() V145() V146() V147() V148() V201() V204() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) .] : ( ( ) (
V142()
V143()
V144()
V204() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) holds
(
r1 : ( ( ) (
V11()
real ext-real )
Real)
< r2 : ( ( ) (
V11()
real ext-real )
Real) iff
q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
> q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) ) ) &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | (Lower_Arc b1 : ( ( non empty compact ) ( non empty functional closed compact ) Subset of ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty )
set ) )
. 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
set )
= E-max P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | (Lower_Arc b1 : ( ( non empty compact ) ( non empty functional closed compact ) Subset of ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty )
set ) )
. 1 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
set )
= W-min P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) ) ;
theorem
for
P being ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) st
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of )
= { p : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) -defined the carrier of ((TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | (Upper_Arc b1 : ( ( non empty compact ) ( non empty functional closed compact ) Subset of ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty strict TopSpace-like T_0 T_1 T_2 ) SubSpace of TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) ) : ( ( ) ( non empty ) set ) -valued Function-like V29( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) ) quasi_total ) Function of ( ( ) ( non empty V142() V143() V144() ) set ) , ( ( ) ( non empty ) set ) ) where p is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) : |.p : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) -defined the carrier of ((TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | (Upper_Arc b1 : ( ( non empty compact ) ( non empty functional closed compact ) Subset of ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty strict TopSpace-like T_0 T_1 T_2 ) SubSpace of TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) ) : ( ( ) ( non empty ) set ) -valued Function-like V29( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) ) quasi_total ) Function of ( ( ) ( non empty V142() V143() V144() ) set ) , ( ( ) ( non empty ) set ) ) .| : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) = 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) } holds
ex
f being ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | (Upper_Arc b1 : ( ( non empty compact ) ( non empty functional closed compact ) Subset of ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty )
set ) ) st
(
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | (Upper_Arc b1 : ( ( non empty compact ) ( non empty functional closed compact ) Subset of ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty )
set ) ) is
being_homeomorphism & ( for
q1,
q2 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
for
r1,
r2 being ( ( ) (
V11()
real ext-real )
Real) st
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | (Upper_Arc b1 : ( ( non empty compact ) ( non empty functional closed compact ) Subset of ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty )
set ) )
. r1 : ( ( ) (
V11()
real ext-real )
Real) : ( ( ) ( )
set )
= q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | (Upper_Arc b1 : ( ( non empty compact ) ( non empty functional closed compact ) Subset of ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty )
set ) )
. r2 : ( ( ) (
V11()
real ext-real )
Real) : ( ( ) ( )
set )
= q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
r1 : ( ( ) (
V11()
real ext-real )
Real)
in [.0 : ( ( ) ( empty natural V11() real ext-real non positive non negative Function-like functional V79() V80() V142() V143() V144() V145() V146() V147() V148() V201() V204() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) .] : ( ( ) (
V142()
V143()
V144()
V204() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) &
r2 : ( ( ) (
V11()
real ext-real )
Real)
in [.0 : ( ( ) ( empty natural V11() real ext-real non positive non negative Function-like functional V79() V80() V142() V143() V144() V145() V146() V147() V148() V201() V204() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) .] : ( ( ) (
V142()
V143()
V144()
V204() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) holds
(
r1 : ( ( ) (
V11()
real ext-real )
Real)
< r2 : ( ( ) (
V11()
real ext-real )
Real) iff
q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) ) ) &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | (Upper_Arc b1 : ( ( non empty compact ) ( non empty functional closed compact ) Subset of ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty )
set ) )
. 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
set )
= W-min P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | (Upper_Arc b1 : ( ( non empty compact ) ( non empty functional closed compact ) Subset of ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty )
set ) )
. 1 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
set )
= E-max P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) ) ;
theorem
for
p1,
p2,
p3,
p4 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
for
P being ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) st
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of )
= { p : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) quasi_total ) Function of ( ( ) ( non empty functional ) set ) , ( ( ) ( non empty functional ) set ) ) where p is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) : |.p : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) quasi_total ) Function of ( ( ) ( non empty functional ) set ) , ( ( ) ( non empty functional ) set ) ) .| : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) = 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) } &
LE p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
LE p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
LE p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
>= 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
>= 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
>= 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
>= 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) holds
ex
f being ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) ) ex
q1,
q2,
q3,
q4 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) st
(
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) ) is
being_homeomorphism & ( for
q being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) holds
|.(f : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) quasi_total ) Function of ( ( ) ( non empty functional ) set ) , ( ( ) ( non empty functional ) set ) ) . q : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) ) : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) .| : ( ( ) (
V11()
real ext-real non
negative )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
= |.q : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) .| : ( ( ) (
V11()
real ext-real non
negative )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) ) &
q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
= f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) )
. p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
= f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) )
. p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
q3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
= f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) )
. p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
q4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
= f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) )
. p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
LE q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
LE q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
q3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
LE q3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
q4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) ) ;
theorem
for
p1,
p2,
p3,
p4 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
for
P being ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) st
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of )
= { p : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) quasi_total ) Function of ( ( ) ( non empty functional ) set ) , ( ( ) ( non empty functional ) set ) ) where p is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) : |.p : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) quasi_total ) Function of ( ( ) ( non empty functional ) set ) , ( ( ) ( non empty functional ) set ) ) .| : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) = 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) } &
LE p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
LE p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
LE p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
>= 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
>= 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
>= 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
> 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) holds
ex
f being ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) ) ex
q1,
q2,
q3,
q4 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) st
(
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) ) is
being_homeomorphism & ( for
q being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) holds
|.(f : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) quasi_total ) Function of ( ( ) ( non empty functional ) set ) , ( ( ) ( non empty functional ) set ) ) . q : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) ) : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) .| : ( ( ) (
V11()
real ext-real non
negative )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
= |.q : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) .| : ( ( ) (
V11()
real ext-real non
negative )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) ) &
q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
= f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) )
. p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
= f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) )
. p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
q3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
= f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) )
. p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
q4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
= f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) )
. p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
>= 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
>= 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
>= 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
>= 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
LE q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
LE q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
q3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
LE q3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
q4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) ) ;
theorem
for
p1,
p2,
p3,
p4 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
for
P being ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) st
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of )
= { p : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) quasi_total ) Function of ( ( ) ( non empty functional ) set ) , ( ( ) ( non empty functional ) set ) ) where p is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) : |.p : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) quasi_total ) Function of ( ( ) ( non empty functional ) set ) , ( ( ) ( non empty functional ) set ) ) .| : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) = 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) } &
LE p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
LE p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
LE p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
>= 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
>= 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
>= 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
> 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) holds
ex
f being ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) ) ex
q1,
q2,
q3,
q4 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) st
(
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) ) is
being_homeomorphism & ( for
q being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) holds
|.(f : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) quasi_total ) Function of ( ( ) ( non empty functional ) set ) , ( ( ) ( non empty functional ) set ) ) . q : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) ) : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) .| : ( ( ) (
V11()
real ext-real non
negative )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
= |.q : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) .| : ( ( ) (
V11()
real ext-real non
negative )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) ) &
q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
= f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) )
. p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
= f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) )
. p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
q3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
= f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) )
. p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
q4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
= f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) )
. p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
LE q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
LE q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
q3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
LE q3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
q4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) ) ;
theorem
for
p1,
p2,
p3,
p4 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
for
P being ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) st
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of )
= { p : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) quasi_total ) Function of ( ( ) ( non empty functional ) set ) , ( ( ) ( non empty functional ) set ) ) where p is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) : |.p : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) quasi_total ) Function of ( ( ) ( non empty functional ) set ) , ( ( ) ( non empty functional ) set ) ) .| : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) = 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) } &
LE p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
LE p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
LE p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) & (
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
>= 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) or
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
>= 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) ) & (
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
>= 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) or
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
>= 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) ) & (
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
>= 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) or
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
>= 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) ) & (
p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
> 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) or
p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
> 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) ) holds
ex
f being ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) ) ex
q1,
q2,
q3,
q4 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) st
(
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) ) is
being_homeomorphism & ( for
q being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) holds
|.(f : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) quasi_total ) Function of ( ( ) ( non empty functional ) set ) , ( ( ) ( non empty functional ) set ) ) . q : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) ) : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) .| : ( ( ) (
V11()
real ext-real non
negative )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
= |.q : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) .| : ( ( ) (
V11()
real ext-real non
negative )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) ) &
q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
= f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) )
. p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
= f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) )
. p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
q3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
= f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) )
. p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
q4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
= f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) )
. p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
>= 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
>= 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
>= 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
> 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
LE q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
LE q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
q3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
LE q3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
q4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) ) ;
theorem
for
p1,
p2,
p3,
p4 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
for
P being ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) st
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of )
= { p : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) quasi_total ) Function of ( ( ) ( non empty functional ) set ) , ( ( ) ( non empty functional ) set ) ) where p is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) : |.p : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) quasi_total ) Function of ( ( ) ( non empty functional ) set ) , ( ( ) ( non empty functional ) set ) ) .| : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) = 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) } &
LE p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
LE p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
LE p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) & (
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
>= 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) or
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
>= 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) ) & (
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
>= 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) or
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
>= 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) ) & (
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
>= 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) or
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
>= 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) ) & (
p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
> 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) or
p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
> 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) ) holds
ex
f being ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) ) ex
q1,
q2,
q3,
q4 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) st
(
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) ) is
being_homeomorphism & ( for
q being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) holds
|.(f : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) quasi_total ) Function of ( ( ) ( non empty functional ) set ) , ( ( ) ( non empty functional ) set ) ) . q : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) ) : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) .| : ( ( ) (
V11()
real ext-real non
negative )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
= |.q : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) .| : ( ( ) (
V11()
real ext-real non
negative )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) ) &
q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
= f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) )
. p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
= f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) )
. p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
q3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
= f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) )
. p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
q4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
= f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) )
. p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
LE q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
LE q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
q3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
LE q3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
q4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) ) ;
theorem
for
p1,
p2,
p3,
p4 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
for
P being ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) st
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of )
= { p : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) quasi_total ) Function of ( ( ) ( non empty functional ) set ) , ( ( ) ( non empty functional ) set ) ) where p is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) : |.p : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) quasi_total ) Function of ( ( ) ( non empty functional ) set ) , ( ( ) ( non empty functional ) set ) ) .| : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) = 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) } &
p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
= W-min P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
LE p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
LE p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
LE p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) holds
ex
f being ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) ) ex
q1,
q2,
q3,
q4 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) st
(
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) ) is
being_homeomorphism & ( for
q being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) holds
|.(f : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) quasi_total ) Function of ( ( ) ( non empty functional ) set ) , ( ( ) ( non empty functional ) set ) ) . q : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) ) : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) .| : ( ( ) (
V11()
real ext-real non
negative )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
= |.q : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) .| : ( ( ) (
V11()
real ext-real non
negative )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) ) &
q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
= f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) )
. p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
= f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) )
. p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
q3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
= f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) )
. p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
q4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
= f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) )
. p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
LE q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
LE q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
q3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
LE q3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
q4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) ) ;
theorem
for
p1,
p2,
p3,
p4 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
for
P being ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) st
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of )
= { p : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) quasi_total ) Function of ( ( ) ( non empty functional ) set ) , ( ( ) ( non empty functional ) set ) ) where p is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) : |.p : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) quasi_total ) Function of ( ( ) ( non empty functional ) set ) , ( ( ) ( non empty functional ) set ) ) .| : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) = 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) } &
LE p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
LE p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
LE p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) holds
ex
f being ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) ) ex
q1,
q2,
q3,
q4 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) st
(
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) ) is
being_homeomorphism & ( for
q being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) holds
|.(f : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) quasi_total ) Function of ( ( ) ( non empty functional ) set ) , ( ( ) ( non empty functional ) set ) ) . q : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) ) : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) .| : ( ( ) (
V11()
real ext-real non
negative )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
= |.q : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) .| : ( ( ) (
V11()
real ext-real non
negative )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) ) &
q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
= f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) )
. p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
= f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) )
. p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
q3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
= f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) )
. p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
q4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
= f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) )
. p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
q4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
LE q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
LE q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
q3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
LE q3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
q4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) ) ;
begin
theorem
for
p1,
p2,
p3,
p4 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
for
P being ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) st
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of )
= { p : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) quasi_total ) Function of ( ( ) ( non empty functional ) set ) , ( ( ) ( non empty functional ) set ) ) where p is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) : |.p : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) quasi_total ) Function of ( ( ) ( non empty functional ) set ) , ( ( ) ( non empty functional ) set ) ) .| : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) = 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) } &
LE p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
LE p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
LE p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
<> p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
<> p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
<> p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`1 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) &
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
`2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
< 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) holds
ex
f being ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) ) st
(
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) ) is
being_homeomorphism & ( for
q being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) holds
|.(f : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) quasi_total ) Function of ( ( ) ( non empty functional ) set ) , ( ( ) ( non empty functional ) set ) ) . q : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) ) : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) .| : ( ( ) (
V11()
real ext-real non
negative )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
= |.q : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) .| : ( ( ) (
V11()
real ext-real non
negative )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) ) &
|[(- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative Function-like functional V79() V80() V142() V143() V144() V145() V146() V147() V148() V201() V204() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
= f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) )
. p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
|[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative Function-like functional V79() V80() V142() V143() V144() V145() V146() V147() V148() V201() V204() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
= f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) )
. p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
|[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative Function-like functional V79() V80() V142() V143() V144() V145() V146() V147() V148() V201() V204() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
= f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) )
. p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
|[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative Function-like functional V79() V80() V142() V143() V144() V145() V146() V147() V148() V201() V204() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ,(- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
= f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) )
. p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) ) ;
theorem
for
p1,
p2,
p3,
p4 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
for
P being ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) st
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of )
= { p : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) quasi_total ) Function of ( ( ) ( non empty functional ) set ) , ( ( ) ( non empty functional ) set ) ) where p is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) : |.p : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) quasi_total ) Function of ( ( ) ( non empty functional ) set ) , ( ( ) ( non empty functional ) set ) ) .| : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) = 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) } &
LE p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
LE p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
LE p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
<> p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
<> p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
<> p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) holds
ex
f being ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) ) st
(
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) ) is
being_homeomorphism & ( for
q being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) holds
|.(f : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) quasi_total ) Function of ( ( ) ( non empty functional ) set ) , ( ( ) ( non empty functional ) set ) ) . q : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) ) : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) ) .| : ( ( ) (
V11()
real ext-real non
negative )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) )
= |.q : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) .| : ( ( ) (
V11()
real ext-real non
negative )
Element of
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) ) &
|[(- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative Function-like functional V79() V80() V142() V143() V144() V145() V146() V147() V148() V201() V204() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
= f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) )
. p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
|[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative Function-like functional V79() V80() V142() V143() V144() V145() V146() V147() V148() V201() V204() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
= f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) )
. p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
|[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative Function-like functional V79() V80() V142() V143() V144() V145() V146() V147() V148() V201() V204() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
= f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) )
. p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) &
|[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative Function-like functional V79() V80() V142() V143() V144() V145() V146() V147() V148() V201() V204() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ,(- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
= f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) )
quasi_total )
Function of ( ( ) ( non
empty functional )
set ) , ( ( ) ( non
empty functional )
set ) )
. p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) ) ;
theorem
for
p1,
p2,
p3,
p4 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
for
P being ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of )
for
C0 being ( ( ) (
functional )
Subset of ) st
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of )
= { p : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) ) quasi_total ) Function of ( ( ) ( non empty V142() V143() V144() ) set ) , ( ( ) ( non empty functional ) set ) ) where p is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) : |.p : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) ) quasi_total ) Function of ( ( ) ( non empty V142() V143() V144() ) set ) , ( ( ) ( non empty functional ) set ) ) .| : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) = 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) } &
LE p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
LE p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
LE p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) holds
for
f,
g being ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) st
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
continuous &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
one-to-one &
g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
continuous &
g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
one-to-one &
C0 : ( ( ) (
functional )
Subset of )
= { p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) where p is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) : |.p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) .| : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) <= 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) } &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set )
= p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. 1 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set )
= p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set )
= p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. 1 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set )
= p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
rng f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) )
c= C0 : ( ( ) (
functional )
Subset of ) &
rng g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) )
c= C0 : ( ( ) (
functional )
Subset of ) holds
rng f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) )
meets rng g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) ;
theorem
for
p1,
p2,
p3,
p4 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
for
P being ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of )
for
C0 being ( ( ) (
functional )
Subset of ) st
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of )
= { p : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) ) quasi_total ) Function of ( ( ) ( non empty V142() V143() V144() ) set ) , ( ( ) ( non empty functional ) set ) ) where p is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) : |.p : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) ) quasi_total ) Function of ( ( ) ( non empty V142() V143() V144() ) set ) , ( ( ) ( non empty functional ) set ) ) .| : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) = 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) } &
LE p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
LE p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
LE p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) holds
for
f,
g being ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) st
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
continuous &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
one-to-one &
g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
continuous &
g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
one-to-one &
C0 : ( ( ) (
functional )
Subset of )
= { p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) where p is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) : |.p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) .| : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) <= 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) } &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set )
= p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. 1 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set )
= p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set )
= p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. 1 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set )
= p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
rng f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) )
c= C0 : ( ( ) (
functional )
Subset of ) &
rng g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) )
c= C0 : ( ( ) (
functional )
Subset of ) holds
rng f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) )
meets rng g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) ;
theorem
for
p1,
p2,
p3,
p4 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
for
P being ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of )
for
C0 being ( ( ) (
functional )
Subset of ) st
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of )
= { p : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) ) quasi_total ) Function of ( ( ) ( non empty V142() V143() V144() ) set ) , ( ( ) ( non empty functional ) set ) ) where p is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) : |.p : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) ) quasi_total ) Function of ( ( ) ( non empty V142() V143() V144() ) set ) , ( ( ) ( non empty functional ) set ) ) .| : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) = 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) } &
LE p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
LE p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
LE p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) holds
for
f,
g being ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) st
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
continuous &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
one-to-one &
g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
continuous &
g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
one-to-one &
C0 : ( ( ) (
functional )
Subset of )
= { p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) where p is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) : |.p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) .| : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) >= 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) } &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set )
= p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. 1 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set )
= p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set )
= p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. 1 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set )
= p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
rng f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) )
c= C0 : ( ( ) (
functional )
Subset of ) &
rng g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) )
c= C0 : ( ( ) (
functional )
Subset of ) holds
rng f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) )
meets rng g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) ;
theorem
for
p1,
p2,
p3,
p4 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) )
for
P being ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of )
for
C0 being ( ( ) (
functional )
Subset of ) st
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of )
= { p : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) ) quasi_total ) Function of ( ( ) ( non empty V142() V143() V144() ) set ) , ( ( ) ( non empty functional ) set ) ) where p is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) : |.p : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like V29( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V196() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V196() ) TopStruct ) ) : ( ( ) ( non empty V142() V143() V144() ) set ) ) quasi_total ) Function of ( ( ) ( non empty V142() V143() V144() ) set ) , ( ( ) ( non empty functional ) set ) ) .| : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) = 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) } &
LE p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
LE p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) &
LE p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( non
empty compact ) ( non
empty functional closed compact )
Subset of ) holds
for
f,
g being ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) st
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
continuous &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
one-to-one &
g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
continuous &
g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) is
one-to-one &
C0 : ( ( ) (
functional )
Subset of )
= { p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) where p is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) : |.p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) V76() V134() ) Point of ( ( ) ( non empty functional ) set ) ) .| : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) >= 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) } &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set )
= p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. 1 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set )
= p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. 0 : ( ( ) (
empty natural V11()
real ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201()
V204() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set )
= p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) )
. 1 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set )
= p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V11()
real ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V199()
V201() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148()
V201() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148()
V201()
V202()
V204() )
set ) ) : ( ( ) ( )
set ) ) ) )
V76()
V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
rng f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) )
c= C0 : ( ( ) (
functional )
Subset of ) &
rng g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) )
c= C0 : ( ( ) (
functional )
Subset of ) holds
rng f : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) )
meets rng g : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like V29( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V196() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V196() )
TopStruct ) ) : ( ( ) ( non
empty V142()
V143()
V144() )
set ) )
quasi_total )
Function of ( ( ) ( non
empty V142()
V143()
V144() )
set ) , ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() V201() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() V201() V202() V204() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) ;