begin
theorem
for
X being ( ( ) ( )
TopStruct )
for
Y,
Z being ( ( non
empty ) ( non
empty )
TopStruct )
for
f being ( (
Function-like V18( the
carrier of
b1 : ( ( ) ( )
TopStruct ) : ( ( ) ( )
set ) , the
carrier of
b2 : ( ( non
empty ) ( non
empty )
TopStruct ) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( ) ( )
TopStruct ) : ( ( ) ( )
set )
-defined the
carrier of
b2 : ( ( non
empty ) ( non
empty )
TopStruct ) : ( ( ) ( non
empty )
set )
-valued Function-like total V18( the
carrier of
b1 : ( ( ) ( )
TopStruct ) : ( ( ) ( )
set ) , the
carrier of
b2 : ( ( non
empty ) ( non
empty )
TopStruct ) : ( ( ) ( non
empty )
set ) ) )
Function of ( ( ) ( )
set ) , ( ( ) ( non
empty )
set ) )
for
g being ( (
Function-like V18( the
carrier of
b1 : ( ( ) ( )
TopStruct ) : ( ( ) ( )
set ) , the
carrier of
b3 : ( ( non
empty ) ( non
empty )
TopStruct ) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( ) ( )
TopStruct ) : ( ( ) ( )
set )
-defined the
carrier of
b3 : ( ( non
empty ) ( non
empty )
TopStruct ) : ( ( ) ( non
empty )
set )
-valued Function-like total V18( the
carrier of
b1 : ( ( ) ( )
TopStruct ) : ( ( ) ( )
set ) , the
carrier of
b3 : ( ( non
empty ) ( non
empty )
TopStruct ) : ( ( ) ( non
empty )
set ) ) )
Function of ( ( ) ( )
set ) , ( ( ) ( non
empty )
set ) ) holds
(
dom f : ( (
Function-like V18( the
carrier of
b1 : ( ( ) ( )
TopStruct ) : ( ( ) ( )
set ) , the
carrier of
b2 : ( ( non
empty ) ( non
empty )
TopStruct ) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( ) ( )
TopStruct ) : ( ( ) ( )
set )
-defined the
carrier of
b2 : ( ( non
empty ) ( non
empty )
TopStruct ) : ( ( ) ( non
empty )
set )
-valued Function-like total V18( the
carrier of
b1 : ( ( ) ( )
TopStruct ) : ( ( ) ( )
set ) , the
carrier of
b2 : ( ( non
empty ) ( non
empty )
TopStruct ) : ( ( ) ( non
empty )
set ) ) )
Function of ( ( ) ( )
set ) , ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
Element of
K19( the
carrier of
b1 : ( ( ) ( )
TopStruct ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) )
= dom g : ( (
Function-like V18( the
carrier of
b1 : ( ( ) ( )
TopStruct ) : ( ( ) ( )
set ) , the
carrier of
b3 : ( ( non
empty ) ( non
empty )
TopStruct ) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( ) ( )
TopStruct ) : ( ( ) ( )
set )
-defined the
carrier of
b3 : ( ( non
empty ) ( non
empty )
TopStruct ) : ( ( ) ( non
empty )
set )
-valued Function-like total V18( the
carrier of
b1 : ( ( ) ( )
TopStruct ) : ( ( ) ( )
set ) , the
carrier of
b3 : ( ( non
empty ) ( non
empty )
TopStruct ) : ( ( ) ( non
empty )
set ) ) )
Function of ( ( ) ( )
set ) , ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
Element of
K19( the
carrier of
b1 : ( ( ) ( )
TopStruct ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) &
dom f : ( (
Function-like V18( the
carrier of
b1 : ( ( ) ( )
TopStruct ) : ( ( ) ( )
set ) , the
carrier of
b2 : ( ( non
empty ) ( non
empty )
TopStruct ) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( ) ( )
TopStruct ) : ( ( ) ( )
set )
-defined the
carrier of
b2 : ( ( non
empty ) ( non
empty )
TopStruct ) : ( ( ) ( non
empty )
set )
-valued Function-like total V18( the
carrier of
b1 : ( ( ) ( )
TopStruct ) : ( ( ) ( )
set ) , the
carrier of
b2 : ( ( non
empty ) ( non
empty )
TopStruct ) : ( ( ) ( non
empty )
set ) ) )
Function of ( ( ) ( )
set ) , ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
Element of
K19( the
carrier of
b1 : ( ( ) ( )
TopStruct ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) )
= the
carrier of
X : ( ( ) ( )
TopStruct ) : ( ( ) ( )
set ) &
dom f : ( (
Function-like V18( the
carrier of
b1 : ( ( ) ( )
TopStruct ) : ( ( ) ( )
set ) , the
carrier of
b2 : ( ( non
empty ) ( non
empty )
TopStruct ) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( ) ( )
TopStruct ) : ( ( ) ( )
set )
-defined the
carrier of
b2 : ( ( non
empty ) ( non
empty )
TopStruct ) : ( ( ) ( non
empty )
set )
-valued Function-like total V18( the
carrier of
b1 : ( ( ) ( )
TopStruct ) : ( ( ) ( )
set ) , the
carrier of
b2 : ( ( non
empty ) ( non
empty )
TopStruct ) : ( ( ) ( non
empty )
set ) ) )
Function of ( ( ) ( )
set ) , ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
Element of
K19( the
carrier of
b1 : ( ( ) ( )
TopStruct ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) )
= [#] X : ( ( ) ( )
TopStruct ) : ( ( ) ( non
proper dense )
Element of
K19( the
carrier of
b1 : ( ( ) ( )
TopStruct ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) ) ;
theorem
for
X being ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace)
for
f1 being ( (
Function-like V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set )
-defined the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-valued Function-like total V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) )
V161()
V162()
V163() )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( non
empty V171()
V172()
V173() )
set ) )
for
a being ( (
real ) (
V28()
real ext-real )
number ) st
f1 : ( (
Function-like V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set )
-defined the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-valued Function-like total V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) )
V161()
V162()
V163() )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( non
empty V171()
V172()
V173() )
set ) ) is
continuous holds
ex
g being ( (
Function-like V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set )
-defined the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-valued Function-like total V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) )
V161()
V162()
V163() )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( non
empty V171()
V172()
V173() )
set ) ) st
( ( for
p being ( ( ) ( )
Point of ( ( ) ( non
empty )
set ) )
for
r1 being ( (
real ) (
V28()
real ext-real )
number ) st
f1 : ( (
Function-like V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set )
-defined the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-valued Function-like total V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) )
V161()
V162()
V163() )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( non
empty V171()
V172()
V173() )
set ) )
. p : ( ( ) ( )
Point of ( ( ) ( non
empty )
set ) ) : ( ( ) (
V28()
real ext-real )
set )
= r1 : ( (
real ) (
V28()
real ext-real )
number ) holds
g : ( (
Function-like V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set )
-defined the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-valued Function-like total V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) )
V161()
V162()
V163() )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( non
empty V171()
V172()
V173() )
set ) )
. p : ( ( ) ( )
Point of ( ( ) ( non
empty )
set ) ) : ( ( ) (
V28()
real ext-real )
set )
= r1 : ( (
real ) (
V28()
real ext-real )
number )
- a : ( (
real ) (
V28()
real ext-real )
number ) : ( ( ) (
V28()
real ext-real )
set ) ) &
g : ( (
Function-like V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set )
-defined the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-valued Function-like total V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) )
V161()
V162()
V163() )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( non
empty V171()
V172()
V173() )
set ) ) is
continuous ) ;
theorem
for
X being ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace)
for
f1 being ( (
Function-like V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set )
-defined the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-valued Function-like total V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) )
V161()
V162()
V163() )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( non
empty V171()
V172()
V173() )
set ) )
for
a being ( (
real ) (
V28()
real ext-real )
number ) st
f1 : ( (
Function-like V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set )
-defined the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-valued Function-like total V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) )
V161()
V162()
V163() )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( non
empty V171()
V172()
V173() )
set ) ) is
continuous holds
ex
g being ( (
Function-like V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set )
-defined the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-valued Function-like total V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) )
V161()
V162()
V163() )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( non
empty V171()
V172()
V173() )
set ) ) st
( ( for
p being ( ( ) ( )
Point of ( ( ) ( non
empty )
set ) )
for
r1 being ( (
real ) (
V28()
real ext-real )
number ) st
f1 : ( (
Function-like V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set )
-defined the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-valued Function-like total V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) )
V161()
V162()
V163() )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( non
empty V171()
V172()
V173() )
set ) )
. p : ( ( ) ( )
Point of ( ( ) ( non
empty )
set ) ) : ( ( ) (
V28()
real ext-real )
set )
= r1 : ( (
real ) (
V28()
real ext-real )
number ) holds
g : ( (
Function-like V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set )
-defined the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-valued Function-like total V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) )
V161()
V162()
V163() )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( non
empty V171()
V172()
V173() )
set ) )
. p : ( ( ) ( )
Point of ( ( ) ( non
empty )
set ) ) : ( ( ) (
V28()
real ext-real )
set )
= a : ( (
real ) (
V28()
real ext-real )
number )
- r1 : ( (
real ) (
V28()
real ext-real )
number ) : ( ( ) (
V28()
real ext-real )
set ) ) &
g : ( (
Function-like V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set )
-defined the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-valued Function-like total V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) )
V161()
V162()
V163() )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( non
empty V171()
V172()
V173() )
set ) ) is
continuous ) ;
theorem
for
X being ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace)
for
n being ( ( ) (
natural V28()
real ext-real V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) )
for
p being ( ( ) (
Relation-like Function-like V43(
b2 : ( ( ) (
natural V28()
real ext-real V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
for
f being ( (
Function-like V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set )
-defined the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-valued Function-like total V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) )
V161()
V162()
V163() )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( non
empty V171()
V172()
V173() )
set ) ) st
f : ( (
Function-like V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set )
-defined the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-valued Function-like total V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) )
V161()
V162()
V163() )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( non
empty V171()
V172()
V173() )
set ) ) is
continuous holds
ex
g being ( (
Function-like V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
(TOP-REAL b2 : ( ( ) ( natural V28() real ext-real V123() V124() V171() V172() V173() V174() V175() V176() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set )
-defined the
carrier of
(TOP-REAL b2 : ( ( ) ( natural V28() real ext-real V123() V124() V171() V172() V173() V174() V175() V176() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like total V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
(TOP-REAL b2 : ( ( ) ( natural V28() real ext-real V123() V124() V171() V172() V173() V174() V175() V176() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty )
set ) , ( ( ) (
functional non
empty )
set ) ) st
( ( for
r being ( ( ) ( )
Point of ( ( ) ( non
empty )
set ) ) holds
g : ( (
Function-like V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
(TOP-REAL b2 : ( ( ) ( natural V28() real ext-real V123() V124() V171() V172() V173() V174() V175() V176() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set )
-defined the
carrier of
(TOP-REAL b2 : ( ( ) ( natural V28() real ext-real V123() V124() V171() V172() V173() V174() V175() V176() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like total V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
(TOP-REAL b2 : ( ( ) ( natural V28() real ext-real V123() V124() V171() V172() V173() V174() V175() V176() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty )
set ) , ( ( ) (
functional non
empty )
set ) )
. r : ( ( ) ( )
Point of ( ( ) ( non
empty )
set ) ) : ( ( ) (
Relation-like Function-like )
set )
= (f : ( ( Function-like V18( the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) , the carrier of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V122() ) TopStruct ) : ( ( ) ( non empty V171() V172() V173() ) set ) ) ) ( Relation-like the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) -defined the carrier of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V122() ) TopStruct ) : ( ( ) ( non empty V171() V172() V173() ) set ) -valued Function-like total V18( the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) , the carrier of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V122() ) TopStruct ) : ( ( ) ( non empty V171() V172() V173() ) set ) ) V161() V162() V163() ) Function of ( ( ) ( non empty ) set ) , ( ( ) ( non empty V171() V172() V173() ) set ) ) . r : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
V28()
real ext-real )
set )
* p : ( ( ) (
Relation-like Function-like V43(
b2 : ( ( ) (
natural V28()
real ext-real V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
Relation-like Function-like V43(
b2 : ( ( ) (
natural V28()
real ext-real V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL b2 : ( ( ) ( natural V28() real ext-real V123() V124() V171() V172() V173() V174() V175() V176() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) &
g : ( (
Function-like V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
(TOP-REAL b2 : ( ( ) ( natural V28() real ext-real V123() V124() V171() V172() V173() V174() V175() V176() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set )
-defined the
carrier of
(TOP-REAL b2 : ( ( ) ( natural V28() real ext-real V123() V124() V171() V172() V173() V174() V175() V176() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like total V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
(TOP-REAL b2 : ( ( ) ( natural V28() real ext-real V123() V124() V171() V172() V173() V174() V175() V176() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty )
set ) , ( ( ) (
functional non
empty )
set ) ) is
continuous ) ;
theorem
for
X being ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace)
for
n being ( ( ) (
natural V28()
real ext-real V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) )
for
p1,
p2 being ( ( ) (
Relation-like Function-like V43(
b2 : ( ( ) (
natural V28()
real ext-real V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
for
f1,
f2 being ( (
Function-like V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set )
-defined the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-valued Function-like total V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) )
V161()
V162()
V163() )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( non
empty V171()
V172()
V173() )
set ) ) st
f1 : ( (
Function-like V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set )
-defined the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-valued Function-like total V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) )
V161()
V162()
V163() )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( non
empty V171()
V172()
V173() )
set ) ) is
continuous &
f2 : ( (
Function-like V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set )
-defined the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-valued Function-like total V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) )
V161()
V162()
V163() )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( non
empty V171()
V172()
V173() )
set ) ) is
continuous holds
ex
g being ( (
Function-like V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
(TOP-REAL b2 : ( ( ) ( natural V28() real ext-real V123() V124() V171() V172() V173() V174() V175() V176() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set )
-defined the
carrier of
(TOP-REAL b2 : ( ( ) ( natural V28() real ext-real V123() V124() V171() V172() V173() V174() V175() V176() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like total V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
(TOP-REAL b2 : ( ( ) ( natural V28() real ext-real V123() V124() V171() V172() V173() V174() V175() V176() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty )
set ) , ( ( ) (
functional non
empty )
set ) ) st
( ( for
r being ( ( ) ( )
Point of ( ( ) ( non
empty )
set ) ) holds
g : ( (
Function-like V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
(TOP-REAL b2 : ( ( ) ( natural V28() real ext-real V123() V124() V171() V172() V173() V174() V175() V176() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set )
-defined the
carrier of
(TOP-REAL b2 : ( ( ) ( natural V28() real ext-real V123() V124() V171() V172() V173() V174() V175() V176() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like total V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
(TOP-REAL b2 : ( ( ) ( natural V28() real ext-real V123() V124() V171() V172() V173() V174() V175() V176() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty )
set ) , ( ( ) (
functional non
empty )
set ) )
. r : ( ( ) ( )
Point of ( ( ) ( non
empty )
set ) ) : ( ( ) (
Relation-like Function-like )
set )
= ((f1 : ( ( Function-like V18( the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) , the carrier of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V122() ) TopStruct ) : ( ( ) ( non empty V171() V172() V173() ) set ) ) ) ( Relation-like the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) -defined the carrier of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V122() ) TopStruct ) : ( ( ) ( non empty V171() V172() V173() ) set ) -valued Function-like total V18( the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) , the carrier of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V122() ) TopStruct ) : ( ( ) ( non empty V171() V172() V173() ) set ) ) V161() V162() V163() ) Function of ( ( ) ( non empty ) set ) , ( ( ) ( non empty V171() V172() V173() ) set ) ) . r : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V28() real ext-real ) set ) * p1 : ( ( ) ( Relation-like Function-like V43(b2 : ( ( ) ( natural V28() real ext-real V123() V124() V171() V172() V173() V174() V175() V176() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) (
Relation-like Function-like V43(
b2 : ( ( ) (
natural V28()
real ext-real V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL b2 : ( ( ) ( natural V28() real ext-real V123() V124() V171() V172() V173() V174() V175() V176() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) )
+ ((f2 : ( ( Function-like V18( the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) , the carrier of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V122() ) TopStruct ) : ( ( ) ( non empty V171() V172() V173() ) set ) ) ) ( Relation-like the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) -defined the carrier of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V122() ) TopStruct ) : ( ( ) ( non empty V171() V172() V173() ) set ) -valued Function-like total V18( the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) , the carrier of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V122() ) TopStruct ) : ( ( ) ( non empty V171() V172() V173() ) set ) ) V161() V162() V163() ) Function of ( ( ) ( non empty ) set ) , ( ( ) ( non empty V171() V172() V173() ) set ) ) . r : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V28() real ext-real ) set ) * p2 : ( ( ) ( Relation-like Function-like V43(b2 : ( ( ) ( natural V28() real ext-real V123() V124() V171() V172() V173() V174() V175() V176() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) (
Relation-like Function-like V43(
b2 : ( ( ) (
natural V28()
real ext-real V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL b2 : ( ( ) ( natural V28() real ext-real V123() V124() V171() V172() V173() V174() V175() V176() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
Relation-like Function-like V43(
b2 : ( ( ) (
natural V28()
real ext-real V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL b2 : ( ( ) ( natural V28() real ext-real V123() V124() V171() V172() V173() V174() V175() V176() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) &
g : ( (
Function-like V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
(TOP-REAL b2 : ( ( ) ( natural V28() real ext-real V123() V124() V171() V172() V173() V174() V175() V176() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set )
-defined the
carrier of
(TOP-REAL b2 : ( ( ) ( natural V28() real ext-real V123() V124() V171() V172() V173() V174() V175() V176() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like total V18( the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) , the
carrier of
(TOP-REAL b2 : ( ( ) ( natural V28() real ext-real V123() V124() V171() V172() V173() V174() V175() V176() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty )
set ) , ( ( ) (
functional non
empty )
set ) ) is
continuous ) ;
begin
theorem
for
f,
g being ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) )
for
C0,
KXP,
KXN,
KYP,
KYN being ( ( ) (
functional )
Subset of )
for
O,
I being ( ( ) (
V28()
real ext-real )
Point of ( ( ) ( non
empty V171()
V172()
V173() )
set ) ) st
O : ( ( ) (
V28()
real ext-real )
Point of ( ( ) ( non
empty V171()
V172()
V173() )
set ) )
= 0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) &
I : ( ( ) (
V28()
real ext-real )
Point of ( ( ) ( non
empty V171()
V172()
V173() )
set ) )
= 1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) &
f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) is
continuous &
f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) is
one-to-one &
g : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) is
continuous &
g : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) is
one-to-one &
C0 : ( ( ) (
functional )
Subset of )
= { p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) where p is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) : |.p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) .| : ( ( ) ( V28() real ext-real non negative ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) <= 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) } &
KXP : ( ( ) (
functional )
Subset of )
= { q1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) where q1 is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) : ( |.q1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) .| : ( ( ) ( V28() real ext-real non negative ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) = 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) & q1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `2 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) <= q1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `1 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) & q1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `2 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) >= - (q1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `1) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ) } &
KXN : ( ( ) (
functional )
Subset of )
= { q2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) where q2 is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) : ( |.q2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) .| : ( ( ) ( V28() real ext-real non negative ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) = 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) & q2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `2 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) >= q2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `1 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) & q2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `2 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) <= - (q2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `1) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ) } &
KYP : ( ( ) (
functional )
Subset of )
= { q3 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) where q3 is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) : ( |.q3 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) .| : ( ( ) ( V28() real ext-real non negative ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) = 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) & q3 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `2 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) >= q3 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `1 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) & q3 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `2 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) >= - (q3 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `1) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ) } &
KYN : ( ( ) (
functional )
Subset of )
= { q4 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) where q4 is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) : ( |.q4 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) .| : ( ( ) ( V28() real ext-real non negative ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) = 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) & q4 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `2 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) <= q4 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `1 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) & q4 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `2 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) <= - (q4 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `1) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ) } &
f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) )
. O : ( ( ) (
V28()
real ext-real )
Point of ( ( ) ( non
empty V171()
V172()
V173() )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) )
in KXP : ( ( ) (
functional )
Subset of ) &
f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) )
. I : ( ( ) (
V28()
real ext-real )
Point of ( ( ) ( non
empty V171()
V172()
V173() )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) )
in KXN : ( ( ) (
functional )
Subset of ) &
g : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) )
. O : ( ( ) (
V28()
real ext-real )
Point of ( ( ) ( non
empty V171()
V172()
V173() )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) )
in KYP : ( ( ) (
functional )
Subset of ) &
g : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) )
. I : ( ( ) (
V28()
real ext-real )
Point of ( ( ) ( non
empty V171()
V172()
V173() )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) )
in KYN : ( ( ) (
functional )
Subset of ) &
rng f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
functional )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
c= C0 : ( ( ) (
functional )
Subset of ) &
rng g : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
functional )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
c= C0 : ( ( ) (
functional )
Subset of ) holds
rng f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
functional )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
meets rng g : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
functional )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) ;
theorem
for
f,
g being ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) )
for
C0,
KXP,
KXN,
KYP,
KYN being ( ( ) (
functional )
Subset of )
for
O,
I being ( ( ) (
V28()
real ext-real )
Point of ( ( ) ( non
empty V171()
V172()
V173() )
set ) ) st
O : ( ( ) (
V28()
real ext-real )
Point of ( ( ) ( non
empty V171()
V172()
V173() )
set ) )
= 0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) &
I : ( ( ) (
V28()
real ext-real )
Point of ( ( ) ( non
empty V171()
V172()
V173() )
set ) )
= 1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) &
f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) is
continuous &
f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) is
one-to-one &
g : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) is
continuous &
g : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) is
one-to-one &
C0 : ( ( ) (
functional )
Subset of )
= { p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) where p is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) : |.p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) .| : ( ( ) ( V28() real ext-real non negative ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) <= 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) } &
KXP : ( ( ) (
functional )
Subset of )
= { q1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) where q1 is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) : ( |.q1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) .| : ( ( ) ( V28() real ext-real non negative ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) = 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) & q1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `2 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) <= q1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `1 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) & q1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `2 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) >= - (q1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `1) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ) } &
KXN : ( ( ) (
functional )
Subset of )
= { q2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) where q2 is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) : ( |.q2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) .| : ( ( ) ( V28() real ext-real non negative ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) = 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) & q2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `2 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) >= q2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `1 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) & q2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `2 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) <= - (q2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `1) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ) } &
KYP : ( ( ) (
functional )
Subset of )
= { q3 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) where q3 is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) : ( |.q3 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) .| : ( ( ) ( V28() real ext-real non negative ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) = 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) & q3 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `2 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) >= q3 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `1 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) & q3 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `2 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) >= - (q3 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `1) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ) } &
KYN : ( ( ) (
functional )
Subset of )
= { q4 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) where q4 is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) : ( |.q4 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) .| : ( ( ) ( V28() real ext-real non negative ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) = 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) & q4 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `2 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) <= q4 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `1 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) & q4 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `2 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) <= - (q4 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `1) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ) } &
f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) )
. O : ( ( ) (
V28()
real ext-real )
Point of ( ( ) ( non
empty V171()
V172()
V173() )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) )
in KXP : ( ( ) (
functional )
Subset of ) &
f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) )
. I : ( ( ) (
V28()
real ext-real )
Point of ( ( ) ( non
empty V171()
V172()
V173() )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) )
in KXN : ( ( ) (
functional )
Subset of ) &
g : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) )
. O : ( ( ) (
V28()
real ext-real )
Point of ( ( ) ( non
empty V171()
V172()
V173() )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) )
in KYN : ( ( ) (
functional )
Subset of ) &
g : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) )
. I : ( ( ) (
V28()
real ext-real )
Point of ( ( ) ( non
empty V171()
V172()
V173() )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) )
in KYP : ( ( ) (
functional )
Subset of ) &
rng f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
functional )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
c= C0 : ( ( ) (
functional )
Subset of ) &
rng g : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
functional )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
c= C0 : ( ( ) (
functional )
Subset of ) holds
rng f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
functional )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
meets rng g : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
functional )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) ;
theorem
for
p1,
p2,
p3,
p4 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
for
P being ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of )
for
C0 being ( ( ) (
functional )
Subset of ) st
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of )
= { p : ( ( Function-like V18( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V122() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V122() ) TopStruct ) ) : ( ( ) ( non empty V171() V172() V173() ) set ) , the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) ( Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V122() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V122() ) TopStruct ) ) : ( ( ) ( non empty V171() V172() V173() ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non empty total V18( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V122() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V122() ) TopStruct ) ) : ( ( ) ( non empty V171() V172() V173() ) set ) , the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) Function of ( ( ) ( non empty V171() V172() V173() ) set ) , ( ( ) ( functional non empty ) set ) ) where p is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) : |.p : ( ( Function-like V18( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V122() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V122() ) TopStruct ) ) : ( ( ) ( non empty V171() V172() V173() ) set ) , the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) ( Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V122() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V122() ) TopStruct ) ) : ( ( ) ( non empty V171() V172() V173() ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non empty total V18( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V122() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V122() ) TopStruct ) ) : ( ( ) ( non empty V171() V172() V173() ) set ) , the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) Function of ( ( ) ( non empty V171() V172() V173() ) set ) , ( ( ) ( functional non empty ) set ) ) .| : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) = 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) } &
LE p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) &
LE p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) &
LE p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) holds
for
f,
g being ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) st
f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) is
continuous &
f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) is
one-to-one &
g : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) is
continuous &
g : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) is
one-to-one &
C0 : ( ( ) (
functional )
Subset of )
= { p8 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) where p8 is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) : |.p8 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) .| : ( ( ) ( V28() real ext-real non negative ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) <= 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) } &
f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) )
. 0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set )
= p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) &
f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) )
. 1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set )
= p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) &
g : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) )
. 0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set )
= p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) &
g : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) )
. 1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set )
= p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) &
rng f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
functional )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
c= C0 : ( ( ) (
functional )
Subset of ) &
rng g : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
functional )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
c= C0 : ( ( ) (
functional )
Subset of ) holds
rng f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
functional )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
meets rng g : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
functional )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) ;
theorem
for
p1,
p2,
p3,
p4 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
for
P being ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of )
for
C0 being ( ( ) (
functional )
Subset of ) st
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of )
= { p : ( ( Function-like V18( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V122() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V122() ) TopStruct ) ) : ( ( ) ( non empty V171() V172() V173() ) set ) , the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) ( Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V122() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V122() ) TopStruct ) ) : ( ( ) ( non empty V171() V172() V173() ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non empty total V18( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V122() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V122() ) TopStruct ) ) : ( ( ) ( non empty V171() V172() V173() ) set ) , the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) Function of ( ( ) ( non empty V171() V172() V173() ) set ) , ( ( ) ( functional non empty ) set ) ) where p is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) : |.p : ( ( Function-like V18( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V122() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V122() ) TopStruct ) ) : ( ( ) ( non empty V171() V172() V173() ) set ) , the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) ( Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V122() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V122() ) TopStruct ) ) : ( ( ) ( non empty V171() V172() V173() ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non empty total V18( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V122() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V122() ) TopStruct ) ) : ( ( ) ( non empty V171() V172() V173() ) set ) , the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) Function of ( ( ) ( non empty V171() V172() V173() ) set ) , ( ( ) ( functional non empty ) set ) ) .| : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) = 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) } &
LE p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) &
LE p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) &
LE p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) holds
for
f,
g being ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) st
f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) is
continuous &
f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) is
one-to-one &
g : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) is
continuous &
g : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) is
one-to-one &
C0 : ( ( ) (
functional )
Subset of )
= { p8 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) where p8 is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) : |.p8 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) .| : ( ( ) ( V28() real ext-real non negative ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) <= 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) } &
f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) )
. 0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set )
= p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) &
f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) )
. 1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set )
= p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) &
g : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) )
. 0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set )
= p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) &
g : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) )
. 1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set )
= p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) &
rng f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
functional )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
c= C0 : ( ( ) (
functional )
Subset of ) &
rng g : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
functional )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
c= C0 : ( ( ) (
functional )
Subset of ) holds
rng f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
functional )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
meets rng g : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
functional )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) ;
theorem
for
p1,
p2,
p3,
p4 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
for
P being ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of )
for
C0 being ( ( ) (
functional )
Subset of ) st
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of )
= { p : ( ( Function-like V18( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V122() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V122() ) TopStruct ) ) : ( ( ) ( non empty V171() V172() V173() ) set ) , the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) ( Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V122() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V122() ) TopStruct ) ) : ( ( ) ( non empty V171() V172() V173() ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non empty total V18( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V122() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V122() ) TopStruct ) ) : ( ( ) ( non empty V171() V172() V173() ) set ) , the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) Function of ( ( ) ( non empty V171() V172() V173() ) set ) , ( ( ) ( functional non empty ) set ) ) where p is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) : |.p : ( ( Function-like V18( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V122() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V122() ) TopStruct ) ) : ( ( ) ( non empty V171() V172() V173() ) set ) , the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) ( Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V122() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V122() ) TopStruct ) ) : ( ( ) ( non empty V171() V172() V173() ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non empty total V18( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V122() ) SubSpace of R^1 : ( ( TopSpace-like ) ( non empty strict TopSpace-like V122() ) TopStruct ) ) : ( ( ) ( non empty V171() V172() V173() ) set ) , the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) Function of ( ( ) ( non empty V171() V172() V173() ) set ) , ( ( ) ( functional non empty ) set ) ) .| : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) = 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) } &
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
are_in_this_order_on P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) holds
for
f,
g being ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) st
f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) is
continuous &
f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) is
one-to-one &
g : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) is
continuous &
g : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) is
one-to-one &
C0 : ( ( ) (
functional )
Subset of )
= { p8 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) where p8 is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) : |.p8 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) .| : ( ( ) ( V28() real ext-real non negative ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) <= 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) } &
f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) )
. 0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set )
= p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) &
f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) )
. 1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set )
= p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) &
g : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) )
. 0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set )
= p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) &
g : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) )
. 1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set )
= p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) &
rng f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
functional )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
c= C0 : ( ( ) (
functional )
Subset of ) &
rng g : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
functional )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
c= C0 : ( ( ) (
functional )
Subset of ) holds
rng f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
functional )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
meets rng g : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
functional )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) ;
begin
definition
let a,
b,
c,
d be ( (
real ) (
V28()
real ext-real )
number ) ;
func inside_of_rectangle (
a,
b,
c,
d)
-> ( ( ) (
functional )
Subset of )
equals
{ p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) where p is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) : ( a : ( ( ) ( ) RLTopStruct ) < p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `1 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) & p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `1 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) < b : ( ( ) ( ) Element of a : ( ( ) ( ) RLTopStruct ) ) & c : ( ( Function-like V18(K20(a : ( ( ) ( ) RLTopStruct ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) ) ( Relation-like K20(a : ( ( ) ( ) RLTopStruct ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) -defined a : ( ( ) ( ) RLTopStruct ) -valued Function-like V18(K20(a : ( ( ) ( ) RLTopStruct ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) ) Element of K19(K20(K20(a : ( ( ) ( ) RLTopStruct ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) < p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `2 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) & p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `2 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) < d : ( ( Function-like V18(K20(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) ) ( Relation-like K20(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) -defined a : ( ( ) ( ) RLTopStruct ) -valued Function-like V18(K20(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) ) Element of K19(K20(K20(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) } ;
end;
definition
let a,
b,
c,
d be ( (
real ) (
V28()
real ext-real )
number ) ;
func closed_inside_of_rectangle (
a,
b,
c,
d)
-> ( ( ) (
functional )
Subset of )
equals
{ p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) where p is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) : ( a : ( ( ) ( ) RLTopStruct ) <= p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `1 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) & p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `1 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) <= b : ( ( ) ( ) Element of a : ( ( ) ( ) RLTopStruct ) ) & c : ( ( Function-like V18(K20(a : ( ( ) ( ) RLTopStruct ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) ) ( Relation-like K20(a : ( ( ) ( ) RLTopStruct ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) -defined a : ( ( ) ( ) RLTopStruct ) -valued Function-like V18(K20(a : ( ( ) ( ) RLTopStruct ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) ) Element of K19(K20(K20(a : ( ( ) ( ) RLTopStruct ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) <= p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `2 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) & p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `2 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) <= d : ( ( Function-like V18(K20(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) ) ( Relation-like K20(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) -defined a : ( ( ) ( ) RLTopStruct ) -valued Function-like V18(K20(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) ) Element of K19(K20(K20(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) } ;
end;
definition
let a,
b,
c,
d be ( (
real ) (
V28()
real ext-real )
number ) ;
func outside_of_rectangle (
a,
b,
c,
d)
-> ( ( ) (
functional )
Subset of )
equals
{ p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) where p is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) : ( not a : ( ( ) ( ) RLTopStruct ) <= p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `1 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) or not p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `1 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) <= b : ( ( ) ( ) Element of a : ( ( ) ( ) RLTopStruct ) ) or not c : ( ( Function-like V18(K20(a : ( ( ) ( ) RLTopStruct ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) ) ( Relation-like K20(a : ( ( ) ( ) RLTopStruct ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) -defined a : ( ( ) ( ) RLTopStruct ) -valued Function-like V18(K20(a : ( ( ) ( ) RLTopStruct ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) ) Element of K19(K20(K20(a : ( ( ) ( ) RLTopStruct ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) <= p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `2 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) or not p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `2 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) <= d : ( ( Function-like V18(K20(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) ) ( Relation-like K20(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) -defined a : ( ( ) ( ) RLTopStruct ) -valued Function-like V18(K20(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) ) Element of K19(K20(K20(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) } ;
end;
definition
let a,
b,
c,
d be ( (
real ) (
V28()
real ext-real )
number ) ;
func closed_outside_of_rectangle (
a,
b,
c,
d)
-> ( ( ) (
functional )
Subset of )
equals
{ p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) where p is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) : ( not a : ( ( ) ( ) RLTopStruct ) < p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `1 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) or not p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `1 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) < b : ( ( ) ( ) Element of a : ( ( ) ( ) RLTopStruct ) ) or not c : ( ( Function-like V18(K20(a : ( ( ) ( ) RLTopStruct ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) ) ( Relation-like K20(a : ( ( ) ( ) RLTopStruct ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) -defined a : ( ( ) ( ) RLTopStruct ) -valued Function-like V18(K20(a : ( ( ) ( ) RLTopStruct ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) ) Element of K19(K20(K20(a : ( ( ) ( ) RLTopStruct ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) < p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `2 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) or not p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `2 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) < d : ( ( Function-like V18(K20(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) ) ( Relation-like K20(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) -defined a : ( ( ) ( ) RLTopStruct ) -valued Function-like V18(K20(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) ) Element of K19(K20(K20(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) } ;
end;
theorem
for
a,
b,
r being ( (
real ) (
V28()
real ext-real )
number )
for
Kb,
Cb being ( ( ) (
functional )
Subset of ) st
r : ( (
real ) (
V28()
real ext-real )
number )
>= 0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) &
Kb : ( ( ) (
functional )
Subset of )
= { q : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) where q is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) : |.q : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) .| : ( ( ) ( V28() real ext-real non negative ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) = 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) } &
Cb : ( ( ) (
functional )
Subset of )
= { p2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) where p2 is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) : |.(p2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) - |[a : ( ( real ) ( V28() real ext-real ) number ) ,b : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) .| : ( ( ) ( V28() real ext-real non negative ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) = r : ( ( real ) ( V28() real ext-real ) number ) } holds
(AffineMap (r : ( ( real ) ( V28() real ext-real ) number ) ,a : ( ( real ) ( V28() real ext-real ) number ) ,r : ( ( real ) ( V28() real ext-real ) number ) ,b : ( ( real ) ( V28() real ext-real ) number ) )) : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) )
continuous )
Element of
K19(
K20( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) )
.: Kb : ( ( ) (
functional )
Subset of ) : ( ( ) (
functional )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
= Cb : ( ( ) (
functional )
Subset of ) ;
definition
let a,
b,
r be ( (
real ) (
V28()
real ext-real )
number ) ;
func circle (
a,
b,
r)
-> ( ( ) (
functional )
Subset of )
equals
{ p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) where p is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) : |.(p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) - |[a : ( ( ) ( ) RLTopStruct ) ,b : ( ( ) ( ) Element of a : ( ( ) ( ) RLTopStruct ) ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) .| : ( ( ) ( V28() real ext-real non negative ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) = r : ( ( Function-like V18(K20(a : ( ( ) ( ) RLTopStruct ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) ) ( Relation-like K20(a : ( ( ) ( ) RLTopStruct ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) -defined a : ( ( ) ( ) RLTopStruct ) -valued Function-like V18(K20(a : ( ( ) ( ) RLTopStruct ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) ) Element of K19(K20(K20(a : ( ( ) ( ) RLTopStruct ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) ,a : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) } ;
end;
theorem
for
r being ( (
real ) (
V28()
real ext-real )
number ) holds
(
inside_of_circle (
0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,
0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,
r : ( (
real ) (
V28()
real ext-real )
number ) ) : ( ( ) (
functional )
Subset of )
= { p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) where p is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) : |.p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) .| : ( ( ) ( V28() real ext-real non negative ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) < r : ( ( real ) ( V28() real ext-real ) number ) } & (
r : ( (
real ) (
V28()
real ext-real )
number )
> 0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) implies
circle (
0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,
0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,
r : ( (
real ) (
V28()
real ext-real )
number ) ) : ( ( ) (
functional closed compact )
Subset of )
= { p2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) where p2 is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) : |.p2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) .| : ( ( ) ( V28() real ext-real non negative ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) = r : ( ( real ) ( V28() real ext-real ) number ) } ) &
outside_of_circle (
0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,
0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,
r : ( (
real ) (
V28()
real ext-real )
number ) ) : ( ( ) (
functional )
Subset of )
= { p3 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) where p3 is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) : |.p3 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) .| : ( ( ) ( V28() real ext-real non negative ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) > r : ( ( real ) ( V28() real ext-real ) number ) } &
closed_inside_of_circle (
0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,
0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,
r : ( (
real ) (
V28()
real ext-real )
number ) ) : ( ( ) (
functional )
Subset of )
= { q : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) where q is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) : |.q : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) .| : ( ( ) ( V28() real ext-real non negative ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) <= r : ( ( real ) ( V28() real ext-real ) number ) } &
closed_outside_of_circle (
0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,
0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,
r : ( (
real ) (
V28()
real ext-real )
number ) ) : ( ( ) (
functional )
Subset of )
= { q2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) where q2 is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) : |.q2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) .| : ( ( ) ( V28() real ext-real non negative ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) >= r : ( ( real ) ( V28() real ext-real ) number ) } ) ;
theorem
for
P0,
P1,
P01,
P11,
K0,
K1,
K01,
K11 being ( ( ) (
functional )
Subset of )
for
P being ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of )
for
f being ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) ) st
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of )
= circle (
0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,
0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
functional non
empty closed compact )
Subset of ) &
P0 : ( ( ) (
functional )
Subset of )
= inside_of_circle (
0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,
0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
functional )
Subset of ) &
P1 : ( ( ) (
functional )
Subset of )
= outside_of_circle (
0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,
0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
functional )
Subset of ) &
P01 : ( ( ) (
functional )
Subset of )
= closed_inside_of_circle (
0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,
0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
functional )
Subset of ) &
P11 : ( ( ) (
functional )
Subset of )
= closed_outside_of_circle (
0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,
0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
functional )
Subset of ) &
K0 : ( ( ) (
functional )
Subset of )
= inside_of_rectangle (
(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real non
positive )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,
(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real non
positive )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
functional )
Subset of ) &
K1 : ( ( ) (
functional )
Subset of )
= outside_of_rectangle (
(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real non
positive )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,
(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real non
positive )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
functional )
Subset of ) &
K01 : ( ( ) (
functional )
Subset of )
= closed_inside_of_rectangle (
(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real non
positive )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,
(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real non
positive )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
functional )
Subset of ) &
K11 : ( ( ) (
functional )
Subset of )
= closed_outside_of_rectangle (
(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real non
positive )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,
(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real non
positive )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
functional )
Subset of ) &
f : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) )
= Sq_Circ : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like one-to-one non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Element of
K19(
K20( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) holds
(
f : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) )
.: (rectangle ((- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real non positive ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ,1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ,(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real non positive ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ,1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) (
functional )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
= P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) &
(f : ( ( Function-like V18( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) , the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) ( Relation-like the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non empty total V18( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) , the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) Function of ( ( ) ( functional non empty ) set ) , ( ( ) ( functional non empty ) set ) ) ") : ( (
Relation-like Function-like ) (
Relation-like Function-like )
set )
.: P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) : ( ( ) ( )
set )
= rectangle (
(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real non
positive )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,
(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real non
positive )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) &
f : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) )
.: K0 : ( ( ) (
functional )
Subset of ) : ( ( ) (
functional )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
= P0 : ( ( ) (
functional )
Subset of ) &
(f : ( ( Function-like V18( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) , the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) ( Relation-like the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non empty total V18( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) , the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) Function of ( ( ) ( functional non empty ) set ) , ( ( ) ( functional non empty ) set ) ) ") : ( (
Relation-like Function-like ) (
Relation-like Function-like )
set )
.: P0 : ( ( ) (
functional )
Subset of ) : ( ( ) ( )
set )
= K0 : ( ( ) (
functional )
Subset of ) &
f : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) )
.: K1 : ( ( ) (
functional )
Subset of ) : ( ( ) (
functional )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
= P1 : ( ( ) (
functional )
Subset of ) &
(f : ( ( Function-like V18( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) , the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) ( Relation-like the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non empty total V18( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) , the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) Function of ( ( ) ( functional non empty ) set ) , ( ( ) ( functional non empty ) set ) ) ") : ( (
Relation-like Function-like ) (
Relation-like Function-like )
set )
.: P1 : ( ( ) (
functional )
Subset of ) : ( ( ) ( )
set )
= K1 : ( ( ) (
functional )
Subset of ) &
f : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) )
.: K01 : ( ( ) (
functional )
Subset of ) : ( ( ) (
functional )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
= P01 : ( ( ) (
functional )
Subset of ) &
f : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) )
.: K11 : ( ( ) (
functional )
Subset of ) : ( ( ) (
functional )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
= P11 : ( ( ) (
functional )
Subset of ) &
(f : ( ( Function-like V18( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) , the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) ( Relation-like the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non empty total V18( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) , the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) Function of ( ( ) ( functional non empty ) set ) , ( ( ) ( functional non empty ) set ) ) ") : ( (
Relation-like Function-like ) (
Relation-like Function-like )
set )
.: P01 : ( ( ) (
functional )
Subset of ) : ( ( ) ( )
set )
= K01 : ( ( ) (
functional )
Subset of ) &
(f : ( ( Function-like V18( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) , the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) ( Relation-like the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non empty total V18( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) , the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) Function of ( ( ) ( functional non empty ) set ) , ( ( ) ( functional non empty ) set ) ) ") : ( (
Relation-like Function-like ) (
Relation-like Function-like )
set )
.: P11 : ( ( ) (
functional )
Subset of ) : ( ( ) ( )
set )
= K11 : ( ( ) (
functional )
Subset of ) ) ;
begin
theorem
for
a,
b,
c,
d being ( (
real ) (
V28()
real ext-real )
number ) st
a : ( (
real ) (
V28()
real ext-real )
number )
<= b : ( (
real ) (
V28()
real ext-real )
number ) &
c : ( (
real ) (
V28()
real ext-real )
number )
<= d : ( (
real ) (
V28()
real ext-real )
number ) holds
(
LSeg (
|[a : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[a : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
= { p1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) where p1 is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) : ( p1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `1 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) = a : ( ( real ) ( V28() real ext-real ) number ) & p1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `2 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) <= d : ( ( real ) ( V28() real ext-real ) number ) & p1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `2 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) >= c : ( ( real ) ( V28() real ext-real ) number ) ) } &
LSeg (
|[a : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[b : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
= { p2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) where p2 is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) : ( p2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `1 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) <= b : ( ( real ) ( V28() real ext-real ) number ) & p2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `1 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) >= a : ( ( real ) ( V28() real ext-real ) number ) & p2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `2 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) = d : ( ( real ) ( V28() real ext-real ) number ) ) } &
LSeg (
|[a : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
= { q1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) where q1 is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) : ( q1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `1 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) <= b : ( ( real ) ( V28() real ext-real ) number ) & q1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `1 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) >= a : ( ( real ) ( V28() real ext-real ) number ) & q1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `2 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) = c : ( ( real ) ( V28() real ext-real ) number ) ) } &
LSeg (
|[b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[b : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
= { q2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) where q2 is ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) : ( q2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `1 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) = b : ( ( real ) ( V28() real ext-real ) number ) & q2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `2 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) <= d : ( ( real ) ( V28() real ext-real ) number ) & q2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `2 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) >= c : ( ( real ) ( V28() real ext-real ) number ) ) } ) ;
theorem
for
a,
b,
c,
d being ( (
real ) (
V28()
real ext-real )
number ) st
a : ( (
real ) (
V28()
real ext-real )
number )
<= b : ( (
real ) (
V28()
real ext-real )
number ) &
c : ( (
real ) (
V28()
real ext-real )
number )
<= d : ( (
real ) (
V28()
real ext-real )
number ) holds
(LSeg (|[a : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ,|[a : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) )) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
/\ (LSeg (|[a : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ,|[b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) )) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) (
functional closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
= {|[a : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) } : ( ( ) (
functional non
empty )
set ) ;
theorem
for
a,
b,
c,
d being ( (
real ) (
V28()
real ext-real )
number ) st
a : ( (
real ) (
V28()
real ext-real )
number )
<= b : ( (
real ) (
V28()
real ext-real )
number ) &
c : ( (
real ) (
V28()
real ext-real )
number )
<= d : ( (
real ) (
V28()
real ext-real )
number ) holds
(LSeg (|[a : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ,|[b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) )) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
/\ (LSeg (|[b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ,|[b : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) )) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) (
functional closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
= {|[b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) } : ( ( ) (
functional non
empty )
set ) ;
theorem
for
a,
b,
c,
d being ( (
real ) (
V28()
real ext-real )
number ) st
a : ( (
real ) (
V28()
real ext-real )
number )
<= b : ( (
real ) (
V28()
real ext-real )
number ) &
c : ( (
real ) (
V28()
real ext-real )
number )
<= d : ( (
real ) (
V28()
real ext-real )
number ) holds
(LSeg (|[a : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ,|[b : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) )) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
/\ (LSeg (|[b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ,|[b : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) )) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) (
functional closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
= {|[b : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) } : ( ( ) (
functional non
empty )
set ) ;
theorem
for
a,
b,
c,
d being ( (
real ) (
V28()
real ext-real )
number ) st
a : ( (
real ) (
V28()
real ext-real )
number )
<= b : ( (
real ) (
V28()
real ext-real )
number ) &
c : ( (
real ) (
V28()
real ext-real )
number )
<= d : ( (
real ) (
V28()
real ext-real )
number ) holds
(LSeg (|[a : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ,|[a : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) )) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
/\ (LSeg (|[a : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ,|[b : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) )) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) (
functional closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
= {|[a : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) } : ( ( ) (
functional non
empty )
set ) ;
theorem
for
a,
b,
c,
d being ( (
real ) (
V28()
real ext-real )
number ) st
a : ( (
real ) (
V28()
real ext-real )
number )
<= b : ( (
real ) (
V28()
real ext-real )
number ) &
c : ( (
real ) (
V28()
real ext-real )
number )
<= d : ( (
real ) (
V28()
real ext-real )
number ) holds
(
W-min (rectangle (a : ( ( real ) ( V28() real ext-real ) number ) ,b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) )
= |[a : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) &
E-max (rectangle (a : ( ( real ) ( V28() real ext-real ) number ) ,b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) )
= |[b : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) ;
theorem
for
a,
b,
c,
d being ( (
real ) (
V28()
real ext-real )
number ) st
a : ( (
real ) (
V28()
real ext-real )
number )
< b : ( (
real ) (
V28()
real ext-real )
number ) &
c : ( (
real ) (
V28()
real ext-real )
number )
< d : ( (
real ) (
V28()
real ext-real )
number ) holds
(
(LSeg (|[a : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ,|[a : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) )) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
\/ (LSeg (|[a : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ,|[b : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) )) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) (
functional non
empty closed )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
is_an_arc_of W-min (rectangle (a : ( ( real ) ( V28() real ext-real ) number ) ,b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
E-max (rectangle (a : ( ( real ) ( V28() real ext-real ) number ) ,b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) &
(LSeg (|[a : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ,|[b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) )) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
\/ (LSeg (|[b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ,|[b : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) )) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) (
functional non
empty closed )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
is_an_arc_of E-max (rectangle (a : ( ( real ) ( V28() real ext-real ) number ) ,b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
W-min (rectangle (a : ( ( real ) ( V28() real ext-real ) number ) ,b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) ;
theorem
for
a,
b,
c,
d being ( (
real ) (
V28()
real ext-real )
number )
for
f1,
f2 being ( ( ) (
Relation-like NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) (
functional non
empty )
set ) )
for
p0,
p1,
p01,
p10 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) st
a : ( (
real ) (
V28()
real ext-real )
number )
< b : ( (
real ) (
V28()
real ext-real )
number ) &
c : ( (
real ) (
V28()
real ext-real )
number )
< d : ( (
real ) (
V28()
real ext-real )
number ) &
p0 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
= |[a : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) &
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
= |[b : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) &
p01 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
= |[a : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) &
p10 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
= |[b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) &
f1 : ( ( ) (
Relation-like NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) (
functional non
empty )
set ) )
= <*p0 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) ,p01 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) ,p1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) *> : ( ( ) (
Relation-like NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like FinSequence-like )
FinSequence of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) &
f2 : ( ( ) (
Relation-like NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) (
functional non
empty )
set ) )
= <*p0 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) ,p10 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) ,p1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) *> : ( ( ) (
Relation-like NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like FinSequence-like )
FinSequence of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) holds
(
f1 : ( ( ) (
Relation-like NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) (
functional non
empty )
set ) ) is
being_S-Seq &
L~ f1 : ( ( ) (
Relation-like NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
functional )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
= (LSeg (p0 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) ,p01 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) )) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
\/ (LSeg (p01 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) ,p1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) )) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) (
functional non
empty closed )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) &
f2 : ( ( ) (
Relation-like NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) (
functional non
empty )
set ) ) is
being_S-Seq &
L~ f2 : ( ( ) (
Relation-like NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
functional )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
= (LSeg (p0 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) ,p10 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) )) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
\/ (LSeg (p10 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) ,p1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) )) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) (
functional non
empty closed )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) &
rectangle (
a : ( (
real ) (
V28()
real ext-real )
number ) ,
b : ( (
real ) (
V28()
real ext-real )
number ) ,
c : ( (
real ) (
V28()
real ext-real )
number ) ,
d : ( (
real ) (
V28()
real ext-real )
number ) ) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
= (L~ f1 : ( ( ) ( Relation-like NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) (
functional )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
\/ (L~ f2 : ( ( ) ( Relation-like NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) (
functional )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) (
functional )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) &
(L~ f1 : ( ( ) ( Relation-like NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) (
functional )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
/\ (L~ f2 : ( ( ) ( Relation-like NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) (
functional )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) (
functional )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
= {p0 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) ,p1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) } : ( ( ) (
functional non
empty )
set ) &
f1 : ( ( ) (
Relation-like NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) (
functional non
empty )
set ) )
/. 1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) )
= p0 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) &
f1 : ( ( ) (
Relation-like NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) (
functional non
empty )
set ) )
/. (len f1 : ( ( ) ( Relation-like NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) (
natural V28()
real ext-real V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) )
= p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) &
f2 : ( ( ) (
Relation-like NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) (
functional non
empty )
set ) )
/. 1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) )
= p0 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) &
f2 : ( ( ) (
Relation-like NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) (
functional non
empty )
set ) )
/. (len f2 : ( ( ) ( Relation-like NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) (
natural V28()
real ext-real V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) )
= p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ) ;
theorem
for
P1,
P2 being ( ( ) (
functional )
Subset of )
for
a,
b,
c,
d being ( (
real ) (
V28()
real ext-real )
number )
for
f1,
f2 being ( ( ) (
Relation-like NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) (
functional non
empty )
set ) )
for
p1,
p2 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) st
a : ( (
real ) (
V28()
real ext-real )
number )
< b : ( (
real ) (
V28()
real ext-real )
number ) &
c : ( (
real ) (
V28()
real ext-real )
number )
< d : ( (
real ) (
V28()
real ext-real )
number ) &
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
= |[a : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) &
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
= |[b : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) &
f1 : ( ( ) (
Relation-like NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) (
functional non
empty )
set ) )
= <*|[a : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ,|[a : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ,|[b : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) *> : ( ( ) (
Relation-like NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like FinSequence-like )
FinSequence of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) &
f2 : ( ( ) (
Relation-like NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) (
functional non
empty )
set ) )
= <*|[a : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ,|[b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ,|[b : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) *> : ( ( ) (
Relation-like NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like FinSequence-like )
FinSequence of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) &
P1 : ( ( ) (
functional )
Subset of )
= L~ f1 : ( ( ) (
Relation-like NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
functional )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) &
P2 : ( ( ) (
functional )
Subset of )
= L~ f2 : ( ( ) (
Relation-like NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
functional )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) holds
(
P1 : ( ( ) (
functional )
Subset of )
is_an_arc_of p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) &
P2 : ( ( ) (
functional )
Subset of )
is_an_arc_of p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) & not
P1 : ( ( ) (
functional )
Subset of ) is
empty & not
P2 : ( ( ) (
functional )
Subset of ) is
empty &
rectangle (
a : ( (
real ) (
V28()
real ext-real )
number ) ,
b : ( (
real ) (
V28()
real ext-real )
number ) ,
c : ( (
real ) (
V28()
real ext-real )
number ) ,
d : ( (
real ) (
V28()
real ext-real )
number ) ) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
= P1 : ( ( ) (
functional )
Subset of )
\/ P2 : ( ( ) (
functional )
Subset of ) : ( ( ) (
functional )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) &
P1 : ( ( ) (
functional )
Subset of )
/\ P2 : ( ( ) (
functional )
Subset of ) : ( ( ) (
functional )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
= {p1 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) ,p2 : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) } : ( ( ) (
functional non
empty )
set ) ) ;
theorem
for
a,
b,
c,
d being ( (
real ) (
V28()
real ext-real )
number ) st
a : ( (
real ) (
V28()
real ext-real )
number )
< b : ( (
real ) (
V28()
real ext-real )
number ) &
c : ( (
real ) (
V28()
real ext-real )
number )
< d : ( (
real ) (
V28()
real ext-real )
number ) holds
Upper_Arc (rectangle (a : ( ( real ) ( V28() real ext-real ) number ) ,b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( non
empty ) (
functional non
empty )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
= (LSeg (|[a : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ,|[a : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) )) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
\/ (LSeg (|[a : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ,|[b : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) )) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) (
functional non
empty closed )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) ;
theorem
for
a,
b,
c,
d being ( (
real ) (
V28()
real ext-real )
number ) st
a : ( (
real ) (
V28()
real ext-real )
number )
< b : ( (
real ) (
V28()
real ext-real )
number ) &
c : ( (
real ) (
V28()
real ext-real )
number )
< d : ( (
real ) (
V28()
real ext-real )
number ) holds
Lower_Arc (rectangle (a : ( ( real ) ( V28() real ext-real ) number ) ,b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( non
empty ) (
functional non
empty )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
= (LSeg (|[a : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ,|[b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) )) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
\/ (LSeg (|[b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ,|[b : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) )) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) (
functional non
empty closed )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) ;
theorem
for
a,
b,
c,
d being ( (
real ) (
V28()
real ext-real )
number ) st
a : ( (
real ) (
V28()
real ext-real )
number )
< b : ( (
real ) (
V28()
real ext-real )
number ) &
c : ( (
real ) (
V28()
real ext-real )
number )
< d : ( (
real ) (
V28()
real ext-real )
number ) holds
ex
f being ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Upper_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Upper_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Upper_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) ( non
empty )
set ) ) st
(
f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Upper_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Upper_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Upper_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) ( non
empty )
set ) ) is
being_homeomorphism &
f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Upper_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Upper_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Upper_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) ( non
empty )
set ) )
. 0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
set )
= W-min (rectangle (a : ( ( real ) ( V28() real ext-real ) number ) ,b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) &
f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Upper_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Upper_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Upper_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) ( non
empty )
set ) )
. 1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
set )
= E-max (rectangle (a : ( ( real ) ( V28() real ext-real ) number ) ,b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) &
rng f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Upper_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Upper_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Upper_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
Element of
K19( the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Upper_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
set ) )
= Upper_Arc (rectangle (a : ( ( real ) ( V28() real ext-real ) number ) ,b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( non
empty ) (
functional non
empty )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) & ( for
r being ( ( ) (
V28()
real ext-real )
Real) st
r : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in [.0 : ( ( ) ( Function-like functional empty natural V28() real ext-real non positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V177() V213() V216() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ,(1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real non negative ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) .] : ( ( ) (
V171()
V172()
V173()
V216() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) holds
f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Upper_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Upper_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Upper_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) ( non
empty )
set ) )
. r : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set )
= ((1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) - (2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) * r : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) * |[a : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) )
+ ((2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) * r : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) * |[a : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) & ( for
r being ( ( ) (
V28()
real ext-real )
Real) st
r : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in [.(1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real non negative ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ,1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) .] : ( ( ) (
V171()
V172()
V173()
V216() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) holds
f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Upper_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Upper_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Upper_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) ( non
empty )
set ) )
. r : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set )
= ((1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) - ((2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) * r : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) - 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) * |[a : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) )
+ (((2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) * r : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) - 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) * |[b : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) & ( for
p being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) st
p : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in LSeg (
|[a : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[a : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) holds
(
0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) )
<= (((p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `2) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) - c : ( ( real ) ( V28() real ext-real ) number ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) / (d : ( ( real ) ( V28() real ext-real ) number ) - c : ( ( real ) ( V28() real ext-real ) number ) ) : ( ( ) ( V28() real ext-real ) set ) ) : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) )
/ 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) &
(((p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `2) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) - c : ( ( real ) ( V28() real ext-real ) number ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) / (d : ( ( real ) ( V28() real ext-real ) number ) - c : ( ( real ) ( V28() real ext-real ) number ) ) : ( ( ) ( V28() real ext-real ) set ) ) : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) )
/ 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) )
<= 1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) &
f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Upper_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Upper_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Upper_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) ( non
empty )
set ) )
. ((((p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `2) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) - c : ( ( real ) ( V28() real ext-real ) number ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) / (d : ( ( real ) ( V28() real ext-real ) number ) - c : ( ( real ) ( V28() real ext-real ) number ) ) : ( ( ) ( V28() real ext-real ) set ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) / 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set )
= p : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ) ) & ( for
p being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) st
p : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in LSeg (
|[a : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[b : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) holds
(
0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) )
<= ((((p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `1) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) - a : ( ( real ) ( V28() real ext-real ) number ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) / (b : ( ( real ) ( V28() real ext-real ) number ) - a : ( ( real ) ( V28() real ext-real ) number ) ) : ( ( ) ( V28() real ext-real ) set ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) / 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) )
+ (1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real non
negative )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) &
((((p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `1) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) - a : ( ( real ) ( V28() real ext-real ) number ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) / (b : ( ( real ) ( V28() real ext-real ) number ) - a : ( ( real ) ( V28() real ext-real ) number ) ) : ( ( ) ( V28() real ext-real ) set ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) / 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) )
+ (1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real non
negative )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) )
<= 1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) &
f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Upper_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Upper_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Upper_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) ( non
empty )
set ) )
. (((((p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `1) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) - a : ( ( real ) ( V28() real ext-real ) number ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) / (b : ( ( real ) ( V28() real ext-real ) number ) - a : ( ( real ) ( V28() real ext-real ) number ) ) : ( ( ) ( V28() real ext-real ) set ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) / 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) + (1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real non negative ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ) : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set )
= p : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ) ) ) ;
theorem
for
a,
b,
c,
d being ( (
real ) (
V28()
real ext-real )
number ) st
a : ( (
real ) (
V28()
real ext-real )
number )
< b : ( (
real ) (
V28()
real ext-real )
number ) &
c : ( (
real ) (
V28()
real ext-real )
number )
< d : ( (
real ) (
V28()
real ext-real )
number ) holds
ex
f being ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Lower_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Lower_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Lower_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) ( non
empty )
set ) ) st
(
f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Lower_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Lower_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Lower_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) ( non
empty )
set ) ) is
being_homeomorphism &
f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Lower_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Lower_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Lower_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) ( non
empty )
set ) )
. 0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
set )
= E-max (rectangle (a : ( ( real ) ( V28() real ext-real ) number ) ,b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) &
f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Lower_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Lower_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Lower_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) ( non
empty )
set ) )
. 1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
set )
= W-min (rectangle (a : ( ( real ) ( V28() real ext-real ) number ) ,b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) &
rng f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Lower_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Lower_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Lower_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
Element of
K19( the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Lower_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
set ) )
= Lower_Arc (rectangle (a : ( ( real ) ( V28() real ext-real ) number ) ,b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( non
empty ) (
functional non
empty )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) & ( for
r being ( ( ) (
V28()
real ext-real )
Real) st
r : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in [.0 : ( ( ) ( Function-like functional empty natural V28() real ext-real non positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V177() V213() V216() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ,(1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real non negative ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) .] : ( ( ) (
V171()
V172()
V173()
V216() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) holds
f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Lower_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Lower_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Lower_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) ( non
empty )
set ) )
. r : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set )
= ((1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) - (2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) * r : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) * |[b : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) )
+ ((2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) * r : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) * |[b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) & ( for
r being ( ( ) (
V28()
real ext-real )
Real) st
r : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in [.(1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real non negative ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ,1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) .] : ( ( ) (
V171()
V172()
V173()
V216() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) holds
f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Lower_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Lower_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Lower_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) ( non
empty )
set ) )
. r : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set )
= ((1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) - ((2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) * r : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) - 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) * |[b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) )
+ (((2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) * r : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) - 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) * |[a : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) & ( for
p being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) st
p : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in LSeg (
|[b : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) holds
(
0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) )
<= (((p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `2) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) - d : ( ( real ) ( V28() real ext-real ) number ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) / (c : ( ( real ) ( V28() real ext-real ) number ) - d : ( ( real ) ( V28() real ext-real ) number ) ) : ( ( ) ( V28() real ext-real ) set ) ) : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) )
/ 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) &
(((p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `2) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) - d : ( ( real ) ( V28() real ext-real ) number ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) / (c : ( ( real ) ( V28() real ext-real ) number ) - d : ( ( real ) ( V28() real ext-real ) number ) ) : ( ( ) ( V28() real ext-real ) set ) ) : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) )
/ 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) )
<= 1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) &
f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Lower_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Lower_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Lower_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) ( non
empty )
set ) )
. ((((p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `2) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) - d : ( ( real ) ( V28() real ext-real ) number ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) / (c : ( ( real ) ( V28() real ext-real ) number ) - d : ( ( real ) ( V28() real ext-real ) number ) ) : ( ( ) ( V28() real ext-real ) set ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) / 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set )
= p : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ) ) & ( for
p being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) st
p : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in LSeg (
|[b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[a : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) holds
(
0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) )
<= ((((p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `1) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) - b : ( ( real ) ( V28() real ext-real ) number ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) / (a : ( ( real ) ( V28() real ext-real ) number ) - b : ( ( real ) ( V28() real ext-real ) number ) ) : ( ( ) ( V28() real ext-real ) set ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) / 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) )
+ (1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real non
negative )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) &
((((p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `1) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) - b : ( ( real ) ( V28() real ext-real ) number ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) / (a : ( ( real ) ( V28() real ext-real ) number ) - b : ( ( real ) ( V28() real ext-real ) number ) ) : ( ( ) ( V28() real ext-real ) set ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) / 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) )
+ (1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real non
negative )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) )
<= 1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) &
f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Lower_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Lower_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) | (Lower_Arc (rectangle (b1 : ( ( real ) ( V28() real ext-real ) number ) ,b2 : ( ( real ) ( V28() real ext-real ) number ) ,b3 : ( ( real ) ( V28() real ext-real ) number ) ,b4 : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) ( functional non empty closed compact ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( functional non empty ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
strict ) ( non
empty strict TopSpace-like T_0 T_1 T_2 )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) : ( ( ) ( non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) ( non
empty )
set ) )
. (((((p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) `1) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) - b : ( ( real ) ( V28() real ext-real ) number ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) / (a : ( ( real ) ( V28() real ext-real ) number ) - b : ( ( real ) ( V28() real ext-real ) number ) ) : ( ( ) ( V28() real ext-real ) set ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) / 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) + (1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real non negative ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ) : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set )
= p : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ) ) ) ;
theorem
for
a,
b,
c,
d being ( (
real ) (
V28()
real ext-real )
number )
for
p1,
p2 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) st
a : ( (
real ) (
V28()
real ext-real )
number )
< b : ( (
real ) (
V28()
real ext-real )
number ) &
c : ( (
real ) (
V28()
real ext-real )
number )
< d : ( (
real ) (
V28()
real ext-real )
number ) &
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in LSeg (
|[a : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[a : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) &
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in LSeg (
|[a : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[a : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) holds
(
LE p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
rectangle (
a : ( (
real ) (
V28()
real ext-real )
number ) ,
b : ( (
real ) (
V28()
real ext-real )
number ) ,
c : ( (
real ) (
V28()
real ext-real )
number ) ,
d : ( (
real ) (
V28()
real ext-real )
number ) ) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) iff
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
`2 : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) )
<= p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
`2 : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ) ;
theorem
for
a,
b,
c,
d being ( (
real ) (
V28()
real ext-real )
number )
for
p1,
p2 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) st
a : ( (
real ) (
V28()
real ext-real )
number )
< b : ( (
real ) (
V28()
real ext-real )
number ) &
c : ( (
real ) (
V28()
real ext-real )
number )
< d : ( (
real ) (
V28()
real ext-real )
number ) &
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in LSeg (
|[a : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[b : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) &
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in LSeg (
|[a : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[b : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) holds
(
LE p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
rectangle (
a : ( (
real ) (
V28()
real ext-real )
number ) ,
b : ( (
real ) (
V28()
real ext-real )
number ) ,
c : ( (
real ) (
V28()
real ext-real )
number ) ,
d : ( (
real ) (
V28()
real ext-real )
number ) ) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) iff
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
`1 : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) )
<= p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
`1 : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ) ;
theorem
for
a,
b,
c,
d being ( (
real ) (
V28()
real ext-real )
number )
for
p1,
p2 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) st
a : ( (
real ) (
V28()
real ext-real )
number )
< b : ( (
real ) (
V28()
real ext-real )
number ) &
c : ( (
real ) (
V28()
real ext-real )
number )
< d : ( (
real ) (
V28()
real ext-real )
number ) &
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in LSeg (
|[b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[b : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) &
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in LSeg (
|[b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[b : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) holds
(
LE p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
rectangle (
a : ( (
real ) (
V28()
real ext-real )
number ) ,
b : ( (
real ) (
V28()
real ext-real )
number ) ,
c : ( (
real ) (
V28()
real ext-real )
number ) ,
d : ( (
real ) (
V28()
real ext-real )
number ) ) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) iff
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
`2 : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) )
>= p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
`2 : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ) ;
theorem
for
a,
b,
c,
d being ( (
real ) (
V28()
real ext-real )
number )
for
p1,
p2 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) st
a : ( (
real ) (
V28()
real ext-real )
number )
< b : ( (
real ) (
V28()
real ext-real )
number ) &
c : ( (
real ) (
V28()
real ext-real )
number )
< d : ( (
real ) (
V28()
real ext-real )
number ) &
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in LSeg (
|[a : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) &
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in LSeg (
|[a : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) holds
(
LE p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
rectangle (
a : ( (
real ) (
V28()
real ext-real )
number ) ,
b : ( (
real ) (
V28()
real ext-real )
number ) ,
c : ( (
real ) (
V28()
real ext-real )
number ) ,
d : ( (
real ) (
V28()
real ext-real )
number ) ) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) &
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
<> W-min (rectangle (a : ( ( real ) ( V28() real ext-real ) number ) ,b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) iff (
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
`1 : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) )
>= p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
`1 : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) &
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
<> W-min (rectangle (a : ( ( real ) ( V28() real ext-real ) number ) ,b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) ) ;
theorem
for
a,
b,
c,
d being ( (
real ) (
V28()
real ext-real )
number )
for
p1,
p2 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) st
a : ( (
real ) (
V28()
real ext-real )
number )
< b : ( (
real ) (
V28()
real ext-real )
number ) &
c : ( (
real ) (
V28()
real ext-real )
number )
< d : ( (
real ) (
V28()
real ext-real )
number ) &
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in LSeg (
|[a : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[a : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) holds
(
LE p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
rectangle (
a : ( (
real ) (
V28()
real ext-real )
number ) ,
b : ( (
real ) (
V28()
real ext-real )
number ) ,
c : ( (
real ) (
V28()
real ext-real )
number ) ,
d : ( (
real ) (
V28()
real ext-real )
number ) ) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) iff ( (
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in LSeg (
|[a : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[a : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) &
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
`2 : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) )
<= p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
`2 : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ) or
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in LSeg (
|[a : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[b : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) or
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in LSeg (
|[b : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) or (
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in LSeg (
|[b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[a : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) &
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
<> W-min (rectangle (a : ( ( real ) ( V28() real ext-real ) number ) ,b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) ) ) ;
theorem
for
a,
b,
c,
d being ( (
real ) (
V28()
real ext-real )
number )
for
p1,
p2 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) st
a : ( (
real ) (
V28()
real ext-real )
number )
< b : ( (
real ) (
V28()
real ext-real )
number ) &
c : ( (
real ) (
V28()
real ext-real )
number )
< d : ( (
real ) (
V28()
real ext-real )
number ) &
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in LSeg (
|[a : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[b : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) holds
(
LE p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
rectangle (
a : ( (
real ) (
V28()
real ext-real )
number ) ,
b : ( (
real ) (
V28()
real ext-real )
number ) ,
c : ( (
real ) (
V28()
real ext-real )
number ) ,
d : ( (
real ) (
V28()
real ext-real )
number ) ) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) iff ( (
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in LSeg (
|[a : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[b : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) &
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
`1 : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) )
<= p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
`1 : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ) or
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in LSeg (
|[b : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) or (
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in LSeg (
|[b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[a : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) &
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
<> W-min (rectangle (a : ( ( real ) ( V28() real ext-real ) number ) ,b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) ) ) ;
theorem
for
a,
b,
c,
d being ( (
real ) (
V28()
real ext-real )
number )
for
p1,
p2 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) st
a : ( (
real ) (
V28()
real ext-real )
number )
< b : ( (
real ) (
V28()
real ext-real )
number ) &
c : ( (
real ) (
V28()
real ext-real )
number )
< d : ( (
real ) (
V28()
real ext-real )
number ) &
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in LSeg (
|[b : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) holds
(
LE p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
rectangle (
a : ( (
real ) (
V28()
real ext-real )
number ) ,
b : ( (
real ) (
V28()
real ext-real )
number ) ,
c : ( (
real ) (
V28()
real ext-real )
number ) ,
d : ( (
real ) (
V28()
real ext-real )
number ) ) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) iff ( (
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in LSeg (
|[b : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) &
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
`2 : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) )
>= p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
`2 : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ) or (
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in LSeg (
|[b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[a : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) &
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
<> W-min (rectangle (a : ( ( real ) ( V28() real ext-real ) number ) ,b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) ) ) ;
theorem
for
a,
b,
c,
d being ( (
real ) (
V28()
real ext-real )
number )
for
p1,
p2 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) st
a : ( (
real ) (
V28()
real ext-real )
number )
< b : ( (
real ) (
V28()
real ext-real )
number ) &
c : ( (
real ) (
V28()
real ext-real )
number )
< d : ( (
real ) (
V28()
real ext-real )
number ) &
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in LSeg (
|[b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[a : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) &
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
<> W-min (rectangle (a : ( ( real ) ( V28() real ext-real ) number ) ,b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) holds
(
LE p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
rectangle (
a : ( (
real ) (
V28()
real ext-real )
number ) ,
b : ( (
real ) (
V28()
real ext-real )
number ) ,
c : ( (
real ) (
V28()
real ext-real )
number ) ,
d : ( (
real ) (
V28()
real ext-real )
number ) ) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) iff (
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in LSeg (
|[b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[a : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) &
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
`1 : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) )
>= p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
`1 : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) &
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
<> W-min (rectangle (a : ( ( real ) ( V28() real ext-real ) number ) ,b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) )) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) ) ;
theorem
for
x being ( ( ) ( )
set )
for
a,
b,
c,
d being ( (
real ) (
V28()
real ext-real )
number ) st
x : ( ( ) ( )
set )
in rectangle (
a : ( (
real ) (
V28()
real ext-real )
number ) ,
b : ( (
real ) (
V28()
real ext-real )
number ) ,
c : ( (
real ) (
V28()
real ext-real )
number ) ,
d : ( (
real ) (
V28()
real ext-real )
number ) ) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) &
a : ( (
real ) (
V28()
real ext-real )
number )
< b : ( (
real ) (
V28()
real ext-real )
number ) &
c : ( (
real ) (
V28()
real ext-real )
number )
< d : ( (
real ) (
V28()
real ext-real )
number ) & not
x : ( ( ) ( )
set )
in LSeg (
|[a : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[a : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) & not
x : ( ( ) ( )
set )
in LSeg (
|[a : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[b : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) & not
x : ( ( ) ( )
set )
in LSeg (
|[b : ( ( real ) ( V28() real ext-real ) number ) ,d : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) holds
x : ( ( ) ( )
set )
in LSeg (
|[b : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[a : ( ( real ) ( V28() real ext-real ) number ) ,c : ( ( real ) ( V28() real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) ;
begin
theorem
for
p1,
p2 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) st
LE p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
rectangle (
(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real non
positive )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,
(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real non
positive )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) &
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in LSeg (
|[(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real non positive ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ,(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real non positive ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real non positive ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ,1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) & not (
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in LSeg (
|[(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real non positive ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ,(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real non positive ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real non positive ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ,1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) &
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
`2 : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) )
>= p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
`2 : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ) & not
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in LSeg (
|[(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real non positive ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ,1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) & not
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in LSeg (
|[1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ,(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real non positive ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) holds
(
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in LSeg (
|[1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ,(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real non positive ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real non positive ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ,(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real non positive ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) &
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
<> |[(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real non positive ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ,(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real non positive ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) ;
theorem
for
p1,
p2 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
for
P being ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of )
for
f being ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) ) st
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of )
= circle (
0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,
0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
functional non
empty closed compact )
Subset of ) &
f : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) )
= Sq_Circ : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like one-to-one non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Element of
K19(
K20( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) &
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in LSeg (
|[(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real non positive ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ,(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real non positive ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real non positive ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ,1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) &
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
`2 : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) )
>= 0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) &
LE p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
rectangle (
(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real non
positive )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,
(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real non
positive )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) holds
LE f : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) )
. p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
f : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) )
. p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) ;
theorem
for
p1,
p2,
p3 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
for
P being ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of )
for
f being ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) ) st
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of )
= circle (
0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,
0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
functional non
empty closed compact )
Subset of ) &
f : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) )
= Sq_Circ : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like one-to-one non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Element of
K19(
K20( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) &
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in LSeg (
|[(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real non positive ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ,(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real non positive ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real non positive ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ,1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) &
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
`2 : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) )
>= 0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) &
LE p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
rectangle (
(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real non
positive )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,
(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real non
positive )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) &
LE p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
rectangle (
(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real non
positive )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,
(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real non
positive )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) holds
LE f : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) )
. p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
f : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) )
. p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) ;
theorem
for
p being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
for
f being ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) ) st
f : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) )
= Sq_Circ : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like one-to-one non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Element of
K19(
K20( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) &
p : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
`1 : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) )
= - 1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V28()
real ext-real non
positive )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) &
p : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
`2 : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) )
< 0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) holds
(
(f : ( ( Function-like V18( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) , the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) ( Relation-like the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non empty total V18( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) , the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) Function of ( ( ) ( functional non empty ) set ) , ( ( ) ( functional non empty ) set ) ) . p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) )
`1 : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) )
< 0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) &
(f : ( ( Function-like V18( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) , the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) ( Relation-like the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non empty total V18( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) , the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) Function of ( ( ) ( functional non empty ) set ) , ( ( ) ( functional non empty ) set ) ) . p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) )
`2 : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) )
< 0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ) ;
theorem
for
p being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
for
P being ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of )
for
f being ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) ) st
f : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) )
= Sq_Circ : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like one-to-one non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Element of
K19(
K20( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) holds
(
(f : ( ( Function-like V18( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) , the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) ( Relation-like the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non empty total V18( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) , the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) Function of ( ( ) ( functional non empty ) set ) , ( ( ) ( functional non empty ) set ) ) . p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) )
`1 : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) )
>= 0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) iff
p : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
`1 : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) )
>= 0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ) ;
theorem
for
p being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
for
P being ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of )
for
f being ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) ) st
f : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) )
= Sq_Circ : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like one-to-one non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Element of
K19(
K20( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) holds
(
(f : ( ( Function-like V18( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) , the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) ( Relation-like the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non empty total V18( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) , the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) Function of ( ( ) ( functional non empty ) set ) , ( ( ) ( functional non empty ) set ) ) . p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) )
`2 : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) )
>= 0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) iff
p : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
`2 : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) )
>= 0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ) ;
theorem
for
p,
q being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
for
f being ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) ) st
f : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) )
= Sq_Circ : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like one-to-one non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Element of
K19(
K20( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) &
p : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in LSeg (
|[(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real non positive ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ,(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real non positive ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real non positive ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ,1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) &
q : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in LSeg (
|[1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ,(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real non positive ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real non positive ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ,(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real non positive ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) holds
(f : ( ( Function-like V18( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) , the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) ( Relation-like the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non empty total V18( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) , the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) Function of ( ( ) ( functional non empty ) set ) , ( ( ) ( functional non empty ) set ) ) . p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) )
`1 : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) )
<= (f : ( ( Function-like V18( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) , the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) ( Relation-like the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non empty total V18( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) , the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) Function of ( ( ) ( functional non empty ) set ) , ( ( ) ( functional non empty ) set ) ) . q : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) )
`1 : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ;
theorem
for
p,
q being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
for
f being ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) ) st
f : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) )
= Sq_Circ : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like one-to-one non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Element of
K19(
K20( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) &
p : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in LSeg (
|[(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real non positive ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ,(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real non positive ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real non positive ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ,1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) &
q : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in LSeg (
|[(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real non positive ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ,(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real non positive ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
|[(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V28() real ext-real non positive ) Element of REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) ,1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) : ( ( ) (
functional non
empty closed compact V237(
TOP-REAL 2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) ) )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) &
p : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
`2 : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) )
>= q : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
`2 : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) &
p : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
`2 : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) )
< 0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) holds
(f : ( ( Function-like V18( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) , the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) ( Relation-like the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non empty total V18( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) , the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) Function of ( ( ) ( functional non empty ) set ) , ( ( ) ( functional non empty ) set ) ) . p : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) )
`2 : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) )
>= (f : ( ( Function-like V18( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) , the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) ( Relation-like the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non empty total V18( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) , the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V137() V183() V184() V185() V186() V187() V188() V189() strict ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) Function of ( ( ) ( functional non empty ) set ) , ( ( ) ( functional non empty ) set ) ) . q : ( ( ) ( Relation-like Function-like V43(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V161() V162() V163() ) Point of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) )
`2 : ( ( ) (
V28()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ;
theorem
for
p1,
p2,
p3,
p4 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
for
P being ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of )
for
f being ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) ) st
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of )
= circle (
0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,
0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
functional non
empty closed compact )
Subset of ) &
f : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) )
= Sq_Circ : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like one-to-one non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Element of
K19(
K20( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) &
LE p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
rectangle (
(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real non
positive )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,
(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real non
positive )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) &
LE p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
rectangle (
(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real non
positive )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,
(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real non
positive )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) &
LE p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
rectangle (
(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real non
positive )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,
(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real non
positive )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) holds
f : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) )
. p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
f : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) )
. p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
f : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) )
. p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
f : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) )
. p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) )
are_in_this_order_on P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) ;
theorem
for
p1,
p2,
p3 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
for
P being ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) st
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) is
being_simple_closed_curve &
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) &
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) &
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) & not (
LE p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) &
LE p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) ) & not (
LE p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) &
LE p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) ) & not (
LE p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) &
LE p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) ) & not (
LE p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) &
LE p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) ) & not (
LE p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) &
LE p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) ) holds
(
LE p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) &
LE p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) ) ;
theorem
for
p1,
p2,
p3 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
for
P being ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) st
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) is
being_simple_closed_curve &
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) &
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) &
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) &
LE p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) & not
LE p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) & not (
LE p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) &
LE p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) ) holds
LE p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) ;
theorem
for
p1,
p2,
p3,
p4 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
for
P being ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) st
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) is
being_simple_closed_curve &
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) &
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) &
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) &
p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
in P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) &
LE p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) &
LE p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) & not
LE p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) & not (
LE p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) &
LE p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) ) & not (
LE p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) &
LE p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) ) holds
LE p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) ;
theorem
for
p1,
p2,
p3,
p4 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
for
P being ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of )
for
f being ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) ) st
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of )
= circle (
0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,
0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
functional non
empty closed compact )
Subset of ) &
f : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) )
= Sq_Circ : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like one-to-one non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Element of
K19(
K20( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) &
LE f : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) )
. p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
f : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) )
. p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) &
LE f : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) )
. p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
f : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) )
. p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) &
LE f : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) )
. p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
f : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) )
. p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) holds
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
are_in_this_order_on rectangle (
(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real non
positive )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,
(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real non
positive )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) ;
theorem
for
p1,
p2,
p3,
p4 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
for
P being ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of )
for
f being ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) ) st
P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of )
= circle (
0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,
0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
functional non
empty closed compact )
Subset of ) &
f : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) )
= Sq_Circ : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like one-to-one non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Element of
K19(
K20( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) holds
(
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
are_in_this_order_on rectangle (
(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real non
positive )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,
(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real non
positive )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) iff
f : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) )
. p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
f : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) )
. p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
f : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) )
. p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ,
f : ( (
Function-like V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) (
functional non
empty )
set ) , ( ( ) (
functional non
empty )
set ) )
. p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) )
are_in_this_order_on P : ( ( non
empty compact ) (
functional non
empty closed compact )
Subset of ) ) ;
theorem
for
p1,
p2,
p3,
p4 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) st
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) ,
p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) )
are_in_this_order_on rectangle (
(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real non
positive )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,
(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real non
positive )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
functional non
empty closed compact )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) holds
for
f,
g being ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) st
f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) is
continuous &
f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) is
one-to-one &
g : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) is
continuous &
g : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) is
one-to-one &
f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) )
. 0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set )
= p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) &
f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) )
. 1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set )
= p3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) &
g : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) )
. 0 : ( ( ) (
Function-like functional empty natural V28()
real ext-real non
positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213()
V216() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set )
= p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) &
g : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) )
. 1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like )
set )
= p4 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V161()
V162()
V163() )
Point of ( ( ) (
functional non
empty )
set ) ) &
rng f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
functional )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
c= closed_inside_of_rectangle (
(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real non
positive )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,
(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real non
positive )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
functional )
Subset of ) &
rng g : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
functional )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
c= closed_inside_of_rectangle (
(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real non
positive )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ,
(- 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V28()
real ext-real non
positive )
Element of
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) ,1 : ( ( ) ( non
empty natural V28()
real ext-real positive non
negative V123()
V124()
V171()
V172()
V173()
V174()
V175()
V176()
V211()
V213() )
Element of
NAT : ( ( ) (
V88()
V171()
V172()
V173()
V174()
V175()
V176()
V177()
V213() )
Element of
K19(
REAL : ( ( ) ( non
empty V36()
V88()
V171()
V172()
V173()
V177()
V213()
V214()
V216() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
functional )
Subset of ) holds
rng f : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
functional )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) )
meets rng g : ( (
Function-like V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like V122() )
SubSpace of
R^1 : ( (
TopSpace-like ) ( non
empty strict TopSpace-like V122() )
TopStruct ) ) : ( ( ) ( non
empty V171()
V172()
V173() )
set ) , the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) )
Function of ( ( ) ( non
empty V171()
V172()
V173() )
set ) , ( ( ) (
functional non
empty )
set ) ) : ( ( ) (
functional )
Element of
K19( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V123() V124() V171() V172() V173() V174() V175() V176() V211() V213() ) Element of NAT : ( ( ) ( V88() V171() V172() V173() V174() V175() V176() V177() V213() ) Element of K19(REAL : ( ( ) ( non empty V36() V88() V171() V172() V173() V177() V213() V214() V216() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V137()
V183()
V184()
V185()
V186()
V187()
V188()
V189()
strict )
RLTopStruct ) : ( ( ) (
functional non
empty )
set ) ) : ( ( ) ( )
set ) ) ;