begin
theorem
for
P,
Q being ( ( ) (
functional )
Subset of )
for
p1,
p2,
q1 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) )
for
f being ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | b1 : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) )
for
s1 being ( ( ) (
V11()
V12()
ext-real )
Real) st
q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) )
in P : ( ( ) (
functional )
Subset of ) &
f : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | b1 : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) )
. s1 : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) ( )
set )
= q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
f : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | b1 : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) ) is
being_homeomorphism &
f : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | b1 : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) )
. 0 : ( ( ) (
empty V10()
V11()
V12()
ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
set )
= p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
f : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | b1 : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) )
. 1 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
set )
= p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
0 : ( ( ) (
empty V10()
V11()
V12()
ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
<= s1 : ( ( ) (
V11()
V12()
ext-real )
Real) &
s1 : ( ( ) (
V11()
V12()
ext-real )
Real)
<= 1 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) & ( for
t being ( ( ) (
V11()
V12()
ext-real )
Real) st
0 : ( ( ) (
empty V10()
V11()
V12()
ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
<= t : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | b1 : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) ) &
t : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | b1 : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) )
< s1 : ( ( ) (
V11()
V12()
ext-real )
Real) holds
not
f : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | b1 : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) )
. t : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | b1 : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) ) : ( ( ) ( )
set )
in Q : ( ( ) (
functional )
Subset of ) ) holds
for
g being ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | b1 : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) )
for
s2 being ( ( ) (
V11()
V12()
ext-real )
Real) st
g : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | b1 : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) ) is
being_homeomorphism &
g : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | b1 : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) )
. 0 : ( ( ) (
empty V10()
V11()
V12()
ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
set )
= p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
g : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | b1 : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) )
. 1 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
set )
= p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
g : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | b1 : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) )
. s2 : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) ( )
set )
= q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
0 : ( ( ) (
empty V10()
V11()
V12()
ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
<= s2 : ( ( ) (
V11()
V12()
ext-real )
Real) &
s2 : ( ( ) (
V11()
V12()
ext-real )
Real)
<= 1 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) holds
for
t being ( ( ) (
V11()
V12()
ext-real )
Real) st
0 : ( ( ) (
empty V10()
V11()
V12()
ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
<= t : ( ( ) (
V11()
V12()
ext-real )
Real) &
t : ( ( ) (
V11()
V12()
ext-real )
Real)
< s2 : ( ( ) (
V11()
V12()
ext-real )
Real) holds
not
g : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | b1 : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) )
. t : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) ( )
set )
in Q : ( ( ) (
functional )
Subset of ) ;
definition
let P,
Q be ( ( ) (
functional )
Subset of ) ;
let p1,
p2 be ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ;
assume that
(
P : ( ( ) (
functional )
Subset of )
meets Q : ( ( ) (
functional )
Subset of ) &
P : ( ( ) (
functional )
Subset of )
/\ Q : ( ( ) (
functional )
Subset of ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) is
closed )
and
P : ( ( ) (
functional )
Subset of )
is_an_arc_of p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) )
;
func First_Point (
P,
p1,
p2,
Q)
-> ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) )
means
(
it : ( ( ) ( )
Element of
K6(
K6(
P : ( ( ) ( )
RLTopStruct ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) )
in P : ( ( ) ( )
RLTopStruct )
/\ Q : ( ( ) ( )
Element of
P : ( ( ) ( )
RLTopStruct ) ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) & ( for
g being ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | P : ( ( ) ( ) RLTopStruct ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) )
for
s2 being ( ( ) (
V11()
V12()
ext-real )
Real) st
g : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | P : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) ) is
being_homeomorphism &
g : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | P : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) )
. 0 : ( ( ) (
empty V10()
V11()
V12()
ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
set )
= p1 : ( (
Function-like quasi_total ) (
Relation-like K7(
P : ( ( ) ( )
RLTopStruct ) ,
P : ( ( ) ( )
RLTopStruct ) ) : ( ( ) ( )
set )
-defined P : ( ( ) ( )
RLTopStruct )
-valued Function-like quasi_total )
Element of
K6(
K7(
K7(
P : ( ( ) ( )
RLTopStruct ) ,
P : ( ( ) ( )
RLTopStruct ) ) : ( ( ) ( )
set ) ,
P : ( ( ) ( )
RLTopStruct ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) &
g : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | P : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) )
. 1 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
set )
= p2 : ( (
Function-like quasi_total ) (
Relation-like K7(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ,
P : ( ( ) ( )
RLTopStruct ) ) : ( ( ) ( )
set )
-defined P : ( ( ) ( )
RLTopStruct )
-valued Function-like quasi_total )
Element of
K6(
K7(
K7(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ,
P : ( ( ) ( )
RLTopStruct ) ) : ( ( ) ( )
set ) ,
P : ( ( ) ( )
RLTopStruct ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) &
g : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | P : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) )
. s2 : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) ( )
set )
= it : ( ( ) ( )
Element of
K6(
K6(
P : ( ( ) ( )
RLTopStruct ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) &
0 : ( ( ) (
empty V10()
V11()
V12()
ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
<= s2 : ( ( ) (
V11()
V12()
ext-real )
Real) &
s2 : ( ( ) (
V11()
V12()
ext-real )
Real)
<= 1 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) holds
for
t being ( ( ) (
V11()
V12()
ext-real )
Real) st
0 : ( ( ) (
empty V10()
V11()
V12()
ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
<= t : ( ( ) (
V11()
V12()
ext-real )
Real) &
t : ( ( ) (
V11()
V12()
ext-real )
Real)
< s2 : ( ( ) (
V11()
V12()
ext-real )
Real) holds
not
g : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | P : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) )
. t : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) ( )
set )
in Q : ( ( ) ( )
Element of
P : ( ( ) ( )
RLTopStruct ) ) ) );
end;
theorem
for
P,
Q being ( ( ) (
functional )
Subset of )
for
p1,
p2,
q1 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) )
for
f being ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | b1 : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) )
for
s1 being ( ( ) (
V11()
V12()
ext-real )
Real) st
q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) )
in P : ( ( ) (
functional )
Subset of ) &
f : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | b1 : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) )
. s1 : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) ( )
set )
= q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
f : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | b1 : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) ) is
being_homeomorphism &
f : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | b1 : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) )
. 0 : ( ( ) (
empty V10()
V11()
V12()
ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
set )
= p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
f : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | b1 : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) )
. 1 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
set )
= p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
0 : ( ( ) (
empty V10()
V11()
V12()
ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
<= s1 : ( ( ) (
V11()
V12()
ext-real )
Real) &
s1 : ( ( ) (
V11()
V12()
ext-real )
Real)
<= 1 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) & ( for
t being ( ( ) (
V11()
V12()
ext-real )
Real) st 1 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
>= t : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | b1 : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) ) &
t : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | b1 : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) )
> s1 : ( ( ) (
V11()
V12()
ext-real )
Real) holds
not
f : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | b1 : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) )
. t : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | b1 : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) ) : ( ( ) ( )
set )
in Q : ( ( ) (
functional )
Subset of ) ) holds
for
g being ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | b1 : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) )
for
s2 being ( ( ) (
V11()
V12()
ext-real )
Real) st
g : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | b1 : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) ) is
being_homeomorphism &
g : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | b1 : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) )
. 0 : ( ( ) (
empty V10()
V11()
V12()
ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
set )
= p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
g : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | b1 : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) )
. 1 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
set )
= p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
g : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | b1 : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) )
. s2 : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) ( )
set )
= q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
0 : ( ( ) (
empty V10()
V11()
V12()
ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
<= s2 : ( ( ) (
V11()
V12()
ext-real )
Real) &
s2 : ( ( ) (
V11()
V12()
ext-real )
Real)
<= 1 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) holds
for
t being ( ( ) (
V11()
V12()
ext-real )
Real) st 1 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
>= t : ( ( ) (
V11()
V12()
ext-real )
Real) &
t : ( ( ) (
V11()
V12()
ext-real )
Real)
> s2 : ( ( ) (
V11()
V12()
ext-real )
Real) holds
not
g : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | b1 : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) )
. t : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) ( )
set )
in Q : ( ( ) (
functional )
Subset of ) ;
definition
let P,
Q be ( ( ) (
functional )
Subset of ) ;
let p1,
p2 be ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ;
assume that
(
P : ( ( ) (
functional )
Subset of )
meets Q : ( ( ) (
functional )
Subset of ) &
P : ( ( ) (
functional )
Subset of )
/\ Q : ( ( ) (
functional )
Subset of ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) is
closed )
and
P : ( ( ) (
functional )
Subset of )
is_an_arc_of p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) )
;
func Last_Point (
P,
p1,
p2,
Q)
-> ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) )
means
(
it : ( ( ) ( )
Element of
K6(
K6(
P : ( ( ) ( )
RLTopStruct ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) )
in P : ( ( ) ( )
RLTopStruct )
/\ Q : ( ( ) ( )
Element of
P : ( ( ) ( )
RLTopStruct ) ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) & ( for
g being ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | P : ( ( ) ( ) RLTopStruct ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) )
for
s2 being ( ( ) (
V11()
V12()
ext-real )
Real) st
g : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | P : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) ) is
being_homeomorphism &
g : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | P : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) )
. 0 : ( ( ) (
empty V10()
V11()
V12()
ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
set )
= p1 : ( (
Function-like quasi_total ) (
Relation-like K7(
P : ( ( ) ( )
RLTopStruct ) ,
P : ( ( ) ( )
RLTopStruct ) ) : ( ( ) ( )
set )
-defined P : ( ( ) ( )
RLTopStruct )
-valued Function-like quasi_total )
Element of
K6(
K7(
K7(
P : ( ( ) ( )
RLTopStruct ) ,
P : ( ( ) ( )
RLTopStruct ) ) : ( ( ) ( )
set ) ,
P : ( ( ) ( )
RLTopStruct ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) &
g : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | P : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) )
. 1 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
set )
= p2 : ( (
Function-like quasi_total ) (
Relation-like K7(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ,
P : ( ( ) ( )
RLTopStruct ) ) : ( ( ) ( )
set )
-defined P : ( ( ) ( )
RLTopStruct )
-valued Function-like quasi_total )
Element of
K6(
K7(
K7(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ,
P : ( ( ) ( )
RLTopStruct ) ) : ( ( ) ( )
set ) ,
P : ( ( ) ( )
RLTopStruct ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) &
g : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | P : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) )
. s2 : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) ( )
set )
= it : ( ( ) ( )
Element of
K6(
K6(
P : ( ( ) ( )
RLTopStruct ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) &
0 : ( ( ) (
empty V10()
V11()
V12()
ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
<= s2 : ( ( ) (
V11()
V12()
ext-real )
Real) &
s2 : ( ( ) (
V11()
V12()
ext-real )
Real)
<= 1 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) holds
for
t being ( ( ) (
V11()
V12()
ext-real )
Real) st 1 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
>= t : ( ( ) (
V11()
V12()
ext-real )
Real) &
t : ( ( ) (
V11()
V12()
ext-real )
Real)
> s2 : ( ( ) (
V11()
V12()
ext-real )
Real) holds
not
g : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | P : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) )
. t : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) ( )
set )
in Q : ( ( ) ( )
Element of
P : ( ( ) ( )
RLTopStruct ) ) ) );
end;
begin
definition
let P be ( ( ) (
functional )
Subset of ) ;
let p1,
p2,
q1,
q2 be ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ;
pred LE q1,
q2,
P,
p1,
p2 means
(
q1 : ( (
Function-like quasi_total ) (
Relation-like K7(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ,
P : ( ( ) ( )
RLTopStruct ) ) : ( ( ) ( )
set )
-defined P : ( ( ) ( )
RLTopStruct )
-valued Function-like quasi_total )
Element of
K6(
K7(
K7(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ,
P : ( ( ) ( )
RLTopStruct ) ) : ( ( ) ( )
set ) ,
P : ( ( ) ( )
RLTopStruct ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) )
in P : ( ( ) ( )
RLTopStruct ) &
q2 : ( ( ) ( )
Element of
K6(
K6(
P : ( ( ) ( )
RLTopStruct ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) )
in P : ( ( ) ( )
RLTopStruct ) & ( for
g being ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | P : ( ( ) ( ) RLTopStruct ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) )
for
s1,
s2 being ( ( ) (
V11()
V12()
ext-real )
Real) st
g : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | P : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) ) is
being_homeomorphism &
g : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | P : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) )
. 0 : ( ( ) (
empty V10()
V11()
V12()
ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
set )
= p1 : ( ( ) ( )
Element of
P : ( ( ) ( )
RLTopStruct ) ) &
g : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | P : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) )
. 1 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
set )
= p2 : ( (
Function-like quasi_total ) (
Relation-like K7(
P : ( ( ) ( )
RLTopStruct ) ,
P : ( ( ) ( )
RLTopStruct ) ) : ( ( ) ( )
set )
-defined P : ( ( ) ( )
RLTopStruct )
-valued Function-like quasi_total )
Element of
K6(
K7(
K7(
P : ( ( ) ( )
RLTopStruct ) ,
P : ( ( ) ( )
RLTopStruct ) ) : ( ( ) ( )
set ) ,
P : ( ( ) ( )
RLTopStruct ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) &
g : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | P : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) )
. s1 : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) ( )
set )
= q1 : ( (
Function-like quasi_total ) (
Relation-like K7(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ,
P : ( ( ) ( )
RLTopStruct ) ) : ( ( ) ( )
set )
-defined P : ( ( ) ( )
RLTopStruct )
-valued Function-like quasi_total )
Element of
K6(
K7(
K7(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ,
P : ( ( ) ( )
RLTopStruct ) ) : ( ( ) ( )
set ) ,
P : ( ( ) ( )
RLTopStruct ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) &
0 : ( ( ) (
empty V10()
V11()
V12()
ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
<= s1 : ( ( ) (
V11()
V12()
ext-real )
Real) &
s1 : ( ( ) (
V11()
V12()
ext-real )
Real)
<= 1 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) &
g : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | P : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) )
. s2 : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) ( )
set )
= q2 : ( ( ) ( )
Element of
K6(
K6(
P : ( ( ) ( )
RLTopStruct ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) &
0 : ( ( ) (
empty V10()
V11()
V12()
ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
<= s2 : ( ( ) (
V11()
V12()
ext-real )
Real) &
s2 : ( ( ) (
V11()
V12()
ext-real )
Real)
<= 1 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) holds
s1 : ( ( ) (
V11()
V12()
ext-real )
Real)
<= s2 : ( ( ) (
V11()
V12()
ext-real )
Real) ) );
end;
theorem
for
P being ( ( ) (
functional )
Subset of )
for
p1,
p2,
q1,
q2 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) )
for
g being ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | b1 : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) )
for
s1,
s2 being ( ( ) (
V11()
V12()
ext-real )
Real) st
P : ( ( ) (
functional )
Subset of )
is_an_arc_of p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
g : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | b1 : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) ) is
being_homeomorphism &
g : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | b1 : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) )
. 0 : ( ( ) (
empty V10()
V11()
V12()
ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
set )
= p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
g : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | b1 : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) )
. 1 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) ( )
set )
= p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
g : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | b1 : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) )
. s1 : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) ( )
set )
= q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
0 : ( ( ) (
empty V10()
V11()
V12()
ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
<= s1 : ( ( ) (
V11()
V12()
ext-real )
Real) &
s1 : ( ( ) (
V11()
V12()
ext-real )
Real)
<= 1 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) &
g : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
I[01] : ( ( ) ( non
empty strict TopSpace-like )
SubSpace of
R^1 : ( (
TopSpace-like ) (
TopSpace-like )
TopStruct ) ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
((TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) | b1 : ( ( ) ( functional ) Subset of ) ) : ( (
strict ) (
strict TopSpace-like )
SubSpace of
TOP-REAL 2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) ) : ( ( ) ( )
set )
-valued Function-like quasi_total )
Function of ( ( ) ( non
empty )
set ) , ( ( ) ( )
set ) )
. s2 : ( ( ) (
V11()
V12()
ext-real )
Real) : ( ( ) ( )
set )
= q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
0 : ( ( ) (
empty V10()
V11()
V12()
ext-real non
positive non
negative Function-like functional V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
<= s2 : ( ( ) (
V11()
V12()
ext-real )
Real) &
s2 : ( ( ) (
V11()
V12()
ext-real )
Real)
<= 1 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) &
s1 : ( ( ) (
V11()
V12()
ext-real )
Real)
<= s2 : ( ( ) (
V11()
V12()
ext-real )
Real) holds
LE q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( ) (
functional )
Subset of ) ,
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ;
theorem
for
P being ( ( ) (
functional )
Subset of )
for
p1,
p2,
q1 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) st
P : ( ( ) (
functional )
Subset of )
is_an_arc_of p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) )
in P : ( ( ) (
functional )
Subset of ) holds
(
LE p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( ) (
functional )
Subset of ) ,
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
LE q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( ) (
functional )
Subset of ) ,
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ) ;
theorem
for
P being ( ( ) (
functional )
Subset of )
for
p1,
p2,
q1,
q2 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) st
P : ( ( ) (
functional )
Subset of )
is_an_arc_of p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
LE q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( ) (
functional )
Subset of ) ,
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
LE q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( ) (
functional )
Subset of ) ,
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) holds
q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) )
= q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ;
theorem
for
P being ( ( ) (
functional )
Subset of )
for
p1,
p2,
q1,
q2,
q3 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) st
LE q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( ) (
functional )
Subset of ) ,
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
LE q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
q3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( ) (
functional )
Subset of ) ,
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) holds
LE q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
q3 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( ) (
functional )
Subset of ) ,
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ;
theorem
for
P being ( ( ) (
functional )
Subset of )
for
p1,
p2,
q1,
q2 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) st
P : ( ( ) (
functional )
Subset of )
is_an_arc_of p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) )
in P : ( ( ) (
functional )
Subset of ) &
q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) )
in P : ( ( ) (
functional )
Subset of ) &
q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) )
<> q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) & not (
LE q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( ) (
functional )
Subset of ) ,
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) & not
LE q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( ) (
functional )
Subset of ) ,
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ) holds
(
LE q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( ) (
functional )
Subset of ) ,
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) & not
LE q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
P : ( ( ) (
functional )
Subset of ) ,
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ) ;
begin
theorem
for
q1,
q2,
p1,
p2 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) st
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) )
<> p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
LE q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
LSeg (
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ) : ( ( ) (
functional closed compact )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) ,
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) holds
LE q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ;
theorem
for
P,
Q being ( ( ) (
functional )
Subset of )
for
p1,
p2 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) st
P : ( ( ) (
functional )
Subset of )
is_an_arc_of p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
P : ( ( ) (
functional )
Subset of )
meets Q : ( ( ) (
functional )
Subset of ) &
P : ( ( ) (
functional )
Subset of )
/\ Q : ( ( ) (
functional )
Subset of ) : ( ( ) (
functional )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) is
closed holds
(
First_Point (
P : ( ( ) (
functional )
Subset of ) ,
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
Q : ( ( ) (
functional )
Subset of ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) )
= Last_Point (
P : ( ( ) (
functional )
Subset of ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
Q : ( ( ) (
functional )
Subset of ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) &
Last_Point (
P : ( ( ) (
functional )
Subset of ) ,
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
Q : ( ( ) (
functional )
Subset of ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) )
= First_Point (
P : ( ( ) (
functional )
Subset of ) ,
p2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
p1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
Q : ( ( ) (
functional )
Subset of ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ) ;
theorem
for
f being ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) )
for
Q being ( ( ) (
functional )
Subset of )
for
i being ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) st
L~ f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional closed )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) )
meets Q : ( ( ) (
functional )
Subset of ) &
Q : ( ( ) (
functional )
Subset of ) is
closed &
f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) ) is
being_S-Seq & 1 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
<= i : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) &
i : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
+ 1 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
<= len f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) &
First_Point (
(L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) ) : ( ( ) (
functional closed )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) ,
(f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) /. 1 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) ,
(f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) ) : ( ( ) ( V10() V11() V12() ext-real V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) ,
Q : ( ( ) (
functional )
Subset of ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) )
in LSeg (
f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) ) ,
i : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
functional closed )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) holds
First_Point (
(L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) ) : ( ( ) (
functional closed )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) ,
(f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) /. 1 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) ,
(f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) ) : ( ( ) ( V10() V11() V12() ext-real V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) ,
Q : ( ( ) (
functional )
Subset of ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) )
= First_Point (
(LSeg (f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) ,i : ( ( ) ( V10() V11() V12() ext-real V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) (
functional closed )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) ,
(f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) /. i : ( ( ) ( V10() V11() V12() ext-real V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) ,
(f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) /. (i : ( ( ) ( V10() V11() V12() ext-real V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V10() V11() V12() ext-real V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) ,
Q : ( ( ) (
functional )
Subset of ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ;
theorem
for
f being ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) )
for
Q being ( ( ) (
functional )
Subset of )
for
i being ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) st
L~ f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional closed )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) )
meets Q : ( ( ) (
functional )
Subset of ) &
Q : ( ( ) (
functional )
Subset of ) is
closed &
f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) ) is
being_S-Seq & 1 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
<= i : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) &
i : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
+ 1 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
<= len f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) &
Last_Point (
(L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) ) : ( ( ) (
functional closed )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) ,
(f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) /. 1 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) ,
(f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) ) : ( ( ) ( V10() V11() V12() ext-real V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) ,
Q : ( ( ) (
functional )
Subset of ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) )
in LSeg (
f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) ) ,
i : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
functional closed )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) holds
Last_Point (
(L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) ) : ( ( ) (
functional closed )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) ,
(f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) /. 1 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) ,
(f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) ) : ( ( ) ( V10() V11() V12() ext-real V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) ,
Q : ( ( ) (
functional )
Subset of ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) )
= Last_Point (
(LSeg (f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) ,i : ( ( ) ( V10() V11() V12() ext-real V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) (
functional closed )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) ,
(f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) /. i : ( ( ) ( V10() V11() V12() ext-real V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) ,
(f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) /. (i : ( ( ) ( V10() V11() V12() ext-real V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V10() V11() V12() ext-real V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) ,
Q : ( ( ) (
functional )
Subset of ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ;
theorem
for
f being ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) )
for
Q being ( ( ) (
functional )
Subset of )
for
q being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) )
for
i,
j being ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) st
L~ f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional closed )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) )
meets Q : ( ( ) (
functional )
Subset of ) &
f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) ) is
being_S-Seq &
Q : ( ( ) (
functional )
Subset of ) is
closed &
First_Point (
(L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) ) : ( ( ) (
functional closed )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) ,
(f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) /. 1 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) ,
(f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) ) : ( ( ) ( V10() V11() V12() ext-real V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) ,
Q : ( ( ) (
functional )
Subset of ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) )
in LSeg (
f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) ) ,
i : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
functional closed )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) & 1 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
<= i : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) &
i : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
+ 1 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
<= len f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) &
q : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) )
in LSeg (
f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) ) ,
j : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
functional closed )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) & 1 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
<= j : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) &
j : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
+ 1 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
<= len f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) &
q : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) )
in Q : ( ( ) (
functional )
Subset of ) &
First_Point (
(L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) ) : ( ( ) (
functional closed )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) ,
(f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) /. 1 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) ,
(f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) ) : ( ( ) ( V10() V11() V12() ext-real V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) ,
Q : ( ( ) (
functional )
Subset of ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) )
<> q : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) holds
(
i : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
<= j : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) & (
i : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
= j : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) implies
LE First_Point (
(L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) ) : ( ( ) (
functional closed )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) ,
(f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) /. 1 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) ,
(f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) ) : ( ( ) ( V10() V11() V12() ext-real V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) ,
Q : ( ( ) (
functional )
Subset of ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
q : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) )
/. i : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) ,
f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) )
/. (i : ( ( ) ( V10() V11() V12() ext-real V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) ) ) ;
theorem
for
f being ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) )
for
Q being ( ( ) (
functional )
Subset of )
for
q being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) )
for
i,
j being ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) st
L~ f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional closed )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) )
meets Q : ( ( ) (
functional )
Subset of ) &
f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) ) is
being_S-Seq &
Q : ( ( ) (
functional )
Subset of ) is
closed &
Last_Point (
(L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) ) : ( ( ) (
functional closed )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) ,
(f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) /. 1 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) ,
(f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) ) : ( ( ) ( V10() V11() V12() ext-real V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) ,
Q : ( ( ) (
functional )
Subset of ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) )
in LSeg (
f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) ) ,
i : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
functional closed )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) & 1 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
<= i : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) &
i : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
+ 1 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
<= len f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) &
q : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) )
in LSeg (
f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) ) ,
j : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
functional closed )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) & 1 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
<= j : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) &
j : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
+ 1 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
<= len f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) &
q : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) )
in Q : ( ( ) (
functional )
Subset of ) &
Last_Point (
(L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) ) : ( ( ) (
functional closed )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) ,
(f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) /. 1 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) ,
(f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) ) : ( ( ) ( V10() V11() V12() ext-real V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) ,
Q : ( ( ) (
functional )
Subset of ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) )
<> q : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) holds
(
i : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
>= j : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) & (
i : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
= j : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) implies
LE q : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
Last_Point (
(L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) ) : ( ( ) (
functional closed )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) ,
(f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) /. 1 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) ,
(f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) ) : ( ( ) ( V10() V11() V12() ext-real V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) ,
Q : ( ( ) (
functional )
Subset of ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) )
/. i : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) ,
f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) )
/. (i : ( ( ) ( V10() V11() V12() ext-real V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) ) ) ;
theorem
for
f being ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) )
for
q1,
q2 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) )
for
i being ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) st
q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) )
in LSeg (
f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) ) ,
i : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
functional closed )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) &
q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) )
in LSeg (
f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) ) ,
i : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
functional closed )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) &
f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) ) is
being_S-Seq & 1 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
<= i : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) &
i : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
+ 1 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
<= len f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) &
LE q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
L~ f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional closed )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) ,
f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) )
/. 1 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) ,
f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) )
/. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) ) : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) holds
LE q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
LSeg (
f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) ) ,
i : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
functional closed )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) ,
f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) )
/. i : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) ,
f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) )
/. (i : ( ( ) ( V10() V11() V12() ext-real V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) ;
theorem
for
f being ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) )
for
q1,
q2 being ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) st
q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) )
in L~ f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional closed )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) &
q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) )
in L~ f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional closed )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) &
f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) ) is
being_S-Seq &
q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) )
<> q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) holds
(
LE q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
L~ f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
functional closed )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) ,
f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) )
/. 1 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) ,
f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) )
/. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict ) RLTopStruct ) : ( ( ) ( non empty functional ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( non empty functional ) set ) ) ) : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) iff for
i,
j being ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) st
q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) )
in LSeg (
f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) ) ,
i : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
functional closed )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) &
q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) )
in LSeg (
f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) ) ,
j : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
functional closed )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) : ( ( ) ( )
set ) ) & 1 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
<= i : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) &
i : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
+ 1 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
<= len f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) & 1 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
<= j : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) &
j : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
+ 1 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
<= len f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) ) : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) holds
(
i : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
<= j : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) & (
i : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) )
= j : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) implies
LE q1 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
q2 : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Point of ( ( ) ( non
empty functional )
set ) ) ,
f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) )
/. i : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) ,
f : ( ( ) (
Relation-like NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set )
-valued Function-like FinSequence-like )
FinSequence of ( ( ) ( non
empty functional )
set ) )
/. (i : ( ( ) ( V10() V11() V12() ext-real V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V10()
V11()
V12()
ext-real V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
Relation-like Function-like V43(2 : ( ( ) ( non
empty V10()
V11()
V12()
ext-real positive non
negative V79()
V80()
V142()
V143()
V144()
V145()
V146()
V147() )
Element of
NAT : ( ( ) (
V142()
V143()
V144()
V145()
V146()
V147()
V148() )
Element of
K6(
REAL : ( ( ) (
V142()
V143()
V144()
V148() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V134() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() ) Element of NAT : ( ( ) ( V142() V143() V144() V145() V146() V147() V148() ) Element of K6(REAL : ( ( ) ( V142() V143() V144() V148() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V108()
V154()
V155()
V156()
V157()
V158()
V159()
V160()
strict )
RLTopStruct ) : ( ( ) ( non
empty functional )
set ) ) ) ) ) ;