begin
definition
let C be ( (
being_simple_closed_curve ) ( non
empty proper closed connected bounded being_simple_closed_curve compact V233()
V234() )
Subset of ) ;
func Y-InitStart C -> ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative V49()
V130()
V131()
V132()
V133()
V134()
V135()
bounded_below )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V130()
V131()
V132()
V133()
V134()
V135()
V136()
left_end bounded_below )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V130()
V131()
V132()
V136() non
bounded_below non
bounded_above interval )
set ) ) : ( ( ) ( non
empty )
set ) ) )
means
(
it : ( ( ) ( )
Element of
C : ( ( ) ( )
RLTopStruct ) )
< width (Gauge (C : ( ( ) ( ) RLTopStruct ) ,(ApproxIndex C : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative V49() V130() V131() V132() V133() V134() V135() bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) )) : ( (
tabular ) (
V21()
V24(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V130()
V131()
V132()
V133()
V134()
V135()
V136()
left_end bounded_below )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V130()
V131()
V132()
V136() non
bounded_below non
bounded_above interval )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V25(
K292( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_2 V153()
V178()
V179()
V180()
V181()
V182()
V183()
V184()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V29() )
set ) ) : ( ( ) ( )
M9( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_2 V153()
V178()
V179()
V180()
V181()
V182()
V183()
V184()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V29() )
set ) )) )
V26()
FinSequence-like tabular )
FinSequence of
K292( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_2 V153()
V178()
V179()
V180()
V181()
V182()
V183()
V184()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V29() )
set ) ) : ( ( ) ( )
M9( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_2 V153()
V178()
V179()
V180()
V181()
V182()
V183()
V184()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V29() )
set ) )) ) : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative V49()
V130()
V131()
V132()
V133()
V134()
V135()
bounded_below )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V130()
V131()
V132()
V133()
V134()
V135()
V136()
left_end bounded_below )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V130()
V131()
V132()
V136() non
bounded_below non
bounded_above interval )
set ) ) : ( ( ) ( non
empty )
set ) ) ) &
cell (
(Gauge (C : ( ( ) ( ) RLTopStruct ) ,(ApproxIndex C : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative V49() V130() V131() V132() V133() V134() V135() bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) )) : ( (
tabular ) (
V21()
V24(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V130()
V131()
V132()
V133()
V134()
V135()
V136()
left_end bounded_below )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V130()
V131()
V132()
V136() non
bounded_below non
bounded_above interval )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V25(
K292( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_2 V153()
V178()
V179()
V180()
V181()
V182()
V183()
V184()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V29() )
set ) ) : ( ( ) ( )
M9( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_2 V153()
V178()
V179()
V180()
V181()
V182()
V183()
V184()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V29() )
set ) )) )
V26()
FinSequence-like tabular )
FinSequence of
K292( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_2 V153()
V178()
V179()
V180()
V181()
V182()
V183()
V184()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V29() )
set ) ) : ( ( ) ( )
M9( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_2 V153()
V178()
V179()
V180()
V181()
V182()
V183()
V184()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V29() )
set ) )) ) ,
((X-SpanStart (C : ( ( ) ( ) RLTopStruct ) ,(ApproxIndex C : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative V49() V130() V131() V132() V133() V134() V135() bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) )) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative V49() V130() V131() V132() V133() V134() V135() bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) -' 1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative V49()
V130()
V131()
V132()
V133()
V134()
V135()
bounded_below )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V130()
V131()
V132()
V133()
V134()
V135()
V136()
left_end bounded_below )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V130()
V131()
V132()
V136() non
bounded_below non
bounded_above interval )
set ) ) : ( ( ) ( non
empty )
set ) ) ) ,
it : ( ( ) ( )
Element of
C : ( ( ) ( )
RLTopStruct ) ) ) : ( ( ) ( )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_2 V153()
V178()
V179()
V180()
V181()
V182()
V183()
V184()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V29() )
set ) ) : ( ( ) ( non
empty )
set ) )
c= BDD C : ( ( ) ( )
RLTopStruct ) : ( ( ) ( )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_2 V153()
V178()
V179()
V180()
V181()
V182()
V183()
V184()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V29() )
set ) ) : ( ( ) ( non
empty )
set ) ) & ( for
j being ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative V49()
V130()
V131()
V132()
V133()
V134()
V135()
bounded_below )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V130()
V131()
V132()
V133()
V134()
V135()
V136()
left_end bounded_below )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V130()
V131()
V132()
V136() non
bounded_below non
bounded_above interval )
set ) ) : ( ( ) ( non
empty )
set ) ) ) st
j : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative V49()
V130()
V131()
V132()
V133()
V134()
V135()
bounded_below )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V130()
V131()
V132()
V133()
V134()
V135()
V136()
left_end bounded_below )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V130()
V131()
V132()
V136() non
bounded_below non
bounded_above interval )
set ) ) : ( ( ) ( non
empty )
set ) ) )
< width (Gauge (C : ( ( ) ( ) RLTopStruct ) ,(ApproxIndex C : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative V49() V130() V131() V132() V133() V134() V135() bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) )) : ( (
tabular ) (
V21()
V24(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V130()
V131()
V132()
V133()
V134()
V135()
V136()
left_end bounded_below )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V130()
V131()
V132()
V136() non
bounded_below non
bounded_above interval )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V25(
K292( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_2 V153()
V178()
V179()
V180()
V181()
V182()
V183()
V184()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V29() )
set ) ) : ( ( ) ( )
M9( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_2 V153()
V178()
V179()
V180()
V181()
V182()
V183()
V184()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V29() )
set ) )) )
V26()
FinSequence-like tabular )
FinSequence of
K292( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_2 V153()
V178()
V179()
V180()
V181()
V182()
V183()
V184()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V29() )
set ) ) : ( ( ) ( )
M9( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_2 V153()
V178()
V179()
V180()
V181()
V182()
V183()
V184()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V29() )
set ) )) ) : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative V49()
V130()
V131()
V132()
V133()
V134()
V135()
bounded_below )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V130()
V131()
V132()
V133()
V134()
V135()
V136()
left_end bounded_below )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V130()
V131()
V132()
V136() non
bounded_below non
bounded_above interval )
set ) ) : ( ( ) ( non
empty )
set ) ) ) &
cell (
(Gauge (C : ( ( ) ( ) RLTopStruct ) ,(ApproxIndex C : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative V49() V130() V131() V132() V133() V134() V135() bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) )) : ( (
tabular ) (
V21()
V24(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V130()
V131()
V132()
V133()
V134()
V135()
V136()
left_end bounded_below )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V130()
V131()
V132()
V136() non
bounded_below non
bounded_above interval )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V25(
K292( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_2 V153()
V178()
V179()
V180()
V181()
V182()
V183()
V184()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V29() )
set ) ) : ( ( ) ( )
M9( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_2 V153()
V178()
V179()
V180()
V181()
V182()
V183()
V184()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V29() )
set ) )) )
V26()
FinSequence-like tabular )
FinSequence of
K292( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_2 V153()
V178()
V179()
V180()
V181()
V182()
V183()
V184()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V29() )
set ) ) : ( ( ) ( )
M9( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_2 V153()
V178()
V179()
V180()
V181()
V182()
V183()
V184()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V29() )
set ) )) ) ,
((X-SpanStart (C : ( ( ) ( ) RLTopStruct ) ,(ApproxIndex C : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative V49() V130() V131() V132() V133() V134() V135() bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) )) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative V49() V130() V131() V132() V133() V134() V135() bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) -' 1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative V49()
V130()
V131()
V132()
V133()
V134()
V135()
bounded_below )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V130()
V131()
V132()
V133()
V134()
V135()
V136()
left_end bounded_below )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V130()
V131()
V132()
V136() non
bounded_below non
bounded_above interval )
set ) ) : ( ( ) ( non
empty )
set ) ) ) ,
j : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative V49()
V130()
V131()
V132()
V133()
V134()
V135()
bounded_below )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V130()
V131()
V132()
V133()
V134()
V135()
V136()
left_end bounded_below )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V130()
V131()
V132()
V136() non
bounded_below non
bounded_above interval )
set ) ) : ( ( ) ( non
empty )
set ) ) ) ) : ( ( ) ( )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_2 V153()
V178()
V179()
V180()
V181()
V182()
V183()
V184()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V29() )
set ) ) : ( ( ) ( non
empty )
set ) )
c= BDD C : ( ( ) ( )
RLTopStruct ) : ( ( ) ( )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_2 V153()
V178()
V179()
V180()
V181()
V182()
V183()
V184()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V29() )
set ) ) : ( ( ) ( non
empty )
set ) ) holds
j : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative V49()
V130()
V131()
V132()
V133()
V134()
V135()
bounded_below )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V130()
V131()
V132()
V133()
V134()
V135()
V136()
left_end bounded_below )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V130()
V131()
V132()
V136() non
bounded_below non
bounded_above interval )
set ) ) : ( ( ) ( non
empty )
set ) ) )
>= it : ( ( ) ( )
Element of
C : ( ( ) ( )
RLTopStruct ) ) ) );
end;
definition
let C be ( (
being_simple_closed_curve ) ( non
empty proper closed connected bounded being_simple_closed_curve compact V233()
V234() )
Subset of ) ;
let n be ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative V49()
V130()
V131()
V132()
V133()
V134()
V135()
bounded_below )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V130()
V131()
V132()
V133()
V134()
V135()
V136()
left_end bounded_below )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V130()
V131()
V132()
V136() non
bounded_below non
bounded_above interval )
set ) ) : ( ( ) ( non
empty )
set ) ) ) ;
assume
n : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative V49()
V130()
V131()
V132()
V133()
V134()
V135()
bounded_below )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V130()
V131()
V132()
V133()
V134()
V135()
V136()
left_end bounded_below )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V130()
V131()
V132()
V136() non
bounded_below non
bounded_above interval )
set ) ) : ( ( ) ( non
empty )
set ) ) )
is_sufficiently_large_for C : ( (
being_simple_closed_curve ) ( non
empty proper closed connected bounded being_simple_closed_curve compact V233()
V234() )
Subset of )
;
func Y-SpanStart (
C,
n)
-> ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative V49()
V130()
V131()
V132()
V133()
V134()
V135()
bounded_below )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V130()
V131()
V132()
V133()
V134()
V135()
V136()
left_end bounded_below )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V130()
V131()
V132()
V136() non
bounded_below non
bounded_above interval )
set ) ) : ( ( ) ( non
empty )
set ) ) )
means
(
it : ( (
V26()
V46(
K7(
C : ( ( ) ( )
RLTopStruct ) ,
C : ( ( ) ( )
RLTopStruct ) ) : ( ( ) ( )
set ) ,
C : ( ( ) ( )
RLTopStruct ) ) ) (
V21()
V24(
K7(
C : ( ( ) ( )
RLTopStruct ) ,
C : ( ( ) ( )
RLTopStruct ) ) : ( ( ) ( )
set ) )
V25(
C : ( ( ) ( )
RLTopStruct ) )
V26()
V46(
K7(
C : ( ( ) ( )
RLTopStruct ) ,
C : ( ( ) ( )
RLTopStruct ) ) : ( ( ) ( )
set ) ,
C : ( ( ) ( )
RLTopStruct ) ) )
Element of
K6(
K7(
K7(
C : ( ( ) ( )
RLTopStruct ) ,
C : ( ( ) ( )
RLTopStruct ) ) : ( ( ) ( )
set ) ,
C : ( ( ) ( )
RLTopStruct ) ) : ( ( ) ( )
set ) ) : ( ( ) ( non
empty )
set ) )
<= width (Gauge (C : ( ( ) ( ) RLTopStruct ) ,n : ( ( ) ( ) Element of C : ( ( ) ( ) RLTopStruct ) ) )) : ( (
tabular ) (
V21()
V24(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V130()
V131()
V132()
V133()
V134()
V135()
V136()
left_end bounded_below )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V130()
V131()
V132()
V136() non
bounded_below non
bounded_above interval )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V25(
K292( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_2 V153()
V178()
V179()
V180()
V181()
V182()
V183()
V184()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V29() )
set ) ) : ( ( ) ( )
M9( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_2 V153()
V178()
V179()
V180()
V181()
V182()
V183()
V184()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V29() )
set ) )) )
V26()
FinSequence-like tabular )
FinSequence of
K292( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_2 V153()
V178()
V179()
V180()
V181()
V182()
V183()
V184()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V29() )
set ) ) : ( ( ) ( )
M9( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_2 V153()
V178()
V179()
V180()
V181()
V182()
V183()
V184()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V29() )
set ) )) ) : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative V49()
V130()
V131()
V132()
V133()
V134()
V135()
bounded_below )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V130()
V131()
V132()
V133()
V134()
V135()
V136()
left_end bounded_below )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V130()
V131()
V132()
V136() non
bounded_below non
bounded_above interval )
set ) ) : ( ( ) ( non
empty )
set ) ) ) & ( for
k being ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative V49()
V130()
V131()
V132()
V133()
V134()
V135()
bounded_below )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V130()
V131()
V132()
V133()
V134()
V135()
V136()
left_end bounded_below )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V130()
V131()
V132()
V136() non
bounded_below non
bounded_above interval )
set ) ) : ( ( ) ( non
empty )
set ) ) ) st
it : ( (
V26()
V46(
K7(
C : ( ( ) ( )
RLTopStruct ) ,
C : ( ( ) ( )
RLTopStruct ) ) : ( ( ) ( )
set ) ,
C : ( ( ) ( )
RLTopStruct ) ) ) (
V21()
V24(
K7(
C : ( ( ) ( )
RLTopStruct ) ,
C : ( ( ) ( )
RLTopStruct ) ) : ( ( ) ( )
set ) )
V25(
C : ( ( ) ( )
RLTopStruct ) )
V26()
V46(
K7(
C : ( ( ) ( )
RLTopStruct ) ,
C : ( ( ) ( )
RLTopStruct ) ) : ( ( ) ( )
set ) ,
C : ( ( ) ( )
RLTopStruct ) ) )
Element of
K6(
K7(
K7(
C : ( ( ) ( )
RLTopStruct ) ,
C : ( ( ) ( )
RLTopStruct ) ) : ( ( ) ( )
set ) ,
C : ( ( ) ( )
RLTopStruct ) ) : ( ( ) ( )
set ) ) : ( ( ) ( non
empty )
set ) )
<= k : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative V49()
V130()
V131()
V132()
V133()
V134()
V135()
bounded_below )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V130()
V131()
V132()
V133()
V134()
V135()
V136()
left_end bounded_below )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V130()
V131()
V132()
V136() non
bounded_below non
bounded_above interval )
set ) ) : ( ( ) ( non
empty )
set ) ) ) &
k : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative V49()
V130()
V131()
V132()
V133()
V134()
V135()
bounded_below )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V130()
V131()
V132()
V133()
V134()
V135()
V136()
left_end bounded_below )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V130()
V131()
V132()
V136() non
bounded_below non
bounded_above interval )
set ) ) : ( ( ) ( non
empty )
set ) ) )
<= ((2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) |^ (n : ( ( ) ( ) Element of C : ( ( ) ( ) RLTopStruct ) ) -' (ApproxIndex C : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative V49() V130() V131() V132() V133() V134() V135() bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative V49() V130() V131() V132() V133() V134() V135() bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative V49() V130() V131() V132() V133() V134() V135() bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) * ((Y-InitStart C : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative V49() V130() V131() V132() V133() V134() V135() bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) -' 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative V49() V130() V131() V132() V133() V134() V135() bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative V49()
V130()
V131()
V132()
V133()
V134()
V135()
bounded_below )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V130()
V131()
V132()
V133()
V134()
V135()
V136()
left_end bounded_below )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V130()
V131()
V132()
V136() non
bounded_below non
bounded_above interval )
set ) ) : ( ( ) ( non
empty )
set ) ) )
+ 2 : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real positive non
negative V49()
V130()
V131()
V132()
V133()
V134()
V135()
left_end bounded_below )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V130()
V131()
V132()
V133()
V134()
V135()
V136()
left_end bounded_below )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V130()
V131()
V132()
V136() non
bounded_below non
bounded_above interval )
set ) ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real positive non
negative V49()
V130()
V131()
V132()
V133()
V134()
V135()
left_end bounded_below )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V130()
V131()
V132()
V133()
V134()
V135()
V136()
left_end bounded_below )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V130()
V131()
V132()
V136() non
bounded_below non
bounded_above interval )
set ) ) : ( ( ) ( non
empty )
set ) ) ) holds
cell (
(Gauge (C : ( ( ) ( ) RLTopStruct ) ,n : ( ( ) ( ) Element of C : ( ( ) ( ) RLTopStruct ) ) )) : ( (
tabular ) (
V21()
V24(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V130()
V131()
V132()
V133()
V134()
V135()
V136()
left_end bounded_below )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V130()
V131()
V132()
V136() non
bounded_below non
bounded_above interval )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V25(
K292( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_2 V153()
V178()
V179()
V180()
V181()
V182()
V183()
V184()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V29() )
set ) ) : ( ( ) ( )
M9( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_2 V153()
V178()
V179()
V180()
V181()
V182()
V183()
V184()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V29() )
set ) )) )
V26()
FinSequence-like tabular )
FinSequence of
K292( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_2 V153()
V178()
V179()
V180()
V181()
V182()
V183()
V184()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V29() )
set ) ) : ( ( ) ( )
M9( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_2 V153()
V178()
V179()
V180()
V181()
V182()
V183()
V184()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V29() )
set ) )) ) ,
((X-SpanStart (C : ( ( ) ( ) RLTopStruct ) ,n : ( ( ) ( ) Element of C : ( ( ) ( ) RLTopStruct ) ) )) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative V49() V130() V131() V132() V133() V134() V135() bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) -' 1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative V49()
V130()
V131()
V132()
V133()
V134()
V135()
bounded_below )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V130()
V131()
V132()
V133()
V134()
V135()
V136()
left_end bounded_below )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V130()
V131()
V132()
V136() non
bounded_below non
bounded_above interval )
set ) ) : ( ( ) ( non
empty )
set ) ) ) ,
k : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative V49()
V130()
V131()
V132()
V133()
V134()
V135()
bounded_below )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V130()
V131()
V132()
V133()
V134()
V135()
V136()
left_end bounded_below )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V130()
V131()
V132()
V136() non
bounded_below non
bounded_above interval )
set ) ) : ( ( ) ( non
empty )
set ) ) ) ) : ( ( ) ( )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_2 V153()
V178()
V179()
V180()
V181()
V182()
V183()
V184()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V29() )
set ) ) : ( ( ) ( non
empty )
set ) )
c= BDD C : ( ( ) ( )
RLTopStruct ) : ( ( ) ( )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_2 V153()
V178()
V179()
V180()
V181()
V182()
V183()
V184()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V29() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) & ( for
j being ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative V49()
V130()
V131()
V132()
V133()
V134()
V135()
bounded_below )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V130()
V131()
V132()
V133()
V134()
V135()
V136()
left_end bounded_below )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V130()
V131()
V132()
V136() non
bounded_below non
bounded_above interval )
set ) ) : ( ( ) ( non
empty )
set ) ) ) st
j : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative V49()
V130()
V131()
V132()
V133()
V134()
V135()
bounded_below )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V130()
V131()
V132()
V133()
V134()
V135()
V136()
left_end bounded_below )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V130()
V131()
V132()
V136() non
bounded_below non
bounded_above interval )
set ) ) : ( ( ) ( non
empty )
set ) ) )
<= width (Gauge (C : ( ( ) ( ) RLTopStruct ) ,n : ( ( ) ( ) Element of C : ( ( ) ( ) RLTopStruct ) ) )) : ( (
tabular ) (
V21()
V24(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V130()
V131()
V132()
V133()
V134()
V135()
V136()
left_end bounded_below )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V130()
V131()
V132()
V136() non
bounded_below non
bounded_above interval )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V25(
K292( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_2 V153()
V178()
V179()
V180()
V181()
V182()
V183()
V184()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V29() )
set ) ) : ( ( ) ( )
M9( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_2 V153()
V178()
V179()
V180()
V181()
V182()
V183()
V184()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V29() )
set ) )) )
V26()
FinSequence-like tabular )
FinSequence of
K292( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_2 V153()
V178()
V179()
V180()
V181()
V182()
V183()
V184()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V29() )
set ) ) : ( ( ) ( )
M9( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_2 V153()
V178()
V179()
V180()
V181()
V182()
V183()
V184()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V29() )
set ) )) ) : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative V49()
V130()
V131()
V132()
V133()
V134()
V135()
bounded_below )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V130()
V131()
V132()
V133()
V134()
V135()
V136()
left_end bounded_below )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V130()
V131()
V132()
V136() non
bounded_below non
bounded_above interval )
set ) ) : ( ( ) ( non
empty )
set ) ) ) & ( for
k being ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative V49()
V130()
V131()
V132()
V133()
V134()
V135()
bounded_below )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V130()
V131()
V132()
V133()
V134()
V135()
V136()
left_end bounded_below )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V130()
V131()
V132()
V136() non
bounded_below non
bounded_above interval )
set ) ) : ( ( ) ( non
empty )
set ) ) ) st
j : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative V49()
V130()
V131()
V132()
V133()
V134()
V135()
bounded_below )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V130()
V131()
V132()
V133()
V134()
V135()
V136()
left_end bounded_below )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V130()
V131()
V132()
V136() non
bounded_below non
bounded_above interval )
set ) ) : ( ( ) ( non
empty )
set ) ) )
<= k : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative V49()
V130()
V131()
V132()
V133()
V134()
V135()
bounded_below )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V130()
V131()
V132()
V133()
V134()
V135()
V136()
left_end bounded_below )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V130()
V131()
V132()
V136() non
bounded_below non
bounded_above interval )
set ) ) : ( ( ) ( non
empty )
set ) ) ) &
k : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative V49()
V130()
V131()
V132()
V133()
V134()
V135()
bounded_below )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V130()
V131()
V132()
V133()
V134()
V135()
V136()
left_end bounded_below )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V130()
V131()
V132()
V136() non
bounded_below non
bounded_above interval )
set ) ) : ( ( ) ( non
empty )
set ) ) )
<= ((2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) |^ (n : ( ( ) ( ) Element of C : ( ( ) ( ) RLTopStruct ) ) -' (ApproxIndex C : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative V49() V130() V131() V132() V133() V134() V135() bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative V49() V130() V131() V132() V133() V134() V135() bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative V49() V130() V131() V132() V133() V134() V135() bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) * ((Y-InitStart C : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative V49() V130() V131() V132() V133() V134() V135() bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) -' 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative V49() V130() V131() V132() V133() V134() V135() bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative V49()
V130()
V131()
V132()
V133()
V134()
V135()
bounded_below )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V130()
V131()
V132()
V133()
V134()
V135()
V136()
left_end bounded_below )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V130()
V131()
V132()
V136() non
bounded_below non
bounded_above interval )
set ) ) : ( ( ) ( non
empty )
set ) ) )
+ 2 : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real positive non
negative V49()
V130()
V131()
V132()
V133()
V134()
V135()
left_end bounded_below )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V130()
V131()
V132()
V133()
V134()
V135()
V136()
left_end bounded_below )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V130()
V131()
V132()
V136() non
bounded_below non
bounded_above interval )
set ) ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real positive non
negative V49()
V130()
V131()
V132()
V133()
V134()
V135()
left_end bounded_below )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V130()
V131()
V132()
V133()
V134()
V135()
V136()
left_end bounded_below )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V130()
V131()
V132()
V136() non
bounded_below non
bounded_above interval )
set ) ) : ( ( ) ( non
empty )
set ) ) ) holds
cell (
(Gauge (C : ( ( ) ( ) RLTopStruct ) ,n : ( ( ) ( ) Element of C : ( ( ) ( ) RLTopStruct ) ) )) : ( (
tabular ) (
V21()
V24(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V130()
V131()
V132()
V133()
V134()
V135()
V136()
left_end bounded_below )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V130()
V131()
V132()
V136() non
bounded_below non
bounded_above interval )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V25(
K292( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_2 V153()
V178()
V179()
V180()
V181()
V182()
V183()
V184()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V29() )
set ) ) : ( ( ) ( )
M9( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_2 V153()
V178()
V179()
V180()
V181()
V182()
V183()
V184()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V29() )
set ) )) )
V26()
FinSequence-like tabular )
FinSequence of
K292( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_2 V153()
V178()
V179()
V180()
V181()
V182()
V183()
V184()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V29() )
set ) ) : ( ( ) ( )
M9( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_2 V153()
V178()
V179()
V180()
V181()
V182()
V183()
V184()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V29() )
set ) )) ) ,
((X-SpanStart (C : ( ( ) ( ) RLTopStruct ) ,n : ( ( ) ( ) Element of C : ( ( ) ( ) RLTopStruct ) ) )) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative V49() V130() V131() V132() V133() V134() V135() bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) -' 1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative V49()
V130()
V131()
V132()
V133()
V134()
V135()
bounded_below )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V130()
V131()
V132()
V133()
V134()
V135()
V136()
left_end bounded_below )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V130()
V131()
V132()
V136() non
bounded_below non
bounded_above interval )
set ) ) : ( ( ) ( non
empty )
set ) ) ) ,
k : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative V49()
V130()
V131()
V132()
V133()
V134()
V135()
bounded_below )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V130()
V131()
V132()
V133()
V134()
V135()
V136()
left_end bounded_below )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V130()
V131()
V132()
V136() non
bounded_below non
bounded_above interval )
set ) ) : ( ( ) ( non
empty )
set ) ) ) ) : ( ( ) ( )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_2 V153()
V178()
V179()
V180()
V181()
V182()
V183()
V184()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V29() )
set ) ) : ( ( ) ( non
empty )
set ) )
c= BDD C : ( ( ) ( )
RLTopStruct ) : ( ( ) ( )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative V49() V130() V131() V132() V133() V134() V135() left_end bounded_below ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V130() V131() V132() V133() V134() V135() V136() left_end bounded_below ) Element of K6(REAL : ( ( ) ( non empty V34() V130() V131() V132() V136() non bounded_below non bounded_above interval ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_2 V153()
V178()
V179()
V180()
V181()
V182()
V183()
V184()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V29() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) holds
j : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative V49()
V130()
V131()
V132()
V133()
V134()
V135()
bounded_below )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V130()
V131()
V132()
V133()
V134()
V135()
V136()
left_end bounded_below )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V130()
V131()
V132()
V136() non
bounded_below non
bounded_above interval )
set ) ) : ( ( ) ( non
empty )
set ) ) )
>= it : ( (
V26()
V46(
K7(
C : ( ( ) ( )
RLTopStruct ) ,
C : ( ( ) ( )
RLTopStruct ) ) : ( ( ) ( )
set ) ,
C : ( ( ) ( )
RLTopStruct ) ) ) (
V21()
V24(
K7(
C : ( ( ) ( )
RLTopStruct ) ,
C : ( ( ) ( )
RLTopStruct ) ) : ( ( ) ( )
set ) )
V25(
C : ( ( ) ( )
RLTopStruct ) )
V26()
V46(
K7(
C : ( ( ) ( )
RLTopStruct ) ,
C : ( ( ) ( )
RLTopStruct ) ) : ( ( ) ( )
set ) ,
C : ( ( ) ( )
RLTopStruct ) ) )
Element of
K6(
K7(
K7(
C : ( ( ) ( )
RLTopStruct ) ,
C : ( ( ) ( )
RLTopStruct ) ) : ( ( ) ( )
set ) ,
C : ( ( ) ( )
RLTopStruct ) ) : ( ( ) ( )
set ) ) : ( ( ) ( non
empty )
set ) ) ) );
end;
begin