begin
begin
begin
theorem
for
i,
k being ( ( ) (
V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real V92()
V93()
V94()
V95()
V96()
V97()
V98() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V93()
V94()
V95()
V96()
V97()
V98()
V99() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V93()
V94()
V95()
V99() )
set ) ) : ( ( ) ( )
set ) ) )
for
C being ( ( non
empty being_simple_closed_curve compact non
horizontal non
vertical ) ( non
empty connected bounded being_simple_closed_curve compact non
horizontal non
vertical )
Subset of )
for
p being ( ( ) (
V33(2 : ( ( ) ( non
empty V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real positive V92()
V93()
V94()
V95()
V96()
V97()
V98() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V93()
V94()
V95()
V96()
V97()
V98()
V99() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V93()
V94()
V95()
V99() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V84() )
Point of ( ( ) ( non
empty V2() )
set ) ) st
p : ( ( ) (
V33(2 : ( ( ) ( non
empty V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real positive V92()
V93()
V94()
V95()
V96()
V97()
V98() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V93()
V94()
V95()
V96()
V97()
V98()
V99() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V93()
V94()
V95()
V99() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V84() )
Point of ( ( ) ( non
empty V2() )
set ) )
`1 : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) ( non
empty V26()
V93()
V94()
V95()
V99() )
set ) )
= ((W-bound C : ( ( non empty being_simple_closed_curve compact non horizontal non vertical ) ( non empty connected bounded being_simple_closed_curve compact non horizontal non vertical ) Subset of ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) + (E-bound C : ( ( non empty being_simple_closed_curve compact non horizontal non vertical ) ( non empty connected bounded being_simple_closed_curve compact non horizontal non vertical ) Subset of ) ) : ( ( ) ( V11() V12() ext-real ) Element of REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) ( non
empty V26()
V93()
V94()
V95()
V99() )
set ) )
/ 2 : ( ( ) ( non
empty V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real positive V92()
V93()
V94()
V95()
V96()
V97()
V98() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V93()
V94()
V95()
V96()
V97()
V98()
V99() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V93()
V94()
V95()
V99() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) ( non
empty V26()
V93()
V94()
V95()
V99() )
set ) ) &
i : ( ( ) (
V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real V92()
V93()
V94()
V95()
V96()
V97()
V98() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V93()
V94()
V95()
V96()
V97()
V98()
V99() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V93()
V94()
V95()
V99() )
set ) ) : ( ( ) ( )
set ) ) )
> 0 : ( ( ) (
empty V4()
V5()
V6()
V8()
V9()
V10()
V11()
V12()
Function-like functional V37()
ext-real V92()
V93()
V94()
V95()
V96()
V97()
V98()
V99() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V93()
V94()
V95()
V96()
V97()
V98()
V99() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V93()
V94()
V95()
V99() )
set ) ) : ( ( ) ( )
set ) ) ) & 1 : ( ( ) ( non
empty V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real positive V92()
V93()
V94()
V95()
V96()
V97()
V98() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V93()
V94()
V95()
V96()
V97()
V98()
V99() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V93()
V94()
V95()
V99() )
set ) ) : ( ( ) ( )
set ) ) )
<= k : ( ( ) (
V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real V92()
V93()
V94()
V95()
V96()
V97()
V98() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V93()
V94()
V95()
V96()
V97()
V98()
V99() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V93()
V94()
V95()
V99() )
set ) ) : ( ( ) ( )
set ) ) ) &
k : ( ( ) (
V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real V92()
V93()
V94()
V95()
V96()
V97()
V98() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V93()
V94()
V95()
V96()
V97()
V98()
V99() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V93()
V94()
V95()
V99() )
set ) ) : ( ( ) ( )
set ) ) )
<= width (Gauge (C : ( ( non empty being_simple_closed_curve compact non horizontal non vertical ) ( non empty connected bounded being_simple_closed_curve compact non horizontal non vertical ) Subset of ) ,i : ( ( ) ( V4() V5() V6() V10() V11() V12() V37() ext-real V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( (
tabular ) (
V13() non
empty-yielding V16(
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V93()
V94()
V95()
V96()
V97()
V98()
V99() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V93()
V94()
V95()
V99() )
set ) ) : ( ( ) ( )
set ) ) )
V17(
K286( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V49()
TopSpace-like V131()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2() )
set ) ) : ( ( ) ( )
M11( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V49()
TopSpace-like V131()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2() )
set ) )) )
Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column )
FinSequence of
K286( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V49()
TopSpace-like V131()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2() )
set ) ) : ( ( ) ( )
M11( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V49()
TopSpace-like V131()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2() )
set ) )) ) : ( ( ) (
V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real V92()
V93()
V94()
V95()
V96()
V97()
V98() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V93()
V94()
V95()
V96()
V97()
V98()
V99() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V93()
V94()
V95()
V99() )
set ) ) : ( ( ) ( )
set ) ) ) &
(Gauge (C : ( ( non empty being_simple_closed_curve compact non horizontal non vertical ) ( non empty connected bounded being_simple_closed_curve compact non horizontal non vertical ) Subset of ) ,i : ( ( ) ( V4() V5() V6() V10() V11() V12() V37() ext-real V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( (
tabular ) (
V13() non
empty-yielding V16(
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V93()
V94()
V95()
V96()
V97()
V98()
V99() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V93()
V94()
V95()
V99() )
set ) ) : ( ( ) ( )
set ) ) )
V17(
K286( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V49()
TopSpace-like V131()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2() )
set ) ) : ( ( ) ( )
M11( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V49()
TopSpace-like V131()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2() )
set ) )) )
Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column )
FinSequence of
K286( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V49()
TopSpace-like V131()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2() )
set ) ) : ( ( ) ( )
M11( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V49()
TopSpace-like V131()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2() )
set ) )) )
* (
(Center (Gauge (C : ( ( non empty being_simple_closed_curve compact non horizontal non vertical ) ( non empty connected bounded being_simple_closed_curve compact non horizontal non vertical ) Subset of ) ,i : ( ( ) ( V4() V5() V6() V10() V11() V12() V37() ext-real V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V13() non empty-yielding V16( NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) V17(K286( the U1 of (TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V49() TopSpace-like V131() V156() V157() V158() V159() V160() V161() V162() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() ) set ) ) : ( ( ) ( ) M11( the U1 of (TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V49() TopSpace-like V131() V156() V157() V158() V159() V160() V161() V162() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K286( the U1 of (TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V49() TopSpace-like V131() V156() V157() V158() V159() V160() V161() V162() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() ) set ) ) : ( ( ) ( ) M11( the U1 of (TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V49() TopSpace-like V131() V156() V157() V158() V159() V160() V161() V162() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() ) set ) )) ) ) : ( ( ) (
V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real V92()
V93()
V94()
V95()
V96()
V97()
V98() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V93()
V94()
V95()
V96()
V97()
V98()
V99() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V93()
V94()
V95()
V99() )
set ) ) : ( ( ) ( )
set ) ) ) ,
k : ( ( ) (
V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real V92()
V93()
V94()
V95()
V96()
V97()
V98() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V93()
V94()
V95()
V96()
V97()
V98()
V99() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V93()
V94()
V95()
V99() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
V33(2 : ( ( ) ( non
empty V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real positive V92()
V93()
V94()
V95()
V96()
V97()
V98() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V93()
V94()
V95()
V96()
V97()
V98()
V99() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V93()
V94()
V95()
V99() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V84() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V49()
TopSpace-like V131()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2() )
set ) )
in Upper_Arc (L~ (Cage (C : ( ( non empty being_simple_closed_curve compact non horizontal non vertical ) ( non empty connected bounded being_simple_closed_curve compact non horizontal non vertical ) Subset of ) ,i : ( ( ) ( V4() V5() V6() V10() V11() V12() V37() ext-real V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard clockwise_oriented ) ( non empty V2() V13() V16( NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) V17( the U1 of (TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V49() TopSpace-like V131() V156() V157() V158() V159() V160() V161() V162() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() ) set ) ) Function-like non constant FinSequence-like circular special unfolded s.c.c. standard clockwise_oriented ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V49() TopSpace-like V131() V156() V157() V158() V159() V160() V161() V162() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() ) set ) ) ) : ( ( ) ( non
empty boundary connected bounded being_simple_closed_curve compact )
Element of
K6( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V49()
TopSpace-like V131()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2() )
set ) ) : ( ( ) ( )
set ) ) : ( ( non
empty ) ( non
empty )
Element of
K6( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V49()
TopSpace-like V131()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2() )
set ) ) : ( ( ) ( )
set ) ) &
p : ( ( ) (
V33(2 : ( ( ) ( non
empty V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real positive V92()
V93()
V94()
V95()
V96()
V97()
V98() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V93()
V94()
V95()
V96()
V97()
V98()
V99() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V93()
V94()
V95()
V99() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V84() )
Point of ( ( ) ( non
empty V2() )
set ) )
`2 : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) ( non
empty V26()
V93()
V94()
V95()
V99() )
set ) )
= upper_bound (proj2 : ( ( Function-like V40( the U1 of (TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V49() TopSpace-like V131() V156() V157() V158() V159() V160() V161() V162() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() ) set ) , REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) ) ( V13() V16( the U1 of (TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V49() TopSpace-like V131() V156() V157() V158() V159() V160() V161() V162() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() ) set ) ) V17( REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) Function-like V40( the U1 of (TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V49() TopSpace-like V131() V156() V157() V158() V159() V160() V161() V162() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() ) set ) , REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) ) Element of K6(K7( the U1 of (TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V49() TopSpace-like V131() V156() V157() V158() V159() V160() V161() V162() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() ) set ) ,REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) .: ((LSeg (((Gauge (C : ( ( non empty being_simple_closed_curve compact non horizontal non vertical ) ( non empty connected bounded being_simple_closed_curve compact non horizontal non vertical ) Subset of ) ,1 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V13() non empty-yielding V16( NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) V17(K286( the U1 of (TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V49() TopSpace-like V131() V156() V157() V158() V159() V160() V161() V162() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() ) set ) ) : ( ( ) ( ) M11( the U1 of (TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V49() TopSpace-like V131() V156() V157() V158() V159() V160() V161() V162() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K286( the U1 of (TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V49() TopSpace-like V131() V156() V157() V158() V159() V160() V161() V162() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() ) set ) ) : ( ( ) ( ) M11( the U1 of (TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V49() TopSpace-like V131() V156() V157() V158() V159() V160() V161() V162() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() ) set ) )) ) * ((Center (Gauge (C : ( ( non empty being_simple_closed_curve compact non horizontal non vertical ) ( non empty connected bounded being_simple_closed_curve compact non horizontal non vertical ) Subset of ) ,1 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V13() non empty-yielding V16( NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) V17(K286( the U1 of (TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V49() TopSpace-like V131() V156() V157() V158() V159() V160() V161() V162() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() ) set ) ) : ( ( ) ( ) M11( the U1 of (TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V49() TopSpace-like V131() V156() V157() V158() V159() V160() V161() V162() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K286( the U1 of (TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V49() TopSpace-like V131() V156() V157() V158() V159() V160() V161() V162() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() ) set ) ) : ( ( ) ( ) M11( the U1 of (TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V49() TopSpace-like V131() V156() V157() V158() V159() V160() V161() V162() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() ) set ) )) ) ) : ( ( ) ( V4() V5() V6() V10() V11() V12() V37() ext-real V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V33(2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V84() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V49() TopSpace-like V131() V156() V157() V158() V159() V160() V161() V162() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() ) set ) ) ,((Gauge (C : ( ( non empty being_simple_closed_curve compact non horizontal non vertical ) ( non empty connected bounded being_simple_closed_curve compact non horizontal non vertical ) Subset of ) ,i : ( ( ) ( V4() V5() V6() V10() V11() V12() V37() ext-real V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V13() non empty-yielding V16( NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) V17(K286( the U1 of (TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V49() TopSpace-like V131() V156() V157() V158() V159() V160() V161() V162() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() ) set ) ) : ( ( ) ( ) M11( the U1 of (TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V49() TopSpace-like V131() V156() V157() V158() V159() V160() V161() V162() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K286( the U1 of (TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V49() TopSpace-like V131() V156() V157() V158() V159() V160() V161() V162() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() ) set ) ) : ( ( ) ( ) M11( the U1 of (TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V49() TopSpace-like V131() V156() V157() V158() V159() V160() V161() V162() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() ) set ) )) ) * ((Center (Gauge (C : ( ( non empty being_simple_closed_curve compact non horizontal non vertical ) ( non empty connected bounded being_simple_closed_curve compact non horizontal non vertical ) Subset of ) ,i : ( ( ) ( V4() V5() V6() V10() V11() V12() V37() ext-real V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V13() non empty-yielding V16( NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) V17(K286( the U1 of (TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V49() TopSpace-like V131() V156() V157() V158() V159() V160() V161() V162() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() ) set ) ) : ( ( ) ( ) M11( the U1 of (TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V49() TopSpace-like V131() V156() V157() V158() V159() V160() V161() V162() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K286( the U1 of (TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V49() TopSpace-like V131() V156() V157() V158() V159() V160() V161() V162() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() ) set ) ) : ( ( ) ( ) M11( the U1 of (TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V49() TopSpace-like V131() V156() V157() V158() V159() V160() V161() V162() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() ) set ) )) ) ) : ( ( ) ( V4() V5() V6() V10() V11() V12() V37() ext-real V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( V4() V5() V6() V10() V11() V12() V37() ext-real V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V33(2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V84() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V49() TopSpace-like V131() V156() V157() V158() V159() V160() V161() V162() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() ) set ) ) )) : ( ( ) ( boundary connected ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V49() TopSpace-like V131() V156() V157() V158() V159() V160() V161() V162() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() ) set ) ) : ( ( ) ( ) set ) ) /\ (Lower_Arc (L~ (Cage (C : ( ( non empty being_simple_closed_curve compact non horizontal non vertical ) ( non empty connected bounded being_simple_closed_curve compact non horizontal non vertical ) Subset of ) ,i : ( ( ) ( V4() V5() V6() V10() V11() V12() V37() ext-real V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard clockwise_oriented ) ( non empty V2() V13() V16( NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) V17( the U1 of (TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V49() TopSpace-like V131() V156() V157() V158() V159() V160() V161() V162() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() ) set ) ) Function-like non constant FinSequence-like circular special unfolded s.c.c. standard clockwise_oriented ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V49() TopSpace-like V131() V156() V157() V158() V159() V160() V161() V162() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() ) set ) ) ) : ( ( ) ( non empty boundary connected bounded being_simple_closed_curve compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V49() TopSpace-like V131() V156() V157() V158() V159() V160() V161() V162() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( non empty ) ( non empty ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V49() TopSpace-like V131() V156() V157() V158() V159() V160() V161() V162() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V49() TopSpace-like V131() V156() V157() V158() V159() V160() V161() V162() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) (
V93()
V94()
V95() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V93()
V94()
V95()
V99() )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) (
V11()
V12()
ext-real )
Element of
REAL : ( ( ) ( non
empty V26()
V93()
V94()
V95()
V99() )
set ) ) holds
ex
j being ( ( ) (
V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real V92()
V93()
V94()
V95()
V96()
V97()
V98() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V93()
V94()
V95()
V96()
V97()
V98()
V99() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V93()
V94()
V95()
V99() )
set ) ) : ( ( ) ( )
set ) ) ) st
( 1 : ( ( ) ( non
empty V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real positive V92()
V93()
V94()
V95()
V96()
V97()
V98() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V93()
V94()
V95()
V96()
V97()
V98()
V99() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V93()
V94()
V95()
V99() )
set ) ) : ( ( ) ( )
set ) ) )
<= j : ( ( ) (
V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real V92()
V93()
V94()
V95()
V96()
V97()
V98() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V93()
V94()
V95()
V96()
V97()
V98()
V99() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V93()
V94()
V95()
V99() )
set ) ) : ( ( ) ( )
set ) ) ) &
j : ( ( ) (
V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real V92()
V93()
V94()
V95()
V96()
V97()
V98() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V93()
V94()
V95()
V96()
V97()
V98()
V99() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V93()
V94()
V95()
V99() )
set ) ) : ( ( ) ( )
set ) ) )
<= width (Gauge (C : ( ( non empty being_simple_closed_curve compact non horizontal non vertical ) ( non empty connected bounded being_simple_closed_curve compact non horizontal non vertical ) Subset of ) ,i : ( ( ) ( V4() V5() V6() V10() V11() V12() V37() ext-real V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( (
tabular ) (
V13() non
empty-yielding V16(
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V93()
V94()
V95()
V96()
V97()
V98()
V99() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V93()
V94()
V95()
V99() )
set ) ) : ( ( ) ( )
set ) ) )
V17(
K286( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V49()
TopSpace-like V131()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2() )
set ) ) : ( ( ) ( )
M11( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V49()
TopSpace-like V131()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2() )
set ) )) )
Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column )
FinSequence of
K286( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V49()
TopSpace-like V131()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2() )
set ) ) : ( ( ) ( )
M11( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V49()
TopSpace-like V131()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2() )
set ) )) ) : ( ( ) (
V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real V92()
V93()
V94()
V95()
V96()
V97()
V98() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V93()
V94()
V95()
V96()
V97()
V98()
V99() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V93()
V94()
V95()
V99() )
set ) ) : ( ( ) ( )
set ) ) ) &
p : ( ( ) (
V33(2 : ( ( ) ( non
empty V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real positive V92()
V93()
V94()
V95()
V96()
V97()
V98() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V93()
V94()
V95()
V96()
V97()
V98()
V99() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V93()
V94()
V95()
V99() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V84() )
Point of ( ( ) ( non
empty V2() )
set ) )
= (Gauge (C : ( ( non empty being_simple_closed_curve compact non horizontal non vertical ) ( non empty connected bounded being_simple_closed_curve compact non horizontal non vertical ) Subset of ) ,i : ( ( ) ( V4() V5() V6() V10() V11() V12() V37() ext-real V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( (
tabular ) (
V13() non
empty-yielding V16(
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V93()
V94()
V95()
V96()
V97()
V98()
V99() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V93()
V94()
V95()
V99() )
set ) ) : ( ( ) ( )
set ) ) )
V17(
K286( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V49()
TopSpace-like V131()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2() )
set ) ) : ( ( ) ( )
M11( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V49()
TopSpace-like V131()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2() )
set ) )) )
Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column )
FinSequence of
K286( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V49()
TopSpace-like V131()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2() )
set ) ) : ( ( ) ( )
M11( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V49()
TopSpace-like V131()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2() )
set ) )) )
* (
(Center (Gauge (C : ( ( non empty being_simple_closed_curve compact non horizontal non vertical ) ( non empty connected bounded being_simple_closed_curve compact non horizontal non vertical ) Subset of ) ,i : ( ( ) ( V4() V5() V6() V10() V11() V12() V37() ext-real V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V13() non empty-yielding V16( NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) V17(K286( the U1 of (TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V49() TopSpace-like V131() V156() V157() V158() V159() V160() V161() V162() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() ) set ) ) : ( ( ) ( ) M11( the U1 of (TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V49() TopSpace-like V131() V156() V157() V158() V159() V160() V161() V162() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K286( the U1 of (TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V49() TopSpace-like V131() V156() V157() V158() V159() V160() V161() V162() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() ) set ) ) : ( ( ) ( ) M11( the U1 of (TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V49() TopSpace-like V131() V156() V157() V158() V159() V160() V161() V162() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() ) set ) )) ) ) : ( ( ) (
V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real V92()
V93()
V94()
V95()
V96()
V97()
V98() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V93()
V94()
V95()
V96()
V97()
V98()
V99() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V93()
V94()
V95()
V99() )
set ) ) : ( ( ) ( )
set ) ) ) ,
j : ( ( ) (
V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real V92()
V93()
V94()
V95()
V96()
V97()
V98() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V93()
V94()
V95()
V96()
V97()
V98()
V99() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V93()
V94()
V95()
V99() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
V33(2 : ( ( ) ( non
empty V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real positive V92()
V93()
V94()
V95()
V96()
V97()
V98() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V93()
V94()
V95()
V96()
V97()
V98()
V99() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V93()
V94()
V95()
V99() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V84() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V92() V93() V94() V95() V96() V97() V98() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V93() V94() V95() V96() V97() V98() V99() ) Element of K6(REAL : ( ( ) ( non empty V26() V93() V94() V95() V99() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V49()
TopSpace-like V131()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2() )
set ) ) ) ;