begin
definition
let X,
Y,
Z be ( ( ) ( )
Subset of ) ;
pred X,
Y,
Z are_concurrent means
( (
X : ( ( ) ( )
RLTopStruct )
is_parallel_to Y : ( ( ) ( )
Element of
X : ( ( ) ( )
RLTopStruct ) ) &
Y : ( ( ) ( )
Element of
X : ( ( ) ( )
RLTopStruct ) )
is_parallel_to Z : ( (
V12()
V21(
[:X : ( ( ) ( ) RLTopStruct ) ,X : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( )
set ) ,
X : ( ( ) ( )
RLTopStruct ) ) ) (
V7()
V10(
[:X : ( ( ) ( ) RLTopStruct ) ,X : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( )
set ) )
V11(
X : ( ( ) ( )
RLTopStruct ) )
V12()
V21(
[:X : ( ( ) ( ) RLTopStruct ) ,X : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( )
set ) ,
X : ( ( ) ( )
RLTopStruct ) ) )
Element of
bool [:[:X : ( ( ) ( ) RLTopStruct ) ,X : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) ,X : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) &
Z : ( (
V12()
V21(
[:X : ( ( ) ( ) RLTopStruct ) ,X : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( )
set ) ,
X : ( ( ) ( )
RLTopStruct ) ) ) (
V7()
V10(
[:X : ( ( ) ( ) RLTopStruct ) ,X : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( )
set ) )
V11(
X : ( ( ) ( )
RLTopStruct ) )
V12()
V21(
[:X : ( ( ) ( ) RLTopStruct ) ,X : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( )
set ) ,
X : ( ( ) ( )
RLTopStruct ) ) )
Element of
bool [:[:X : ( ( ) ( ) RLTopStruct ) ,X : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) ,X : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
is_parallel_to X : ( ( ) ( )
RLTopStruct ) ) or ex
A being ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) st
(
A : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
in X : ( ( ) ( )
RLTopStruct ) &
A : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
in Y : ( ( ) ( )
Element of
X : ( ( ) ( )
RLTopStruct ) ) &
A : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
in Z : ( (
V12()
V21(
[:X : ( ( ) ( ) RLTopStruct ) ,X : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( )
set ) ,
X : ( ( ) ( )
RLTopStruct ) ) ) (
V7()
V10(
[:X : ( ( ) ( ) RLTopStruct ) ,X : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( )
set ) )
V11(
X : ( ( ) ( )
RLTopStruct ) )
V12()
V21(
[:X : ( ( ) ( ) RLTopStruct ) ,X : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( )
set ) ,
X : ( ( ) ( )
RLTopStruct ) ) )
Element of
bool [:[:X : ( ( ) ( ) RLTopStruct ) ,X : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) ,X : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) );
end;
theorem
for
A,
B,
C being ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) st
angle (
A : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
B : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
C : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ) : ( ( ) (
ext-real V66()
V67() )
Element of
K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) )
= 0 : ( ( ) (
ext-real non
positive non
negative empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) &
A : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
B : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
C : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
are_mutually_different & not
angle (
B : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
C : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
A : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ) : ( ( ) (
ext-real V66()
V67() )
Element of
K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) )
= PI : ( ( ) (
ext-real positive non
negative non
empty V66()
V67() )
Element of
K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) ) holds
angle (
B : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
A : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
C : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ) : ( ( ) (
ext-real V66()
V67() )
Element of
K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) )
= PI : ( ( ) (
ext-real positive non
negative non
empty V66()
V67() )
Element of
K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) ) ;
theorem
for
A,
A1,
B,
C being ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) holds
the_area_of_polygon3 (
(A : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) + A1 : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) ) ,
B : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
C : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ) : ( (
V67() ) (
ext-real V66()
V67() )
set )
= ((the_area_of_polygon3 (A : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ,B : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ,C : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) )) : ( ( V67() ) ( ext-real V66() V67() ) set ) + (the_area_of_polygon3 (A1 : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ,B : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ,C : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) )) : ( ( V67() ) ( ext-real V66() V67() ) set ) ) : ( ( ) (
ext-real V66()
V67() )
Element of
K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) )
- (the_area_of_polygon3 ((0. (TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V85() V146() V147() V148() V149() V150() V151() V152() strict V203() V204() ) RLTopStruct ) ) : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V47( TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( strict ) ( non empty TopSpace-like V85() V146() V147() V148() V149() V150() V151() V152() strict V203() V204() ) RLTopStruct ) ) V70() V109() V110() V111() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V85() V146() V147() V148() V149() V150() V151() V152() strict V203() V204() ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,B : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ,C : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) )) : ( (
V67() ) (
ext-real V66()
V67() )
set ) : ( ( ) (
ext-real V66()
V67() )
Element of
K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) ) ;
theorem
for
A,
B,
C being ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) st
A : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
B : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
C : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
is_a_triangle holds
(
A : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
C : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
B : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
is_a_triangle &
B : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
A : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
C : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
is_a_triangle &
B : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
C : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
A : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
is_a_triangle &
C : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
A : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
B : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
is_a_triangle &
C : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
B : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
A : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
is_a_triangle ) ;
begin
theorem
for
A1,
B,
C,
B1,
A,
C1 being ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
for
lambda,
mu,
nu being ( ( ) (
ext-real V66()
V67() )
Real) st
A1 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
= ((1 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) - lambda : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) * B : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) )
+ (lambda : ( ( ) ( ext-real V66() V67() ) Real) * C : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) ) &
B1 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
= ((1 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) - mu : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) * C : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) )
+ (mu : ( ( ) ( ext-real V66() V67() ) Real) * A : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) ) &
C1 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
= ((1 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) - nu : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) * A : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) )
+ (nu : ( ( ) ( ext-real V66() V67() ) Real) * B : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) ) holds
the_area_of_polygon3 (
A1 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
B1 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
C1 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ) : ( (
V67() ) (
ext-real V66()
V67() )
set )
= ((((1 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) - lambda : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) * (1 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) - mu : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) * (1 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) - nu : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) + ((lambda : ( ( ) ( ext-real V66() V67() ) Real) * mu : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) * nu : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) ) : ( ( ) (
ext-real V66()
V67() )
Element of
K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) )
* (the_area_of_polygon3 (A : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ,B : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ,C : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) )) : ( (
V67() ) (
ext-real V66()
V67() )
set ) : ( ( ) (
ext-real V66()
V67() )
Element of
K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) ) ;
theorem
for
A,
B,
C,
A1,
B1,
C1 being ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
for
lambda,
mu,
nu being ( ( ) (
ext-real V66()
V67() )
Real) st
A : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
B : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
C : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
is_a_triangle &
A1 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
= ((1 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) - lambda : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) * B : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) )
+ (lambda : ( ( ) ( ext-real V66() V67() ) Real) * C : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) ) &
B1 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
= ((1 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) - mu : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) * C : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) )
+ (mu : ( ( ) ( ext-real V66() V67() ) Real) * A : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) ) &
C1 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
= ((1 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) - nu : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) * A : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) )
+ (nu : ( ( ) ( ext-real V66() V67() ) Real) * B : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) ) &
lambda : ( ( ) (
ext-real V66()
V67() )
Real)
<> 1 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) &
mu : ( ( ) (
ext-real V66()
V67() )
Real)
<> 1 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) &
nu : ( ( ) (
ext-real V66()
V67() )
Real)
<> 1 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) holds
(
A1 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
B1 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
C1 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
is_collinear iff
((lambda : ( ( ) ( ext-real V66() V67() ) Real) / (1 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) - lambda : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) * (mu : ( ( ) ( ext-real V66() V67() ) Real) / (1 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) - mu : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) ) : ( ( ) (
ext-real V66()
V67() )
Element of
K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) )
* (nu : ( ( ) ( ext-real V66() V67() ) Real) / (1 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) - nu : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) ) : ( ( ) (
ext-real V66()
V67() )
Element of
K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) ) : ( ( ) (
ext-real V66()
V67() )
Element of
K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) )
= - 1 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) (
ext-real non
positive negative non
empty V66()
V67()
V68()
V69() )
Element of
K113() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V122()
V123()
V125() )
set ) ) ) ;
theorem
for
A,
B,
C,
A1,
B1,
C1,
C2,
A2,
B2 being ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
for
lambda,
mu,
nu being ( ( ) (
ext-real V66()
V67() )
Real) st
A : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
B : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
C : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
is_a_triangle &
A1 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
= ((1 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) - lambda : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) * B : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) )
+ (lambda : ( ( ) ( ext-real V66() V67() ) Real) * C : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) ) &
B1 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
= ((1 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) - mu : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) * C : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) )
+ (mu : ( ( ) ( ext-real V66() V67() ) Real) * A : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) ) &
C1 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
= ((1 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) - nu : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) * A : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) )
+ (nu : ( ( ) ( ext-real V66() V67() ) Real) * B : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) ) &
lambda : ( ( ) (
ext-real V66()
V67() )
Real)
<> 1 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) &
mu : ( ( ) (
ext-real V66()
V67() )
Real)
<> 1 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) &
nu : ( ( ) (
ext-real V66()
V67() )
Real)
<> 1 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) &
A : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
A1 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
C2 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
is_collinear &
B : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
B1 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
C2 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
is_collinear &
B : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
B1 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
A2 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
is_collinear &
C : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
C1 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
A2 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
is_collinear &
A : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
A1 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
B2 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
is_collinear &
C : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
C1 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
B2 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
is_collinear holds
(
(((1 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) - mu : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) + (lambda : ( ( ) ( ext-real V66() V67() ) Real) * mu : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) * ((1 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) - lambda : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) + (nu : ( ( ) ( ext-real V66() V67() ) Real) * lambda : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) ) : ( ( ) (
ext-real V66()
V67() )
Element of
K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) )
* ((1 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) - nu : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) + (mu : ( ( ) ( ext-real V66() V67() ) Real) * nu : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) ) : ( ( ) (
ext-real V66()
V67() )
Element of
K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) ) : ( ( ) (
ext-real V66()
V67() )
Element of
K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) )
<> 0 : ( ( ) (
ext-real non
positive non
negative empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) &
the_area_of_polygon3 (
A2 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
B2 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
C2 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ) : ( (
V67() ) (
ext-real V66()
V67() )
set )
= (((((mu : ( ( ) ( ext-real V66() V67() ) Real) * nu : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) * lambda : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) - (((1 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) - mu : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) * (1 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) - nu : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) * (1 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) - lambda : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) ^2) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) / ((((1 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) - mu : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) + (lambda : ( ( ) ( ext-real V66() V67() ) Real) * mu : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) * ((1 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) - lambda : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) + (nu : ( ( ) ( ext-real V66() V67() ) Real) * lambda : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) * ((1 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) - nu : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) + (mu : ( ( ) ( ext-real V66() V67() ) Real) * nu : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) ) : ( ( ) (
ext-real V66()
V67() )
Element of
K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) )
* (the_area_of_polygon3 (A : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ,B : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ,C : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) )) : ( (
V67() ) (
ext-real V66()
V67() )
set ) : ( ( ) (
ext-real V66()
V67() )
Element of
K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) ) ) ;
theorem
for
A,
B,
C,
A1,
B1,
C1,
C2,
A2,
B2 being ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) st
A : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
B : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
C : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
is_a_triangle &
A1 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
= ((2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) / 3 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( ext-real positive non negative non empty V66() V67() V69() ) Element of K112() : ( ( ) ( non empty V31() V119() V120() V121() V122() V125() ) set ) ) * B : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) )
+ ((1 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) / 3 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( ext-real positive non negative non empty V66() V67() V69() ) Element of K112() : ( ( ) ( non empty V31() V119() V120() V121() V122() V125() ) set ) ) * C : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) ) &
B1 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
= ((2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) / 3 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( ext-real positive non negative non empty V66() V67() V69() ) Element of K112() : ( ( ) ( non empty V31() V119() V120() V121() V122() V125() ) set ) ) * C : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) )
+ ((1 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) / 3 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( ext-real positive non negative non empty V66() V67() V69() ) Element of K112() : ( ( ) ( non empty V31() V119() V120() V121() V122() V125() ) set ) ) * A : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) ) &
C1 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
= ((2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) / 3 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( ext-real positive non negative non empty V66() V67() V69() ) Element of K112() : ( ( ) ( non empty V31() V119() V120() V121() V122() V125() ) set ) ) * A : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) )
+ ((1 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) / 3 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( ext-real positive non negative non empty V66() V67() V69() ) Element of K112() : ( ( ) ( non empty V31() V119() V120() V121() V122() V125() ) set ) ) * B : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) ) &
A : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
A1 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
C2 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
is_collinear &
B : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
B1 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
C2 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
is_collinear &
B : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
B1 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
A2 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
is_collinear &
C : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
C1 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
A2 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
is_collinear &
A : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
A1 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
B2 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
is_collinear &
C : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
C1 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
B2 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
is_collinear holds
the_area_of_polygon3 (
A2 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
B2 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
C2 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ) : ( (
V67() ) (
ext-real V66()
V67() )
set )
= (the_area_of_polygon3 (A : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ,B : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ,C : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) )) : ( (
V67() ) (
ext-real V66()
V67() )
set )
/ 7 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) (
ext-real V66()
V67() )
Element of
K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) ) ;
theorem
for
A,
B,
C,
A1,
B1,
C1 being ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
for
lambda,
mu,
nu being ( ( ) (
ext-real V66()
V67() )
Real) st
A : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
B : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
C : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
is_a_triangle &
A1 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
= ((1 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) - lambda : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) * B : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) )
+ (lambda : ( ( ) ( ext-real V66() V67() ) Real) * C : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) ) &
B1 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
= ((1 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) - mu : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) * C : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) )
+ (mu : ( ( ) ( ext-real V66() V67() ) Real) * A : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) ) &
C1 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
= ((1 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) - nu : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) * A : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) )
+ (nu : ( ( ) ( ext-real V66() V67() ) Real) * B : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) ) &
lambda : ( ( ) (
ext-real V66()
V67() )
Real)
<> 1 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) &
mu : ( ( ) (
ext-real V66()
V67() )
Real)
<> 1 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) &
nu : ( ( ) (
ext-real V66()
V67() )
Real)
<> 1 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) &
(1 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) - mu : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) (
ext-real V66()
V67() )
Element of
K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) )
+ (lambda : ( ( ) ( ext-real V66() V67() ) Real) * mu : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) (
ext-real V66()
V67() )
Element of
K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) ) : ( ( ) (
ext-real V66()
V67() )
Element of
K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) )
<> 0 : ( ( ) (
ext-real non
positive non
negative empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) &
(1 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) - lambda : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) (
ext-real V66()
V67() )
Element of
K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) )
+ (nu : ( ( ) ( ext-real V66() V67() ) Real) * lambda : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) (
ext-real V66()
V67() )
Element of
K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) ) : ( ( ) (
ext-real V66()
V67() )
Element of
K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) )
<> 0 : ( ( ) (
ext-real non
positive non
negative empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) &
(1 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) - nu : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) (
ext-real V66()
V67() )
Element of
K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) )
+ (mu : ( ( ) ( ext-real V66() V67() ) Real) * nu : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) (
ext-real V66()
V67() )
Element of
K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) ) : ( ( ) (
ext-real V66()
V67() )
Element of
K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) )
<> 0 : ( ( ) (
ext-real non
positive non
negative empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) holds
(
((lambda : ( ( ) ( ext-real V66() V67() ) Real) / (1 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) - lambda : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) * (mu : ( ( ) ( ext-real V66() V67() ) Real) / (1 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) - mu : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) ) : ( ( ) (
ext-real V66()
V67() )
Element of
K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) )
* (nu : ( ( ) ( ext-real V66() V67() ) Real) / (1 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) - nu : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) ) : ( ( ) (
ext-real V66()
V67() )
Element of
K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) ) : ( ( ) (
ext-real V66()
V67() )
Element of
K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) )
= 1 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) iff ex
A2 being ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) st
(
A : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
A1 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
A2 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
is_collinear &
B : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
B1 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
A2 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
is_collinear &
C : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
C1 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
A2 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
is_collinear ) ) ;
theorem
for
A,
B,
C,
A1,
B1,
C1 being ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
for
lambda,
mu,
nu being ( ( ) (
ext-real V66()
V67() )
Real) st
A : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
B : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
C : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
is_a_triangle &
A1 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
= ((1 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) - lambda : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) * B : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) )
+ (lambda : ( ( ) ( ext-real V66() V67() ) Real) * C : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) ) &
B1 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
= ((1 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) - mu : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) * C : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) )
+ (mu : ( ( ) ( ext-real V66() V67() ) Real) * A : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) ) &
C1 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) )
= ((1 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) - nu : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) * A : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) )
+ (nu : ( ( ) ( ext-real V66() V67() ) Real) * B : ( ( ) ( V7() V12() V38(2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) V70() V109() V110() V111() ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) ) : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) ) &
lambda : ( ( ) (
ext-real V66()
V67() )
Real)
<> 1 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) &
mu : ( ( ) (
ext-real V66()
V67() )
Real)
<> 1 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) &
nu : ( ( ) (
ext-real V66()
V67() )
Real)
<> 1 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) holds
(
((lambda : ( ( ) ( ext-real V66() V67() ) Real) / (1 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) - lambda : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) * (mu : ( ( ) ( ext-real V66() V67() ) Real) / (1 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) - mu : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) ) : ( ( ) (
ext-real V66()
V67() )
Element of
K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) )
* (nu : ( ( ) ( ext-real V66() V67() ) Real) / (1 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) - nu : ( ( ) ( ext-real V66() V67() ) Real) ) : ( ( ) ( ext-real V66() V67() ) Element of K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) ) ) : ( ( ) (
ext-real V66()
V67() )
Element of
K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) ) : ( ( ) (
ext-real V66()
V67() )
Element of
K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) )
= 1 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) iff
Line (
A : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
A1 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Element of
bool the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ,
Line (
B : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
B1 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Element of
bool the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ,
Line (
C : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ,
C1 : ( ( ) (
V7()
V12()
V38(2 : ( ( ) (
ext-real positive non
negative non
empty V30()
V66()
V67()
V68()
V69()
V119()
V120()
V121()
V122()
V123()
V124() )
Element of
K114() : ( ( ) (
V119()
V120()
V121()
V122()
V123()
V124()
V125() )
Element of
bool K110() : ( ( ) ( non
empty V31()
V119()
V120()
V121()
V125() )
set ) : ( ( ) ( non
empty )
set ) ) ) )
V70()
V109()
V110()
V111() )
Point of ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Element of
bool the
U1 of
(TOP-REAL 2 : ( ( ) ( ext-real positive non negative non empty V30() V66() V67() V68() V69() V119() V120() V121() V122() V123() V124() ) Element of K114() : ( ( ) ( V119() V120() V121() V122() V123() V124() V125() ) Element of bool K110() : ( ( ) ( non empty V31() V119() V120() V121() V125() ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V85()
V146()
V147()
V148()
V149()
V150()
V151()
V152()
strict V203()
V204() )
RLTopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
are_concurrent ) ;