for
p1,
p2,
p,
pc being ( ( ) (
Relation-like Function-like V42(2 : ( ( ) ( non
empty natural complex real ext-real positive non
negative V33()
V34()
V126()
V127()
V128()
V129()
V130()
V131() )
Element of
NAT : ( ( ) (
V126()
V127()
V128()
V129()
V130()
V131()
V132() )
Element of
bool REAL : ( ( ) ( non
empty V35()
V126()
V127()
V128()
V132() )
set ) : ( ( ) ( )
set ) ) ) )
FinSequence-like complex-valued ext-real-valued real-valued )
Point of ( ( ) ( non
empty )
set ) )
for
a,
b,
r being ( (
real ) (
complex real ext-real )
number ) st
p1 : ( ( ) (
Relation-like Function-like V42(2 : ( ( ) ( non
empty natural complex real ext-real positive non
negative V33()
V34()
V126()
V127()
V128()
V129()
V130()
V131() )
Element of
NAT : ( ( ) (
V126()
V127()
V128()
V129()
V130()
V131()
V132() )
Element of
bool REAL : ( ( ) ( non
empty V35()
V126()
V127()
V128()
V132() )
set ) : ( ( ) ( )
set ) ) ) )
FinSequence-like complex-valued ext-real-valued real-valued )
Point of ( ( ) ( non
empty )
set ) )
in circle (
a : ( (
real ) (
complex real ext-real )
number ) ,
b : ( (
real ) (
complex real ext-real )
number ) ,
r : ( (
real ) (
complex real ext-real )
number ) ) : ( ( ) ( )
Element of
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural complex real ext-real positive non negative V33() V34() V126() V127() V128() V129() V130() V131() ) Element of NAT : ( ( ) ( V126() V127() V128() V129() V130() V131() V132() ) Element of bool REAL : ( ( ) ( non empty V35() V126() V127() V128() V132() ) set ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V73()
V138()
V139()
TopSpace-like V186()
V187()
V188()
V189()
V190()
V191()
V192()
strict )
RLTopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) &
p2 : ( ( ) (
Relation-like Function-like V42(2 : ( ( ) ( non
empty natural complex real ext-real positive non
negative V33()
V34()
V126()
V127()
V128()
V129()
V130()
V131() )
Element of
NAT : ( ( ) (
V126()
V127()
V128()
V129()
V130()
V131()
V132() )
Element of
bool REAL : ( ( ) ( non
empty V35()
V126()
V127()
V128()
V132() )
set ) : ( ( ) ( )
set ) ) ) )
FinSequence-like complex-valued ext-real-valued real-valued )
Point of ( ( ) ( non
empty )
set ) )
in circle (
a : ( (
real ) (
complex real ext-real )
number ) ,
b : ( (
real ) (
complex real ext-real )
number ) ,
r : ( (
real ) (
complex real ext-real )
number ) ) : ( ( ) ( )
Element of
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural complex real ext-real positive non negative V33() V34() V126() V127() V128() V129() V130() V131() ) Element of NAT : ( ( ) ( V126() V127() V128() V129() V130() V131() V132() ) Element of bool REAL : ( ( ) ( non empty V35() V126() V127() V128() V132() ) set ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V73()
V138()
V139()
TopSpace-like V186()
V187()
V188()
V189()
V190()
V191()
V192()
strict )
RLTopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) &
p : ( ( ) (
Relation-like Function-like V42(2 : ( ( ) ( non
empty natural complex real ext-real positive non
negative V33()
V34()
V126()
V127()
V128()
V129()
V130()
V131() )
Element of
NAT : ( ( ) (
V126()
V127()
V128()
V129()
V130()
V131()
V132() )
Element of
bool REAL : ( ( ) ( non
empty V35()
V126()
V127()
V128()
V132() )
set ) : ( ( ) ( )
set ) ) ) )
FinSequence-like complex-valued ext-real-valued real-valued )
Point of ( ( ) ( non
empty )
set ) )
in circle (
a : ( (
real ) (
complex real ext-real )
number ) ,
b : ( (
real ) (
complex real ext-real )
number ) ,
r : ( (
real ) (
complex real ext-real )
number ) ) : ( ( ) ( )
Element of
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural complex real ext-real positive non negative V33() V34() V126() V127() V128() V129() V130() V131() ) Element of NAT : ( ( ) ( V126() V127() V128() V129() V130() V131() V132() ) Element of bool REAL : ( ( ) ( non empty V35() V126() V127() V128() V132() ) set ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V73()
V138()
V139()
TopSpace-like V186()
V187()
V188()
V189()
V190()
V191()
V192()
strict )
RLTopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) &
pc : ( ( ) (
Relation-like Function-like V42(2 : ( ( ) ( non
empty natural complex real ext-real positive non
negative V33()
V34()
V126()
V127()
V128()
V129()
V130()
V131() )
Element of
NAT : ( ( ) (
V126()
V127()
V128()
V129()
V130()
V131()
V132() )
Element of
bool REAL : ( ( ) ( non
empty V35()
V126()
V127()
V128()
V132() )
set ) : ( ( ) ( )
set ) ) ) )
FinSequence-like complex-valued ext-real-valued real-valued )
Point of ( ( ) ( non
empty )
set ) )
= |[a : ( ( real ) ( complex real ext-real ) number ) ,b : ( ( real ) ( complex real ext-real ) number ) ]| : ( ( ) (
Relation-like Function-like V42(2 : ( ( ) ( non
empty natural complex real ext-real positive non
negative V33()
V34()
V126()
V127()
V128()
V129()
V130()
V131() )
Element of
NAT : ( ( ) (
V126()
V127()
V128()
V129()
V130()
V131()
V132() )
Element of
bool REAL : ( ( ) ( non
empty V35()
V126()
V127()
V128()
V132() )
set ) : ( ( ) ( )
set ) ) ) )
FinSequence-like complex-valued ext-real-valued real-valued )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural complex real ext-real positive non negative V33() V34() V126() V127() V128() V129() V130() V131() ) Element of NAT : ( ( ) ( V126() V127() V128() V129() V130() V131() V132() ) Element of bool REAL : ( ( ) ( non empty V35() V126() V127() V128() V132() ) set ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V73()
V138()
V139()
TopSpace-like V186()
V187()
V188()
V189()
V190()
V191()
V192()
strict )
RLTopStruct ) : ( ( ) ( non
empty )
set ) ) &
pc : ( ( ) (
Relation-like Function-like V42(2 : ( ( ) ( non
empty natural complex real ext-real positive non
negative V33()
V34()
V126()
V127()
V128()
V129()
V130()
V131() )
Element of
NAT : ( ( ) (
V126()
V127()
V128()
V129()
V130()
V131()
V132() )
Element of
bool REAL : ( ( ) ( non
empty V35()
V126()
V127()
V128()
V132() )
set ) : ( ( ) ( )
set ) ) ) )
FinSequence-like complex-valued ext-real-valued real-valued )
Point of ( ( ) ( non
empty )
set ) )
in LSeg (
p : ( ( ) (
Relation-like Function-like V42(2 : ( ( ) ( non
empty natural complex real ext-real positive non
negative V33()
V34()
V126()
V127()
V128()
V129()
V130()
V131() )
Element of
NAT : ( ( ) (
V126()
V127()
V128()
V129()
V130()
V131()
V132() )
Element of
bool REAL : ( ( ) ( non
empty V35()
V126()
V127()
V128()
V132() )
set ) : ( ( ) ( )
set ) ) ) )
FinSequence-like complex-valued ext-real-valued real-valued )
Point of ( ( ) ( non
empty )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V42(2 : ( ( ) ( non
empty natural complex real ext-real positive non
negative V33()
V34()
V126()
V127()
V128()
V129()
V130()
V131() )
Element of
NAT : ( ( ) (
V126()
V127()
V128()
V129()
V130()
V131()
V132() )
Element of
bool REAL : ( ( ) ( non
empty V35()
V126()
V127()
V128()
V132() )
set ) : ( ( ) ( )
set ) ) ) )
FinSequence-like complex-valued ext-real-valued real-valued )
Point of ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( non
empty V244(
TOP-REAL 2 : ( ( ) ( non
empty natural complex real ext-real positive non
negative V33()
V34()
V126()
V127()
V128()
V129()
V130()
V131() )
Element of
NAT : ( ( ) (
V126()
V127()
V128()
V129()
V130()
V131()
V132() )
Element of
bool REAL : ( ( ) ( non
empty V35()
V126()
V127()
V128()
V132() )
set ) : ( ( ) ( )
set ) ) ) : ( (
strict ) ( non
empty V73()
V138()
V139()
TopSpace-like V186()
V187()
V188()
V189()
V190()
V191()
V192()
strict )
RLTopStruct ) ) )
Element of
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty natural complex real ext-real positive non negative V33() V34() V126() V127() V128() V129() V130() V131() ) Element of NAT : ( ( ) ( V126() V127() V128() V129() V130() V131() V132() ) Element of bool REAL : ( ( ) ( non empty V35() V126() V127() V128() V132() ) set ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V73()
V138()
V139()
TopSpace-like V186()
V187()
V188()
V189()
V190()
V191()
V192()
strict )
RLTopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( )
set ) ) &
p1 : ( ( ) (
Relation-like Function-like V42(2 : ( ( ) ( non
empty natural complex real ext-real positive non
negative V33()
V34()
V126()
V127()
V128()
V129()
V130()
V131() )
Element of
NAT : ( ( ) (
V126()
V127()
V128()
V129()
V130()
V131()
V132() )
Element of
bool REAL : ( ( ) ( non
empty V35()
V126()
V127()
V128()
V132() )
set ) : ( ( ) ( )
set ) ) ) )
FinSequence-like complex-valued ext-real-valued real-valued )
Point of ( ( ) ( non
empty )
set ) )
<> p : ( ( ) (
Relation-like Function-like V42(2 : ( ( ) ( non
empty natural complex real ext-real positive non
negative V33()
V34()
V126()
V127()
V128()
V129()
V130()
V131() )
Element of
NAT : ( ( ) (
V126()
V127()
V128()
V129()
V130()
V131()
V132() )
Element of
bool REAL : ( ( ) ( non
empty V35()
V126()
V127()
V128()
V132() )
set ) : ( ( ) ( )
set ) ) ) )
FinSequence-like complex-valued ext-real-valued real-valued )
Point of ( ( ) ( non
empty )
set ) ) & not 2 : ( ( ) ( non
empty natural complex real ext-real positive non
negative V33()
V34()
V126()
V127()
V128()
V129()
V130()
V131() )
Element of
NAT : ( ( ) (
V126()
V127()
V128()
V129()
V130()
V131()
V132() )
Element of
bool REAL : ( ( ) ( non
empty V35()
V126()
V127()
V128()
V132() )
set ) : ( ( ) ( )
set ) ) )
* (angle (p1 : ( ( ) ( Relation-like Function-like V42(2 : ( ( ) ( non empty natural complex real ext-real positive non negative V33() V34() V126() V127() V128() V129() V130() V131() ) Element of NAT : ( ( ) ( V126() V127() V128() V129() V130() V131() V132() ) Element of bool REAL : ( ( ) ( non empty V35() V126() V127() V128() V132() ) set ) : ( ( ) ( ) set ) ) ) ) FinSequence-like complex-valued ext-real-valued real-valued ) Point of ( ( ) ( non empty ) set ) ) ,p : ( ( ) ( Relation-like Function-like V42(2 : ( ( ) ( non empty natural complex real ext-real positive non negative V33() V34() V126() V127() V128() V129() V130() V131() ) Element of NAT : ( ( ) ( V126() V127() V128() V129() V130() V131() V132() ) Element of bool REAL : ( ( ) ( non empty V35() V126() V127() V128() V132() ) set ) : ( ( ) ( ) set ) ) ) ) FinSequence-like complex-valued ext-real-valued real-valued ) Point of ( ( ) ( non empty ) set ) ) ,p2 : ( ( ) ( Relation-like Function-like V42(2 : ( ( ) ( non empty natural complex real ext-real positive non negative V33() V34() V126() V127() V128() V129() V130() V131() ) Element of NAT : ( ( ) ( V126() V127() V128() V129() V130() V131() V132() ) Element of bool REAL : ( ( ) ( non empty V35() V126() V127() V128() V132() ) set ) : ( ( ) ( ) set ) ) ) ) FinSequence-like complex-valued ext-real-valued real-valued ) Point of ( ( ) ( non empty ) set ) ) )) : ( ( ) (
complex real ext-real )
Element of
REAL : ( ( ) ( non
empty V35()
V126()
V127()
V128()
V132() )
set ) ) : ( ( ) (
complex real ext-real )
Element of
REAL : ( ( ) ( non
empty V35()
V126()
V127()
V128()
V132() )
set ) )
= angle (
p1 : ( ( ) (
Relation-like Function-like V42(2 : ( ( ) ( non
empty natural complex real ext-real positive non
negative V33()
V34()
V126()
V127()
V128()
V129()
V130()
V131() )
Element of
NAT : ( ( ) (
V126()
V127()
V128()
V129()
V130()
V131()
V132() )
Element of
bool REAL : ( ( ) ( non
empty V35()
V126()
V127()
V128()
V132() )
set ) : ( ( ) ( )
set ) ) ) )
FinSequence-like complex-valued ext-real-valued real-valued )
Point of ( ( ) ( non
empty )
set ) ) ,
pc : ( ( ) (
Relation-like Function-like V42(2 : ( ( ) ( non
empty natural complex real ext-real positive non
negative V33()
V34()
V126()
V127()
V128()
V129()
V130()
V131() )
Element of
NAT : ( ( ) (
V126()
V127()
V128()
V129()
V130()
V131()
V132() )
Element of
bool REAL : ( ( ) ( non
empty V35()
V126()
V127()
V128()
V132() )
set ) : ( ( ) ( )
set ) ) ) )
FinSequence-like complex-valued ext-real-valued real-valued )
Point of ( ( ) ( non
empty )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V42(2 : ( ( ) ( non
empty natural complex real ext-real positive non
negative V33()
V34()
V126()
V127()
V128()
V129()
V130()
V131() )
Element of
NAT : ( ( ) (
V126()
V127()
V128()
V129()
V130()
V131()
V132() )
Element of
bool REAL : ( ( ) ( non
empty V35()
V126()
V127()
V128()
V132() )
set ) : ( ( ) ( )
set ) ) ) )
FinSequence-like complex-valued ext-real-valued real-valued )
Point of ( ( ) ( non
empty )
set ) ) ) : ( ( ) (
complex real ext-real )
Element of
REAL : ( ( ) ( non
empty V35()
V126()
V127()
V128()
V132() )
set ) ) holds
2 : ( ( ) ( non
empty natural complex real ext-real positive non
negative V33()
V34()
V126()
V127()
V128()
V129()
V130()
V131() )
Element of
NAT : ( ( ) (
V126()
V127()
V128()
V129()
V130()
V131()
V132() )
Element of
bool REAL : ( ( ) ( non
empty V35()
V126()
V127()
V128()
V132() )
set ) : ( ( ) ( )
set ) ) )
* ((angle (p1 : ( ( ) ( Relation-like Function-like V42(2 : ( ( ) ( non empty natural complex real ext-real positive non negative V33() V34() V126() V127() V128() V129() V130() V131() ) Element of NAT : ( ( ) ( V126() V127() V128() V129() V130() V131() V132() ) Element of bool REAL : ( ( ) ( non empty V35() V126() V127() V128() V132() ) set ) : ( ( ) ( ) set ) ) ) ) FinSequence-like complex-valued ext-real-valued real-valued ) Point of ( ( ) ( non empty ) set ) ) ,p : ( ( ) ( Relation-like Function-like V42(2 : ( ( ) ( non empty natural complex real ext-real positive non negative V33() V34() V126() V127() V128() V129() V130() V131() ) Element of NAT : ( ( ) ( V126() V127() V128() V129() V130() V131() V132() ) Element of bool REAL : ( ( ) ( non empty V35() V126() V127() V128() V132() ) set ) : ( ( ) ( ) set ) ) ) ) FinSequence-like complex-valued ext-real-valued real-valued ) Point of ( ( ) ( non empty ) set ) ) ,p2 : ( ( ) ( Relation-like Function-like V42(2 : ( ( ) ( non empty natural complex real ext-real positive non negative V33() V34() V126() V127() V128() V129() V130() V131() ) Element of NAT : ( ( ) ( V126() V127() V128() V129() V130() V131() V132() ) Element of bool REAL : ( ( ) ( non empty V35() V126() V127() V128() V132() ) set ) : ( ( ) ( ) set ) ) ) ) FinSequence-like complex-valued ext-real-valued real-valued ) Point of ( ( ) ( non empty ) set ) ) )) : ( ( ) ( complex real ext-real ) Element of REAL : ( ( ) ( non empty V35() V126() V127() V128() V132() ) set ) ) - PI : ( ( ) ( non empty complex real ext-real positive non negative ) Element of REAL : ( ( ) ( non empty V35() V126() V127() V128() V132() ) set ) ) ) : ( ( ) (
complex real ext-real )
Element of
REAL : ( ( ) ( non
empty V35()
V126()
V127()
V128()
V132() )
set ) ) : ( ( ) (
complex real ext-real )
Element of
REAL : ( ( ) ( non
empty V35()
V126()
V127()
V128()
V132() )
set ) )
= angle (
p1 : ( ( ) (
Relation-like Function-like V42(2 : ( ( ) ( non
empty natural complex real ext-real positive non
negative V33()
V34()
V126()
V127()
V128()
V129()
V130()
V131() )
Element of
NAT : ( ( ) (
V126()
V127()
V128()
V129()
V130()
V131()
V132() )
Element of
bool REAL : ( ( ) ( non
empty V35()
V126()
V127()
V128()
V132() )
set ) : ( ( ) ( )
set ) ) ) )
FinSequence-like complex-valued ext-real-valued real-valued )
Point of ( ( ) ( non
empty )
set ) ) ,
pc : ( ( ) (
Relation-like Function-like V42(2 : ( ( ) ( non
empty natural complex real ext-real positive non
negative V33()
V34()
V126()
V127()
V128()
V129()
V130()
V131() )
Element of
NAT : ( ( ) (
V126()
V127()
V128()
V129()
V130()
V131()
V132() )
Element of
bool REAL : ( ( ) ( non
empty V35()
V126()
V127()
V128()
V132() )
set ) : ( ( ) ( )
set ) ) ) )
FinSequence-like complex-valued ext-real-valued real-valued )
Point of ( ( ) ( non
empty )
set ) ) ,
p2 : ( ( ) (
Relation-like Function-like V42(2 : ( ( ) ( non
empty natural complex real ext-real positive non
negative V33()
V34()
V126()
V127()
V128()
V129()
V130()
V131() )
Element of
NAT : ( ( ) (
V126()
V127()
V128()
V129()
V130()
V131()
V132() )
Element of
bool REAL : ( ( ) ( non
empty V35()
V126()
V127()
V128()
V132() )
set ) : ( ( ) ( )
set ) ) ) )
FinSequence-like complex-valued ext-real-valued real-valued )
Point of ( ( ) ( non
empty )
set ) ) ) : ( ( ) (
complex real ext-real )
Element of
REAL : ( ( ) ( non
empty V35()
V126()
V127()
V128()
V132() )
set ) ) ;