REAL is non empty V35() V126() V127() V128() V132() set
NAT is V126() V127() V128() V129() V130() V131() V132() Element of bool REAL
bool REAL is set
COMPLEX is non empty V35() V126() V132() set
RAT is non empty V35() V126() V127() V128() V129() V132() set
INT is non empty V35() V126() V127() V128() V129() V130() V132() set
[:COMPLEX,COMPLEX:] is complex-valued set
bool [:COMPLEX,COMPLEX:] is set
[:[:COMPLEX,COMPLEX:],COMPLEX:] is complex-valued set
bool [:[:COMPLEX,COMPLEX:],COMPLEX:] is set
[:REAL,REAL:] is complex-valued ext-real-valued real-valued set
bool [:REAL,REAL:] is set
[:[:REAL,REAL:],REAL:] is complex-valued ext-real-valued real-valued set
bool [:[:REAL,REAL:],REAL:] is set
[:RAT,RAT:] is RAT -valued complex-valued ext-real-valued real-valued set
bool [:RAT,RAT:] is set
[:[:RAT,RAT:],RAT:] is RAT -valued complex-valued ext-real-valued real-valued set
bool [:[:RAT,RAT:],RAT:] is set
[:INT,INT:] is RAT -valued INT -valued complex-valued ext-real-valued real-valued set
bool [:INT,INT:] is set
[:[:INT,INT:],INT:] is RAT -valued INT -valued complex-valued ext-real-valued real-valued set
bool [:[:INT,INT:],INT:] is set
[:NAT,NAT:] is RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
[:[:NAT,NAT:],NAT:] is RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
bool [:[:NAT,NAT:],NAT:] is set
omega is V126() V127() V128() V129() V130() V131() V132() set
bool omega is set
bool NAT is set
K346() is non empty V75() L8()
the carrier of K346() is non empty set
K351() is non empty V75() V97() V98() V99() V101() V148() V149() V150() V151() V152() V153() L8()
K352() is non empty V75() V99() V101() V151() V152() V153() M13(K351())
K353() is non empty V75() V97() V99() V101() V151() V152() V153() V154() M16(K351(),K352())
K355() is non empty V75() V97() V99() V101() L8()
K356() is non empty V75() V97() V99() V101() V154() M13(K355())
[:NAT,REAL:] is complex-valued ext-real-valued real-valued set
bool [:NAT,REAL:] is set
[:NAT,COMPLEX:] is complex-valued set
bool [:NAT,COMPLEX:] is set
1 is non empty natural complex real ext-real positive non negative V33() V34() V126() V127() V128() V129() V130() V131() Element of NAT
[:1,1:] is RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
bool [:1,1:] is set
[:[:1,1:],1:] is RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
bool [:[:1,1:],1:] is set
[:[:1,1:],REAL:] is complex-valued ext-real-valued real-valued set
bool [:[:1,1:],REAL:] is set
2 is non empty natural complex real ext-real positive non negative V33() V34() V126() V127() V128() V129() V130() V131() Element of NAT
[:2,2:] is RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
[:[:2,2:],REAL:] is complex-valued ext-real-valued real-valued set
bool [:[:2,2:],REAL:] is set
TOP-REAL 2 is non empty V73() V138() V139() TopSpace-like V186() V187() V188() V189() V190() V191() V192() strict RLTopStruct
the carrier of (TOP-REAL 2) is non empty set
bool the carrier of (TOP-REAL 2) is set
K559() is non empty strict TopSpace-like V222() TopStruct
the carrier of K559() is non empty V126() V127() V128() set
RealSpace is non empty strict Reflexive discerning V180() triangle Discerning V222() MetrStruct
R^1 is non empty strict TopSpace-like V222() TopStruct
the carrier of R^1 is non empty V126() V127() V128() set
[: the carrier of (TOP-REAL 2), the carrier of R^1:] is complex-valued ext-real-valued real-valued set
bool [: the carrier of (TOP-REAL 2), the carrier of R^1:] is set
{} is empty V126() V127() V128() V129() V130() V131() V132() set
0 is empty natural complex real ext-real non positive non negative V33() V34() V126() V127() V128() V129() V130() V131() V132() Element of NAT
<i> is complex Element of COMPLEX
|.0.| is complex real ext-real Element of REAL
Re 0 is complex real ext-real Element of REAL
(Re 0) ^2 is complex real ext-real Element of REAL
(Re 0) * (Re 0) is complex real ext-real set
Im 0 is complex real ext-real Element of REAL
(Im 0) ^2 is complex real ext-real Element of REAL
(Im 0) * (Im 0) is complex real ext-real set
((Re 0) ^2) + ((Im 0) ^2) is complex real ext-real Element of REAL
sqrt (((Re 0) ^2) + ((Im 0) ^2)) is complex real ext-real Element of REAL
PI is non empty complex real ext-real positive non negative Element of REAL
2 * PI is non empty complex real ext-real positive non negative Element of REAL
5 is non empty natural complex real ext-real positive non negative V33() V34() V126() V127() V128() V129() V130() V131() Element of NAT
5 * PI is non empty complex real ext-real positive non negative Element of REAL
PI / 2 is non empty complex real ext-real positive non negative Element of REAL
3 is non empty natural complex real ext-real positive non negative V33() V34() V126() V127() V128() V129() V130() V131() Element of NAT
3 / 2 is non empty complex real ext-real positive non negative Element of REAL
(3 / 2) * PI is non empty complex real ext-real positive non negative Element of REAL
0. (TOP-REAL 2) is Relation-like Function-like V42(2) FinSequence-like zero complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
euc2cpx (0. (TOP-REAL 2)) is complex Element of COMPLEX
(0. (TOP-REAL 2)) `1 is complex real ext-real Element of REAL
K367((0. (TOP-REAL 2)),1) is complex real ext-real Element of REAL
(0. (TOP-REAL 2)) `2 is complex real ext-real Element of REAL
K367((0. (TOP-REAL 2)),2) is complex real ext-real Element of REAL
((0. (TOP-REAL 2)) `2) * <i> is complex set
((0. (TOP-REAL 2)) `1) + (((0. (TOP-REAL 2)) `2) * <i>) is complex set
0c is empty complex V126() V127() V128() V129() V130() V131() V132() Element of COMPLEX
cos is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
sin is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
K535(REAL,sin) is V126() V127() V128() Element of bool REAL
K535(REAL,cos) is V126() V127() V128() Element of bool REAL
K367(cos,0) is complex real ext-real Element of REAL
K367(sin,0) is complex real ext-real Element of REAL
cos 0 is complex real ext-real Element of REAL
sin 0 is complex real ext-real Element of REAL
cos (PI / 2) is complex real ext-real Element of REAL
sin (PI / 2) is complex real ext-real Element of REAL
cos PI is complex real ext-real Element of REAL
- 1 is non empty complex real ext-real non positive negative Element of REAL
sin PI is complex real ext-real Element of REAL
PI + (PI / 2) is non empty complex real ext-real positive non negative Element of REAL
cos (PI + (PI / 2)) is complex real ext-real Element of REAL
sin (PI + (PI / 2)) is complex real ext-real Element of REAL
cos (2 * PI) is complex real ext-real Element of REAL
sin (2 * PI) is complex real ext-real Element of REAL
ExtREAL is non empty V127() set
I[01] is non empty strict TopSpace-like V222() SubSpace of R^1
the carrier of I[01] is non empty V126() V127() V128() set
[.0,1.] is V126() V127() V128() Element of bool REAL
TopSpaceMetr RealSpace is TopStruct
Closed-Interval-TSpace (0,1) is non empty strict TopSpace-like V222() SubSpace of R^1
real_dist is Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-valued ext-real-valued real-valued Element of bool [:[:REAL,REAL:],REAL:]
MetrStruct(# REAL,real_dist #) is strict MetrStruct
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
- 1 is non empty complex real ext-real non positive negative set
(- 1) * p2 is Relation-like Function-like set
K214((TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
the U5 of (TOP-REAL 2) is Relation-like [: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):] -defined the carrier of (TOP-REAL 2) -valued Function-like total V30([: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2)) Element of bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):]
[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):] is set
[:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is set
bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is set
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p2) is Relation-like Function-like complex-valued set
K251(p1,K280(p2)) is Relation-like Function-like set
|.(p1 - p2).| is complex real ext-real non negative Element of REAL
sqr (p1 - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p1 - p2),(p1 - p2)) is Relation-like Function-like set
K339((sqr (p1 - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr (p1 - p2))) is complex real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
- 1 is non empty complex real ext-real non positive negative set
(- 1) * p2 is Relation-like Function-like set
K214((TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
the U5 of (TOP-REAL 2) is Relation-like [: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):] -defined the carrier of (TOP-REAL 2) -valued Function-like total V30([: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2)) Element of bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):]
[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):] is set
[:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is set
bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is set
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p2) is Relation-like Function-like complex-valued set
K251(p1,K280(p2)) is Relation-like Function-like set
|.(p1 - p2).| is complex real ext-real non negative Element of REAL
sqr (p1 - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p1 - p2),(p1 - p2)) is Relation-like Function-like set
K339((sqr (p1 - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr (p1 - p2))) is complex real ext-real Element of REAL
p2 - p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p1 is Relation-like Function-like set
K214((TOP-REAL 2),p2,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p1) is Relation-like Function-like complex-valued set
K251(p2,K280(p1)) is Relation-like Function-like set
|.(p2 - p1).| is complex real ext-real non negative Element of REAL
sqr (p2 - p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p2 - p1),(p2 - p1)) is Relation-like Function-like set
K339((sqr (p2 - p1))) is complex real ext-real Element of REAL
sqrt K339((sqr (p2 - p1))) is complex real ext-real Element of REAL
REAL 2 is non empty FinSequence-membered M10( REAL )
K318(2,REAL) is FinSequence-membered M10( REAL )
p3 is Relation-like NAT -defined REAL -valued Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL 2
|.p3.| is complex real ext-real non negative Element of REAL
sqr p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt (p3,p3) is Relation-like Function-like set
K339((sqr p3)) is complex real ext-real Element of REAL
sqrt K339((sqr p3)) is complex real ext-real Element of REAL
- p3 is Relation-like NAT -defined REAL -valued Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL 2
(- 1) * p3 is Relation-like Function-like set
|.(- p3).| is complex real ext-real non negative Element of REAL
sqr (- p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((- p3),(- p3)) is Relation-like Function-like set
K339((sqr (- p3))) is complex real ext-real Element of REAL
sqrt K339((sqr (- p3))) is complex real ext-real Element of REAL
- (p1 - p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- (p1 - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * (p1 - p2) is Relation-like Function-like set
|.(- (p1 - p2)).| is complex real ext-real non negative Element of REAL
sqr (- (p1 - p2)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((- (p1 - p2)),(- (p1 - p2))) is Relation-like Function-like set
K339((sqr (- (p1 - p2)))) is complex real ext-real Element of REAL
sqrt K339((sqr (- (p1 - p2)))) is complex real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p1,p2,p3) is complex real ext-real Element of REAL
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx p2),(euc2cpx p3)) is complex real ext-real set
sin (angle (p1,p2,p3)) is complex real ext-real Element of REAL
cos (angle (p1,p2,p3)) is complex real ext-real Element of REAL
p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
a is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p4,p,a) is complex real ext-real Element of REAL
euc2cpx p4 is complex Element of COMPLEX
p4 `1 is complex real ext-real Element of REAL
K367(p4,1) is complex real ext-real Element of REAL
p4 `2 is complex real ext-real Element of REAL
K367(p4,2) is complex real ext-real Element of REAL
(p4 `2) * <i> is complex set
(p4 `1) + ((p4 `2) * <i>) is complex set
euc2cpx p is complex Element of COMPLEX
p `1 is complex real ext-real Element of REAL
K367(p,1) is complex real ext-real Element of REAL
p `2 is complex real ext-real Element of REAL
K367(p,2) is complex real ext-real Element of REAL
(p `2) * <i> is complex set
(p `1) + ((p `2) * <i>) is complex set
euc2cpx a is complex Element of COMPLEX
a `1 is complex real ext-real Element of REAL
K367(a,1) is complex real ext-real Element of REAL
a `2 is complex real ext-real Element of REAL
K367(a,2) is complex real ext-real Element of REAL
(a `2) * <i> is complex set
(a `1) + ((a `2) * <i>) is complex set
angle ((euc2cpx p4),(euc2cpx p),(euc2cpx a)) is complex real ext-real set
sin (angle (p4,p,a)) is complex real ext-real Element of REAL
cos (angle (p4,p,a)) is complex real ext-real Element of REAL
(2 * PI) * 0 is empty complex real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() Element of REAL
(2 * PI) + ((2 * PI) * 0) is non empty complex real ext-real positive non negative Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p1,p2,p3) is complex real ext-real Element of REAL
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx p2),(euc2cpx p3)) is complex real ext-real set
sin (angle (p1,p2,p3)) is complex real ext-real Element of REAL
angle (p3,p2,p1) is complex real ext-real Element of REAL
angle ((euc2cpx p3),(euc2cpx p2),(euc2cpx p1)) is complex real ext-real set
sin (angle (p3,p2,p1)) is complex real ext-real Element of REAL
- (sin (angle (p3,p2,p1))) is complex real ext-real Element of REAL
(2 * PI) - (angle (p1,p2,p3)) is complex real ext-real Element of REAL
- (angle (p3,p2,p1)) is complex real ext-real Element of REAL
(- (angle (p3,p2,p1))) + (2 * PI) is complex real ext-real Element of REAL
sin ((- (angle (p3,p2,p1))) + (2 * PI)) is complex real ext-real Element of REAL
sin (- (angle (p3,p2,p1))) is complex real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p1,p2,p3) is complex real ext-real Element of REAL
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx p2),(euc2cpx p3)) is complex real ext-real set
cos (angle (p1,p2,p3)) is complex real ext-real Element of REAL
angle (p3,p2,p1) is complex real ext-real Element of REAL
angle ((euc2cpx p3),(euc2cpx p2),(euc2cpx p1)) is complex real ext-real set
cos (angle (p3,p2,p1)) is complex real ext-real Element of REAL
(2 * PI) - (angle (p1,p2,p3)) is complex real ext-real Element of REAL
- (angle (p3,p2,p1)) is complex real ext-real Element of REAL
(- (angle (p3,p2,p1))) + (2 * PI) is complex real ext-real Element of REAL
cos ((- (angle (p3,p2,p1))) + (2 * PI)) is complex real ext-real Element of REAL
cos (- (angle (p3,p2,p1))) is complex real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p1,p2,p3) is complex real ext-real Element of REAL
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx p2),(euc2cpx p3)) is complex real ext-real set
p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
a is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p4,p,a) is complex real ext-real Element of REAL
euc2cpx p4 is complex Element of COMPLEX
p4 `1 is complex real ext-real Element of REAL
K367(p4,1) is complex real ext-real Element of REAL
p4 `2 is complex real ext-real Element of REAL
K367(p4,2) is complex real ext-real Element of REAL
(p4 `2) * <i> is complex set
(p4 `1) + ((p4 `2) * <i>) is complex set
euc2cpx p is complex Element of COMPLEX
p `1 is complex real ext-real Element of REAL
K367(p,1) is complex real ext-real Element of REAL
p `2 is complex real ext-real Element of REAL
K367(p,2) is complex real ext-real Element of REAL
(p `2) * <i> is complex set
(p `1) + ((p `2) * <i>) is complex set
euc2cpx a is complex Element of COMPLEX
a `1 is complex real ext-real Element of REAL
K367(a,1) is complex real ext-real Element of REAL
a `2 is complex real ext-real Element of REAL
K367(a,2) is complex real ext-real Element of REAL
(a `2) * <i> is complex set
(a `1) + ((a `2) * <i>) is complex set
angle ((euc2cpx p4),(euc2cpx p),(euc2cpx a)) is complex real ext-real set
2 * (angle (p4,p,a)) is complex real ext-real Element of REAL
(2 * (angle (p4,p,a))) + (2 * PI) is complex real ext-real Element of REAL
0 + (2 * PI) is non empty complex real ext-real positive non negative Element of REAL
(angle (p4,p,a)) * 2 is complex real ext-real Element of REAL
((angle (p4,p,a)) * 2) + (2 * PI) is complex real ext-real Element of REAL
4 is non empty natural complex real ext-real positive non negative V33() V34() V126() V127() V128() V129() V130() V131() Element of NAT
4 * PI is non empty complex real ext-real positive non negative Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p1,p2,p3) is complex real ext-real Element of REAL
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx p2),(euc2cpx p3)) is complex real ext-real set
p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
a is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p4,p,a) is complex real ext-real Element of REAL
euc2cpx p4 is complex Element of COMPLEX
p4 `1 is complex real ext-real Element of REAL
K367(p4,1) is complex real ext-real Element of REAL
p4 `2 is complex real ext-real Element of REAL
K367(p4,2) is complex real ext-real Element of REAL
(p4 `2) * <i> is complex set
(p4 `1) + ((p4 `2) * <i>) is complex set
euc2cpx p is complex Element of COMPLEX
p `1 is complex real ext-real Element of REAL
K367(p,1) is complex real ext-real Element of REAL
p `2 is complex real ext-real Element of REAL
K367(p,2) is complex real ext-real Element of REAL
(p `2) * <i> is complex set
(p `1) + ((p `2) * <i>) is complex set
euc2cpx a is complex Element of COMPLEX
a `1 is complex real ext-real Element of REAL
K367(a,1) is complex real ext-real Element of REAL
a `2 is complex real ext-real Element of REAL
K367(a,2) is complex real ext-real Element of REAL
(a `2) * <i> is complex set
(a `1) + ((a `2) * <i>) is complex set
angle ((euc2cpx p4),(euc2cpx p),(euc2cpx a)) is complex real ext-real set
2 * (angle (p4,p,a)) is complex real ext-real Element of REAL
(2 * (angle (p4,p,a))) + (4 * PI) is complex real ext-real Element of REAL
0 + (4 * PI) is non empty complex real ext-real positive non negative Element of REAL
(angle (p4,p,a)) * 2 is complex real ext-real Element of REAL
((angle (p4,p,a)) * 2) + (4 * PI) is complex real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p1,p2,p3) is complex real ext-real Element of REAL
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx p2),(euc2cpx p3)) is complex real ext-real set
p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
a is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p4,p,a) is complex real ext-real Element of REAL
euc2cpx p4 is complex Element of COMPLEX
p4 `1 is complex real ext-real Element of REAL
K367(p4,1) is complex real ext-real Element of REAL
p4 `2 is complex real ext-real Element of REAL
K367(p4,2) is complex real ext-real Element of REAL
(p4 `2) * <i> is complex set
(p4 `1) + ((p4 `2) * <i>) is complex set
euc2cpx p is complex Element of COMPLEX
p `1 is complex real ext-real Element of REAL
K367(p,1) is complex real ext-real Element of REAL
p `2 is complex real ext-real Element of REAL
K367(p,2) is complex real ext-real Element of REAL
(p `2) * <i> is complex set
(p `1) + ((p `2) * <i>) is complex set
euc2cpx a is complex Element of COMPLEX
a `1 is complex real ext-real Element of REAL
K367(a,1) is complex real ext-real Element of REAL
a `2 is complex real ext-real Element of REAL
K367(a,2) is complex real ext-real Element of REAL
(a `2) * <i> is complex set
(a `1) + ((a `2) * <i>) is complex set
angle ((euc2cpx p4),(euc2cpx p),(euc2cpx a)) is complex real ext-real set
2 * (angle (p4,p,a)) is complex real ext-real Element of REAL
(2 * (angle (p4,p,a))) - (4 * PI) is complex real ext-real Element of REAL
(2 * PI) * 2 is non empty complex real ext-real positive non negative Element of REAL
(angle (p4,p,a)) * 2 is complex real ext-real Element of REAL
(4 * PI) - (4 * PI) is complex real ext-real Element of REAL
((angle (p4,p,a)) * 2) - (4 * PI) is complex real ext-real Element of REAL
6 is non empty natural complex real ext-real positive non negative V33() V34() V126() V127() V128() V129() V130() V131() Element of NAT
6 * PI is non empty complex real ext-real positive non negative Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p1,p2,p3) is complex real ext-real Element of REAL
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx p2),(euc2cpx p3)) is complex real ext-real set
p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
a is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p4,p,a) is complex real ext-real Element of REAL
euc2cpx p4 is complex Element of COMPLEX
p4 `1 is complex real ext-real Element of REAL
K367(p4,1) is complex real ext-real Element of REAL
p4 `2 is complex real ext-real Element of REAL
K367(p4,2) is complex real ext-real Element of REAL
(p4 `2) * <i> is complex set
(p4 `1) + ((p4 `2) * <i>) is complex set
euc2cpx p is complex Element of COMPLEX
p `1 is complex real ext-real Element of REAL
K367(p,1) is complex real ext-real Element of REAL
p `2 is complex real ext-real Element of REAL
K367(p,2) is complex real ext-real Element of REAL
(p `2) * <i> is complex set
(p `1) + ((p `2) * <i>) is complex set
euc2cpx a is complex Element of COMPLEX
a `1 is complex real ext-real Element of REAL
K367(a,1) is complex real ext-real Element of REAL
a `2 is complex real ext-real Element of REAL
K367(a,2) is complex real ext-real Element of REAL
(a `2) * <i> is complex set
(a `1) + ((a `2) * <i>) is complex set
angle ((euc2cpx p4),(euc2cpx p),(euc2cpx a)) is complex real ext-real set
2 * (angle (p4,p,a)) is complex real ext-real Element of REAL
(2 * (angle (p4,p,a))) - (6 * PI) is complex real ext-real Element of REAL
(2 * PI) * 2 is non empty complex real ext-real positive non negative Element of REAL
(angle (p4,p,a)) * 2 is complex real ext-real Element of REAL
- 2 is non empty complex real ext-real non positive negative Element of REAL
PI * (- 2) is non empty complex real ext-real non positive negative Element of REAL
0 * (- 2) is empty complex real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() Element of REAL
(4 * PI) - (6 * PI) is complex real ext-real Element of REAL
((angle (p4,p,a)) * 2) - (6 * PI) is complex real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
- 1 is non empty complex real ext-real non positive negative set
(- 1) * p2 is Relation-like Function-like set
K214((TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
the U5 of (TOP-REAL 2) is Relation-like [: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):] -defined the carrier of (TOP-REAL 2) -valued Function-like total V30([: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2)) Element of bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):]
[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):] is set
[:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is set
bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is set
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p2) is Relation-like Function-like complex-valued set
K251(p1,K280(p2)) is Relation-like Function-like set
euc2cpx (p1 - p2) is complex Element of COMPLEX
(p1 - p2) `1 is complex real ext-real Element of REAL
K367((p1 - p2),1) is complex real ext-real Element of REAL
(p1 - p2) `2 is complex real ext-real Element of REAL
K367((p1 - p2),2) is complex real ext-real Element of REAL
((p1 - p2) `2) * <i> is complex set
((p1 - p2) `1) + (((p1 - p2) `2) * <i>) is complex set
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p3,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p3,K280(p2)) is Relation-like Function-like set
euc2cpx (p3 - p2) is complex Element of COMPLEX
(p3 - p2) `1 is complex real ext-real Element of REAL
K367((p3 - p2),1) is complex real ext-real Element of REAL
(p3 - p2) `2 is complex real ext-real Element of REAL
K367((p3 - p2),2) is complex real ext-real Element of REAL
((p3 - p2) `2) * <i> is complex set
((p3 - p2) `1) + (((p3 - p2) `2) * <i>) is complex set
angle (p1,p2,p3) is complex real ext-real Element of REAL
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx p2),(euc2cpx p3)) is complex real ext-real set
p4 is complex Element of COMPLEX
p is complex Element of COMPLEX
angle (p4,p) is complex real ext-real Element of REAL
angle ((p1 - p2),(0. (TOP-REAL 2)),(p3 - p2)) is complex real ext-real Element of REAL
angle ((euc2cpx (p1 - p2)),(euc2cpx (0. (TOP-REAL 2))),(euc2cpx (p3 - p2))) is complex real ext-real set
p2 is complex Element of COMPLEX
p1 is complex Element of COMPLEX
Arg p1 is complex real ext-real Element of REAL
- (Arg p1) is complex real ext-real Element of REAL
Rotate (p2,(- (Arg p1))) is complex Element of COMPLEX
Arg (Rotate (p2,(- (Arg p1)))) is complex real ext-real Element of REAL
p2 is complex Element of COMPLEX
p1 is complex Element of COMPLEX
Arg p1 is complex real ext-real Element of REAL
angle (p1,p2) is complex real ext-real Element of REAL
- (Arg p1) is complex real ext-real Element of REAL
Rotate (p2,(- (Arg p1))) is complex Element of COMPLEX
Arg (Rotate (p2,(- (Arg p1)))) is complex real ext-real Element of REAL
p2 is complex Element of COMPLEX
Arg p2 is complex real ext-real Element of REAL
p1 is complex Element of COMPLEX
Arg p1 is complex real ext-real Element of REAL
(Arg p2) - (Arg p1) is complex real ext-real Element of REAL
- (Arg p1) is complex real ext-real Element of REAL
Rotate (p2,(- (Arg p1))) is complex Element of COMPLEX
Arg (Rotate (p2,(- (Arg p1)))) is complex real ext-real Element of REAL
(- (Arg p1)) + (Arg p2) is complex real ext-real Element of REAL
(2 * PI) + (Arg p1) is complex real ext-real Element of REAL
(Arg p2) + 0 is complex real ext-real Element of REAL
|.p2.| is complex real ext-real Element of REAL
Re p2 is complex real ext-real Element of REAL
(Re p2) ^2 is complex real ext-real Element of REAL
(Re p2) * (Re p2) is complex real ext-real set
Im p2 is complex real ext-real Element of REAL
(Im p2) ^2 is complex real ext-real Element of REAL
(Im p2) * (Im p2) is complex real ext-real set
((Re p2) ^2) + ((Im p2) ^2) is complex real ext-real Element of REAL
sqrt (((Re p2) ^2) + ((Im p2) ^2)) is complex real ext-real Element of REAL
cos ((- (Arg p1)) + (Arg p2)) is complex real ext-real Element of REAL
|.p2.| * (cos ((- (Arg p1)) + (Arg p2))) is complex real ext-real Element of REAL
sin ((- (Arg p1)) + (Arg p2)) is complex real ext-real Element of REAL
|.p2.| * (sin ((- (Arg p1)) + (Arg p2))) is complex real ext-real Element of REAL
(|.p2.| * (sin ((- (Arg p1)) + (Arg p2)))) * <i> is complex set
(|.p2.| * (cos ((- (Arg p1)) + (Arg p2)))) + ((|.p2.| * (sin ((- (Arg p1)) + (Arg p2)))) * <i>) is complex set
((2 * PI) + (Arg p1)) - (Arg p1) is complex real ext-real Element of REAL
|.(Rotate (p2,(- (Arg p1)))).| is complex real ext-real Element of REAL
Re (Rotate (p2,(- (Arg p1)))) is complex real ext-real Element of REAL
(Re (Rotate (p2,(- (Arg p1))))) ^2 is complex real ext-real Element of REAL
(Re (Rotate (p2,(- (Arg p1))))) * (Re (Rotate (p2,(- (Arg p1))))) is complex real ext-real set
Im (Rotate (p2,(- (Arg p1)))) is complex real ext-real Element of REAL
(Im (Rotate (p2,(- (Arg p1))))) ^2 is complex real ext-real Element of REAL
(Im (Rotate (p2,(- (Arg p1))))) * (Im (Rotate (p2,(- (Arg p1))))) is complex real ext-real set
((Re (Rotate (p2,(- (Arg p1))))) ^2) + ((Im (Rotate (p2,(- (Arg p1))))) ^2) is complex real ext-real Element of REAL
sqrt (((Re (Rotate (p2,(- (Arg p1))))) ^2) + ((Im (Rotate (p2,(- (Arg p1))))) ^2)) is complex real ext-real Element of REAL
p2 is complex Element of COMPLEX
Arg p2 is complex real ext-real Element of REAL
p1 is complex Element of COMPLEX
Arg p1 is complex real ext-real Element of REAL
(Arg p2) - (Arg p1) is complex real ext-real Element of REAL
angle (p1,p2) is complex real ext-real Element of REAL
- (Arg p1) is complex real ext-real Element of REAL
Rotate (p2,(- (Arg p1))) is complex Element of COMPLEX
Arg (Rotate (p2,(- (Arg p1)))) is complex real ext-real Element of REAL
p2 is complex Element of COMPLEX
Arg p2 is complex real ext-real Element of REAL
p1 is complex Element of COMPLEX
Arg p1 is complex real ext-real Element of REAL
(Arg p2) - (Arg p1) is complex real ext-real Element of REAL
- (Arg p1) is complex real ext-real Element of REAL
Rotate (p2,(- (Arg p1))) is complex Element of COMPLEX
Arg (Rotate (p2,(- (Arg p1)))) is complex real ext-real Element of REAL
(2 * PI) - (Arg p1) is complex real ext-real Element of REAL
((2 * PI) - (Arg p1)) + (Arg p2) is complex real ext-real Element of REAL
(- (Arg p1)) + (Arg p2) is complex real ext-real Element of REAL
0 + (2 * PI) is non empty complex real ext-real positive non negative Element of REAL
((- (Arg p1)) + (Arg p2)) + (2 * PI) is complex real ext-real Element of REAL
|.p2.| is complex real ext-real Element of REAL
Re p2 is complex real ext-real Element of REAL
(Re p2) ^2 is complex real ext-real Element of REAL
(Re p2) * (Re p2) is complex real ext-real set
Im p2 is complex real ext-real Element of REAL
(Im p2) ^2 is complex real ext-real Element of REAL
(Im p2) * (Im p2) is complex real ext-real set
((Re p2) ^2) + ((Im p2) ^2) is complex real ext-real Element of REAL
sqrt (((Re p2) ^2) + ((Im p2) ^2)) is complex real ext-real Element of REAL
cos ((- (Arg p1)) + (Arg p2)) is complex real ext-real Element of REAL
|.p2.| * (cos ((- (Arg p1)) + (Arg p2))) is complex real ext-real Element of REAL
sin ((- (Arg p1)) + (Arg p2)) is complex real ext-real Element of REAL
|.p2.| * (sin ((- (Arg p1)) + (Arg p2))) is complex real ext-real Element of REAL
(|.p2.| * (sin ((- (Arg p1)) + (Arg p2)))) * <i> is complex set
(|.p2.| * (cos ((- (Arg p1)) + (Arg p2)))) + ((|.p2.| * (sin ((- (Arg p1)) + (Arg p2)))) * <i>) is complex set
(2 * PI) * 1 is non empty complex real ext-real positive non negative Element of REAL
((2 * PI) * 1) + ((- (Arg p1)) + (Arg p2)) is complex real ext-real Element of REAL
cos (((2 * PI) * 1) + ((- (Arg p1)) + (Arg p2))) is complex real ext-real Element of REAL
|.p2.| * (cos (((2 * PI) * 1) + ((- (Arg p1)) + (Arg p2)))) is complex real ext-real Element of REAL
(|.p2.| * (cos (((2 * PI) * 1) + ((- (Arg p1)) + (Arg p2))))) + ((|.p2.| * (sin ((- (Arg p1)) + (Arg p2)))) * <i>) is complex set
(2 * PI) + ((- (Arg p1)) + (Arg p2)) is complex real ext-real Element of REAL
cos ((2 * PI) + ((- (Arg p1)) + (Arg p2))) is complex real ext-real Element of REAL
|.p2.| * (cos ((2 * PI) + ((- (Arg p1)) + (Arg p2)))) is complex real ext-real Element of REAL
sin (((2 * PI) * 1) + ((- (Arg p1)) + (Arg p2))) is complex real ext-real Element of REAL
|.p2.| * (sin (((2 * PI) * 1) + ((- (Arg p1)) + (Arg p2)))) is complex real ext-real Element of REAL
(|.p2.| * (sin (((2 * PI) * 1) + ((- (Arg p1)) + (Arg p2))))) * <i> is complex set
(|.p2.| * (cos ((2 * PI) + ((- (Arg p1)) + (Arg p2))))) + ((|.p2.| * (sin (((2 * PI) * 1) + ((- (Arg p1)) + (Arg p2))))) * <i>) is complex set
(Arg p1) + 0 is complex real ext-real Element of REAL
(2 * PI) + (Arg p2) is complex real ext-real Element of REAL
(Arg p1) - (Arg p1) is complex real ext-real Element of REAL
((2 * PI) + (Arg p2)) - (Arg p1) is complex real ext-real Element of REAL
|.(Rotate (p2,(- (Arg p1)))).| is complex real ext-real Element of REAL
Re (Rotate (p2,(- (Arg p1)))) is complex real ext-real Element of REAL
(Re (Rotate (p2,(- (Arg p1))))) ^2 is complex real ext-real Element of REAL
(Re (Rotate (p2,(- (Arg p1))))) * (Re (Rotate (p2,(- (Arg p1))))) is complex real ext-real set
Im (Rotate (p2,(- (Arg p1)))) is complex real ext-real Element of REAL
(Im (Rotate (p2,(- (Arg p1))))) ^2 is complex real ext-real Element of REAL
(Im (Rotate (p2,(- (Arg p1))))) * (Im (Rotate (p2,(- (Arg p1))))) is complex real ext-real set
((Re (Rotate (p2,(- (Arg p1))))) ^2) + ((Im (Rotate (p2,(- (Arg p1))))) ^2) is complex real ext-real Element of REAL
sqrt (((Re (Rotate (p2,(- (Arg p1))))) ^2) + ((Im (Rotate (p2,(- (Arg p1))))) ^2)) is complex real ext-real Element of REAL
p2 is complex Element of COMPLEX
Arg p2 is complex real ext-real Element of REAL
p1 is complex Element of COMPLEX
Arg p1 is complex real ext-real Element of REAL
(Arg p2) - (Arg p1) is complex real ext-real Element of REAL
angle (p1,p2) is complex real ext-real Element of REAL
(2 * PI) - (Arg p1) is complex real ext-real Element of REAL
((2 * PI) - (Arg p1)) + (Arg p2) is complex real ext-real Element of REAL
- (Arg p1) is complex real ext-real Element of REAL
Rotate (p2,(- (Arg p1))) is complex Element of COMPLEX
Arg (Rotate (p2,(- (Arg p1)))) is complex real ext-real Element of REAL
p1 is complex Element of COMPLEX
p2 is complex Element of COMPLEX
angle (p1,p2) is complex real ext-real Element of REAL
p3 is complex Element of COMPLEX
angle (p2,p3) is complex real ext-real Element of REAL
(angle (p1,p2)) + (angle (p2,p3)) is complex real ext-real Element of REAL
angle (p1,p3) is complex real ext-real Element of REAL
(angle (p1,p3)) + (2 * PI) is complex real ext-real Element of REAL
Arg p2 is complex real ext-real Element of REAL
Arg p1 is complex real ext-real Element of REAL
0 + (angle (p2,p3)) is complex real ext-real Element of REAL
Arg p1 is complex real ext-real Element of REAL
(2 * PI) - (Arg p1) is complex real ext-real Element of REAL
((2 * PI) - (Arg p1)) + (angle (p2,p3)) is complex real ext-real Element of REAL
((2 * PI) - (Arg p1)) + 0 is complex real ext-real Element of REAL
Arg p1 is complex real ext-real Element of REAL
Arg p1 is complex real ext-real Element of REAL
Arg p2 is complex real ext-real Element of REAL
(Arg p2) - (Arg p1) is complex real ext-real Element of REAL
(Arg p2) - (Arg p1) is complex real ext-real Element of REAL
((Arg p2) - (Arg p1)) + (angle (p2,p3)) is complex real ext-real Element of REAL
(Arg p2) - (Arg p1) is complex real ext-real Element of REAL
Arg p1 is complex real ext-real Element of REAL
Arg p2 is complex real ext-real Element of REAL
(Arg p2) - (Arg p1) is complex real ext-real Element of REAL
(2 * PI) - (Arg p1) is complex real ext-real Element of REAL
((2 * PI) - (Arg p1)) + (Arg p2) is complex real ext-real Element of REAL
(((2 * PI) - (Arg p1)) + (Arg p2)) + (angle (p2,p3)) is complex real ext-real Element of REAL
(Arg p2) - (Arg p1) is complex real ext-real Element of REAL
- (Arg p1) is complex real ext-real Element of REAL
- (- (Arg p1)) is complex real ext-real Element of REAL
- 0 is empty complex real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() Element of REAL
(Arg p2) - (Arg p1) is complex real ext-real Element of REAL
Arg p1 is complex real ext-real Element of REAL
Arg p2 is complex real ext-real Element of REAL
(Arg p2) - (Arg p1) is complex real ext-real Element of REAL
(Arg p2) - (Arg p1) is complex real ext-real Element of REAL
((Arg p2) - (Arg p1)) + (angle (p2,p3)) is complex real ext-real Element of REAL
(2 * PI) - (Arg p2) is complex real ext-real Element of REAL
(Arg p2) + ((2 * PI) - (Arg p2)) is complex real ext-real Element of REAL
(Arg p2) - (Arg p1) is complex real ext-real Element of REAL
Arg p1 is complex real ext-real Element of REAL
Arg p2 is complex real ext-real Element of REAL
(Arg p2) - (Arg p1) is complex real ext-real Element of REAL
(2 * PI) - (Arg p1) is complex real ext-real Element of REAL
((2 * PI) - (Arg p1)) + (Arg p2) is complex real ext-real Element of REAL
(((2 * PI) - (Arg p1)) + (Arg p2)) + (angle (p2,p3)) is complex real ext-real Element of REAL
(2 * PI) - (Arg p2) is complex real ext-real Element of REAL
(((2 * PI) - (Arg p1)) + (Arg p2)) + ((2 * PI) - (Arg p2)) is complex real ext-real Element of REAL
(2 * PI) + (2 * PI) is non empty complex real ext-real positive non negative Element of REAL
((2 * PI) + (2 * PI)) - (Arg p1) is complex real ext-real Element of REAL
(Arg p2) - (Arg p1) is complex real ext-real Element of REAL
(2 * PI) - (Arg p1) is complex real ext-real Element of REAL
((Arg p2) - (Arg p1)) + (angle (p2,p3)) is complex real ext-real Element of REAL
(2 * PI) - (Arg p2) is complex real ext-real Element of REAL
((Arg p2) - (Arg p1)) + ((2 * PI) - (Arg p2)) is complex real ext-real Element of REAL
(Arg p2) - (Arg p1) is complex real ext-real Element of REAL
Arg p1 is complex real ext-real Element of REAL
Arg p2 is complex real ext-real Element of REAL
Arg p3 is complex real ext-real Element of REAL
Arg p2 is complex real ext-real Element of REAL
(Arg p3) - (Arg p2) is complex real ext-real Element of REAL
Arg p1 is complex real ext-real Element of REAL
(Arg p3) - (Arg p1) is complex real ext-real Element of REAL
(Arg p3) - 0 is complex real ext-real Element of REAL
Arg p3 is complex real ext-real Element of REAL
Arg p2 is complex real ext-real Element of REAL
(Arg p3) - (Arg p2) is complex real ext-real Element of REAL
Arg p1 is complex real ext-real Element of REAL
(Arg p3) - (Arg p1) is complex real ext-real Element of REAL
(2 * PI) - (Arg p1) is complex real ext-real Element of REAL
((2 * PI) - (Arg p1)) + (angle (p2,p3)) is complex real ext-real Element of REAL
((2 * PI) - (Arg p1)) + ((Arg p3) - (Arg p2)) is complex real ext-real Element of REAL
(Arg p3) - 0 is complex real ext-real Element of REAL
((2 * PI) - (Arg p1)) + ((Arg p3) - 0) is complex real ext-real Element of REAL
((2 * PI) - (Arg p1)) + (Arg p3) is complex real ext-real Element of REAL
Arg p3 is complex real ext-real Element of REAL
Arg p2 is complex real ext-real Element of REAL
(Arg p3) - (Arg p2) is complex real ext-real Element of REAL
Arg p1 is complex real ext-real Element of REAL
(Arg p3) - (Arg p1) is complex real ext-real Element of REAL
(Arg p3) - 0 is complex real ext-real Element of REAL
Arg p3 is complex real ext-real Element of REAL
Arg p2 is complex real ext-real Element of REAL
(Arg p3) - (Arg p2) is complex real ext-real Element of REAL
Arg p1 is complex real ext-real Element of REAL
(Arg p3) - (Arg p1) is complex real ext-real Element of REAL
0 + (angle (p2,p3)) is complex real ext-real Element of REAL
0 + ((Arg p3) - (Arg p2)) is complex real ext-real Element of REAL
(Arg p3) - 0 is complex real ext-real Element of REAL
0 + ((Arg p3) - 0) is complex real ext-real Element of REAL
(2 * PI) - (Arg p1) is complex real ext-real Element of REAL
((2 * PI) - (Arg p1)) + (angle (p2,p3)) is complex real ext-real Element of REAL
((2 * PI) - (Arg p1)) + ((Arg p3) - (Arg p2)) is complex real ext-real Element of REAL
(Arg p3) - 0 is complex real ext-real Element of REAL
((2 * PI) - (Arg p1)) + ((Arg p3) - 0) is complex real ext-real Element of REAL
Arg p3 is complex real ext-real Element of REAL
Arg p2 is complex real ext-real Element of REAL
(Arg p3) - (Arg p2) is complex real ext-real Element of REAL
Arg p1 is complex real ext-real Element of REAL
(Arg p3) - (Arg p1) is complex real ext-real Element of REAL
Arg p3 is complex real ext-real Element of REAL
Arg p2 is complex real ext-real Element of REAL
(Arg p3) - (Arg p2) is complex real ext-real Element of REAL
Arg p1 is complex real ext-real Element of REAL
(Arg p3) - (Arg p1) is complex real ext-real Element of REAL
(Arg p2) - (Arg p1) is complex real ext-real Element of REAL
(2 * PI) - (Arg p1) is complex real ext-real Element of REAL
((2 * PI) - (Arg p1)) + (Arg p3) is complex real ext-real Element of REAL
((2 * PI) - (Arg p1)) + (Arg p2) is complex real ext-real Element of REAL
(((2 * PI) - (Arg p1)) + (Arg p2)) + (angle (p2,p3)) is complex real ext-real Element of REAL
(2 * PI) - (Arg p2) is complex real ext-real Element of REAL
((2 * PI) - (Arg p2)) + (Arg p3) is complex real ext-real Element of REAL
(((2 * PI) - (Arg p1)) + (Arg p2)) + (((2 * PI) - (Arg p2)) + (Arg p3)) is complex real ext-real Element of REAL
(2 * PI) + (2 * PI) is non empty complex real ext-real positive non negative Element of REAL
((2 * PI) + (2 * PI)) - (Arg p1) is complex real ext-real Element of REAL
(((2 * PI) + (2 * PI)) - (Arg p1)) + (Arg p3) is complex real ext-real Element of REAL
(Arg p2) - (Arg p1) is complex real ext-real Element of REAL
((Arg p2) - (Arg p1)) + (angle (p2,p3)) is complex real ext-real Element of REAL
(2 * PI) - (Arg p2) is complex real ext-real Element of REAL
((2 * PI) - (Arg p2)) + (Arg p3) is complex real ext-real Element of REAL
((Arg p2) - (Arg p1)) + (((2 * PI) - (Arg p2)) + (Arg p3)) is complex real ext-real Element of REAL
(2 * PI) - (Arg p1) is complex real ext-real Element of REAL
((2 * PI) - (Arg p1)) + (Arg p3) is complex real ext-real Element of REAL
(Arg p2) - (Arg p1) is complex real ext-real Element of REAL
Arg p3 is complex real ext-real Element of REAL
Arg p2 is complex real ext-real Element of REAL
(Arg p3) - (Arg p2) is complex real ext-real Element of REAL
Arg p1 is complex real ext-real Element of REAL
(Arg p3) - (Arg p1) is complex real ext-real Element of REAL
(Arg p2) - (Arg p1) is complex real ext-real Element of REAL
(2 * PI) - (Arg p1) is complex real ext-real Element of REAL
((2 * PI) - (Arg p1)) + (Arg p2) is complex real ext-real Element of REAL
(((2 * PI) - (Arg p1)) + (Arg p2)) + (angle (p2,p3)) is complex real ext-real Element of REAL
(((2 * PI) - (Arg p1)) + (Arg p2)) + ((Arg p3) - (Arg p2)) is complex real ext-real Element of REAL
((2 * PI) - (Arg p1)) + (Arg p3) is complex real ext-real Element of REAL
(Arg p2) - (Arg p1) is complex real ext-real Element of REAL
0 + 0 is empty complex real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() Element of REAL
((Arg p2) - (Arg p1)) + ((Arg p3) - (Arg p2)) is complex real ext-real Element of REAL
(Arg p2) - (Arg p1) is complex real ext-real Element of REAL
Arg p3 is complex real ext-real Element of REAL
Arg p2 is complex real ext-real Element of REAL
(Arg p3) - (Arg p2) is complex real ext-real Element of REAL
Arg p1 is complex real ext-real Element of REAL
(Arg p3) - (Arg p1) is complex real ext-real Element of REAL
(Arg p2) - (Arg p1) is complex real ext-real Element of REAL
0 + 0 is empty complex real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() Element of REAL
((Arg p2) - (Arg p1)) + ((Arg p3) - (Arg p2)) is complex real ext-real Element of REAL
(Arg p2) - (Arg p1) is complex real ext-real Element of REAL
((Arg p2) - (Arg p1)) + (angle (p2,p3)) is complex real ext-real Element of REAL
(2 * PI) - (Arg p2) is complex real ext-real Element of REAL
((2 * PI) - (Arg p2)) + (Arg p3) is complex real ext-real Element of REAL
((Arg p2) - (Arg p1)) + (((2 * PI) - (Arg p2)) + (Arg p3)) is complex real ext-real Element of REAL
(2 * PI) - (Arg p1) is complex real ext-real Element of REAL
((2 * PI) - (Arg p1)) + (Arg p3) is complex real ext-real Element of REAL
(Arg p2) - (Arg p1) is complex real ext-real Element of REAL
Arg p3 is complex real ext-real Element of REAL
Arg p2 is complex real ext-real Element of REAL
(Arg p3) - (Arg p2) is complex real ext-real Element of REAL
Arg p1 is complex real ext-real Element of REAL
(Arg p3) - (Arg p1) is complex real ext-real Element of REAL
(Arg p2) - (Arg p1) is complex real ext-real Element of REAL
(2 * PI) - (Arg p1) is complex real ext-real Element of REAL
((2 * PI) - (Arg p1)) + (Arg p2) is complex real ext-real Element of REAL
(((2 * PI) - (Arg p1)) + (Arg p2)) + (angle (p2,p3)) is complex real ext-real Element of REAL
(2 * PI) + (Arg p2) is complex real ext-real Element of REAL
((2 * PI) + (Arg p2)) - (Arg p1) is complex real ext-real Element of REAL
(((2 * PI) + (Arg p2)) - (Arg p1)) + ((Arg p3) - (Arg p2)) is complex real ext-real Element of REAL
((2 * PI) - (Arg p1)) + (Arg p3) is complex real ext-real Element of REAL
(Arg p2) - (Arg p1) is complex real ext-real Element of REAL
((Arg p2) - (Arg p1)) + (angle (p2,p3)) is complex real ext-real Element of REAL
((Arg p2) - (Arg p1)) + ((Arg p3) - (Arg p2)) is complex real ext-real Element of REAL
- (Arg p1) is complex real ext-real Element of REAL
(- (Arg p1)) + (Arg p3) is complex real ext-real Element of REAL
(Arg p2) - (Arg p1) is complex real ext-real Element of REAL
Arg p3 is complex real ext-real Element of REAL
Arg p2 is complex real ext-real Element of REAL
(Arg p3) - (Arg p2) is complex real ext-real Element of REAL
Arg p1 is complex real ext-real Element of REAL
(Arg p3) - (Arg p1) is complex real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p1,p2,p3) is complex real ext-real Element of REAL
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx p2),(euc2cpx p3)) is complex real ext-real set
p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p3,p2,p4) is complex real ext-real Element of REAL
euc2cpx p4 is complex Element of COMPLEX
p4 `1 is complex real ext-real Element of REAL
K367(p4,1) is complex real ext-real Element of REAL
p4 `2 is complex real ext-real Element of REAL
K367(p4,2) is complex real ext-real Element of REAL
(p4 `2) * <i> is complex set
(p4 `1) + ((p4 `2) * <i>) is complex set
angle ((euc2cpx p3),(euc2cpx p2),(euc2cpx p4)) is complex real ext-real set
(angle (p1,p2,p3)) + (angle (p3,p2,p4)) is complex real ext-real Element of REAL
angle (p1,p2,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p1),(euc2cpx p2),(euc2cpx p4)) is complex real ext-real set
(angle (p1,p2,p4)) + (2 * PI) is complex real ext-real Element of REAL
p1 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
- 1 is non empty complex real ext-real non positive negative set
(- 1) * p2 is Relation-like Function-like set
K214((TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
the U5 of (TOP-REAL 2) is Relation-like [: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):] -defined the carrier of (TOP-REAL 2) -valued Function-like total V30([: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2)) Element of bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):]
[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):] is set
[:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is set
bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is set
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p2) is Relation-like Function-like complex-valued set
K251(p1,K280(p2)) is Relation-like Function-like set
euc2cpx (p1 - p2) is complex Element of COMPLEX
(p1 - p2) `1 is complex real ext-real Element of REAL
K367((p1 - p2),1) is complex real ext-real Element of REAL
(p1 - p2) `2 is complex real ext-real Element of REAL
K367((p1 - p2),2) is complex real ext-real Element of REAL
((p1 - p2) `2) * <i> is complex set
((p1 - p2) `1) + (((p1 - p2) `2) * <i>) is complex set
p3 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p3,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p3,K280(p2)) is Relation-like Function-like set
euc2cpx (p3 - p2) is complex Element of COMPLEX
(p3 - p2) `1 is complex real ext-real Element of REAL
K367((p3 - p2),1) is complex real ext-real Element of REAL
(p3 - p2) `2 is complex real ext-real Element of REAL
K367((p3 - p2),2) is complex real ext-real Element of REAL
((p3 - p2) `2) * <i> is complex set
((p3 - p2) `1) + (((p3 - p2) `2) * <i>) is complex set
p4 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p4,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p4,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p4 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p4 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p4,K280(p2)) is Relation-like Function-like set
euc2cpx (p4 - p2) is complex Element of COMPLEX
(p4 - p2) `1 is complex real ext-real Element of REAL
K367((p4 - p2),1) is complex real ext-real Element of REAL
(p4 - p2) `2 is complex real ext-real Element of REAL
K367((p4 - p2),2) is complex real ext-real Element of REAL
((p4 - p2) `2) * <i> is complex set
((p4 - p2) `1) + (((p4 - p2) `2) * <i>) is complex set
angle ((euc2cpx (p1 - p2)),(euc2cpx (p3 - p2))) is complex real ext-real Element of REAL
angle ((euc2cpx (p3 - p2)),(euc2cpx (p4 - p2))) is complex real ext-real Element of REAL
(angle ((euc2cpx (p1 - p2)),(euc2cpx (p3 - p2)))) + (angle ((euc2cpx (p3 - p2)),(euc2cpx (p4 - p2)))) is complex real ext-real Element of REAL
angle ((euc2cpx (p1 - p2)),(euc2cpx (p4 - p2))) is complex real ext-real Element of REAL
(angle ((euc2cpx (p1 - p2)),(euc2cpx (p4 - p2)))) + (2 * PI) is complex real ext-real Element of REAL
(angle ((euc2cpx (p1 - p2)),(euc2cpx (p3 - p2)))) + (angle (p3,p2,p4)) is complex real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
- 1 is non empty complex real ext-real non positive negative set
(- 1) * p2 is Relation-like Function-like set
K214((TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
the U5 of (TOP-REAL 2) is Relation-like [: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):] -defined the carrier of (TOP-REAL 2) -valued Function-like total V30([: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2)) Element of bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):]
[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):] is set
[:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is set
bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is set
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p2) is Relation-like Function-like complex-valued set
K251(p1,K280(p2)) is Relation-like Function-like set
(p1 - p2) `1 is complex real ext-real Element of REAL
K367((p1 - p2),1) is complex real ext-real Element of REAL
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
(p1 `1) - (p2 `1) is complex real ext-real Element of REAL
(p1 - p2) `2 is complex real ext-real Element of REAL
K367((p1 - p2),2) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p1 `2) - (p2 `2) is complex real ext-real Element of REAL
REAL 2 is non empty FinSequence-membered M10( REAL )
K318(2,REAL) is FinSequence-membered M10( REAL )
(- p2) `1 is complex real ext-real Element of REAL
K367((- p2),1) is complex real ext-real Element of REAL
p3 is Relation-like NAT -defined REAL -valued Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL 2
- p3 is Relation-like NAT -defined REAL -valued Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL 2
(- 1) * p3 is Relation-like Function-like set
(- p3) . 1 is complex real ext-real set
p3 . 1 is complex real ext-real set
- (p3 . 1) is complex real ext-real set
- (p2 `1) is complex real ext-real Element of REAL
euc2cpx (p1 - p2) is complex Element of COMPLEX
((p1 - p2) `2) * <i> is complex set
((p1 - p2) `1) + (((p1 - p2) `2) * <i>) is complex set
euc2cpx p1 is complex Element of COMPLEX
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
euc2cpx p2 is complex Element of COMPLEX
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
(euc2cpx p1) - (euc2cpx p2) is complex Element of COMPLEX
- (euc2cpx p2) is complex Element of COMPLEX
(euc2cpx p1) + (- (euc2cpx p2)) is complex Element of COMPLEX
euc2cpx (- p2) is complex Element of COMPLEX
(- p2) `2 is complex real ext-real Element of REAL
K367((- p2),2) is complex real ext-real Element of REAL
((- p2) `2) * <i> is complex set
((- p2) `1) + (((- p2) `2) * <i>) is complex set
(euc2cpx p1) + (euc2cpx (- p2)) is complex Element of COMPLEX
Re ((euc2cpx p1) + (euc2cpx (- p2))) is complex real ext-real Element of REAL
Re (euc2cpx p1) is complex real ext-real Element of REAL
Re (euc2cpx (- p2)) is complex real ext-real Element of REAL
(Re (euc2cpx p1)) + (Re (euc2cpx (- p2))) is complex real ext-real Element of REAL
(p1 `1) + (Re (euc2cpx (- p2))) is complex real ext-real Element of REAL
(p1 `1) + ((- p2) `1) is complex real ext-real Element of REAL
(- p3) . 2 is complex real ext-real set
p3 . 2 is complex real ext-real set
- (p3 . 2) is complex real ext-real set
- (p2 `2) is complex real ext-real Element of REAL
Im ((euc2cpx p1) + (euc2cpx (- p2))) is complex real ext-real Element of REAL
Im (euc2cpx p1) is complex real ext-real Element of REAL
Im (euc2cpx (- p2)) is complex real ext-real Element of REAL
(Im (euc2cpx p1)) + (Im (euc2cpx (- p2))) is complex real ext-real Element of REAL
(p1 `2) + (Im (euc2cpx (- p2))) is complex real ext-real Element of REAL
(p1 `2) + ((- p2) `2) is complex real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
- 1 is non empty complex real ext-real non positive negative set
(- 1) * p2 is Relation-like Function-like set
K214((TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
the U5 of (TOP-REAL 2) is Relation-like [: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):] -defined the carrier of (TOP-REAL 2) -valued Function-like total V30([: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2)) Element of bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):]
[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):] is set
[:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is set
bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is set
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p2) is Relation-like Function-like complex-valued set
K251(p1,K280(p2)) is Relation-like Function-like set
euc2cpx (p1 - p2) is complex Element of COMPLEX
(p1 - p2) `1 is complex real ext-real Element of REAL
K367((p1 - p2),1) is complex real ext-real Element of REAL
(p1 - p2) `2 is complex real ext-real Element of REAL
K367((p1 - p2),2) is complex real ext-real Element of REAL
((p1 - p2) `2) * <i> is complex set
((p1 - p2) `1) + (((p1 - p2) `2) * <i>) is complex set
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
(p1 `1) - (p2 `1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p1 `2) - (p2 `2) is complex real ext-real Element of REAL
((p1 `1) - (p2 `1)) ^2 is complex real ext-real Element of REAL
((p1 `1) - (p2 `1)) * ((p1 `1) - (p2 `1)) is complex real ext-real set
((p1 `2) - (p2 `2)) ^2 is complex real ext-real Element of REAL
((p1 `2) - (p2 `2)) * ((p1 `2) - (p2 `2)) is complex real ext-real set
(((p1 `1) - (p2 `1)) ^2) + (((p1 `2) - (p2 `2)) ^2) is complex real ext-real Element of REAL
sqrt ((((p1 `1) - (p2 `1)) ^2) + (((p1 `2) - (p2 `2)) ^2)) is complex real ext-real Element of REAL
|.(p1 - p2).| is complex real ext-real non negative Element of REAL
sqr (p1 - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p1 - p2),(p1 - p2)) is Relation-like Function-like set
K339((sqr (p1 - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr (p1 - p2))) is complex real ext-real Element of REAL
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p3,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p3,K280(p2)) is Relation-like Function-like set
euc2cpx (p3 - p2) is complex Element of COMPLEX
(p3 - p2) `1 is complex real ext-real Element of REAL
K367((p3 - p2),1) is complex real ext-real Element of REAL
(p3 - p2) `2 is complex real ext-real Element of REAL
K367((p3 - p2),2) is complex real ext-real Element of REAL
((p3 - p2) `2) * <i> is complex set
((p3 - p2) `1) + (((p3 - p2) `2) * <i>) is complex set
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
(p3 `1) - (p2 `1) is complex real ext-real Element of REAL
((p1 `1) - (p2 `1)) * ((p3 `1) - (p2 `1)) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) - (p2 `2) is complex real ext-real Element of REAL
((p1 `2) - (p2 `2)) * ((p3 `2) - (p2 `2)) is complex real ext-real Element of REAL
(((p1 `1) - (p2 `1)) * ((p3 `1) - (p2 `1))) + (((p1 `2) - (p2 `2)) * ((p3 `2) - (p2 `2))) is complex real ext-real Element of REAL
((p1 `1) - (p2 `1)) * ((p3 `2) - (p2 `2)) is complex real ext-real Element of REAL
- (((p1 `1) - (p2 `1)) * ((p3 `2) - (p2 `2))) is complex real ext-real Element of REAL
((p1 `2) - (p2 `2)) * ((p3 `1) - (p2 `1)) is complex real ext-real Element of REAL
(- (((p1 `1) - (p2 `1)) * ((p3 `2) - (p2 `2)))) + (((p1 `2) - (p2 `2)) * ((p3 `1) - (p2 `1))) is complex real ext-real Element of REAL
p4 is complex Element of COMPLEX
p is complex Element of COMPLEX
p4 .|. p is complex Element of COMPLEX
Re (p4 .|. p) is complex real ext-real Element of REAL
Im (p4 .|. p) is complex real ext-real Element of REAL
|.p4.| is complex real ext-real Element of REAL
Re p4 is complex real ext-real Element of REAL
(Re p4) ^2 is complex real ext-real Element of REAL
(Re p4) * (Re p4) is complex real ext-real set
Im p4 is complex real ext-real Element of REAL
(Im p4) ^2 is complex real ext-real Element of REAL
(Im p4) * (Im p4) is complex real ext-real set
((Re p4) ^2) + ((Im p4) ^2) is complex real ext-real Element of REAL
sqrt (((Re p4) ^2) + ((Im p4) ^2)) is complex real ext-real Element of REAL
Re p is complex real ext-real Element of REAL
Im p is complex real ext-real Element of REAL
((p1 - p2) `1) ^2 is complex real ext-real Element of REAL
((p1 - p2) `1) * ((p1 - p2) `1) is complex real ext-real set
(((p1 - p2) `1) ^2) + ((Im p4) ^2) is complex real ext-real Element of REAL
sqrt ((((p1 - p2) `1) ^2) + ((Im p4) ^2)) is complex real ext-real Element of REAL
((p1 - p2) `2) ^2 is complex real ext-real Element of REAL
((p1 - p2) `2) * ((p1 - p2) `2) is complex real ext-real set
(((p1 - p2) `1) ^2) + (((p1 - p2) `2) ^2) is complex real ext-real Element of REAL
sqrt ((((p1 - p2) `1) ^2) + (((p1 - p2) `2) ^2)) is complex real ext-real Element of REAL
(((p1 `1) - (p2 `1)) ^2) + (((p1 - p2) `2) ^2) is complex real ext-real Element of REAL
sqrt ((((p1 `1) - (p2 `1)) ^2) + (((p1 - p2) `2) ^2)) is complex real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p1 `1) * (p2 `2) is complex real ext-real Element of REAL
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p2 `1) * (p1 `2) is complex real ext-real Element of REAL
((p1 `1) * (p2 `2)) - ((p2 `1) * (p1 `2)) is complex real ext-real Element of REAL
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p2 `1) * (p3 `2) is complex real ext-real Element of REAL
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
(p3 `1) * (p2 `2) is complex real ext-real Element of REAL
((p2 `1) * (p3 `2)) - ((p3 `1) * (p2 `2)) is complex real ext-real Element of REAL
(((p1 `1) * (p2 `2)) - ((p2 `1) * (p1 `2))) + (((p2 `1) * (p3 `2)) - ((p3 `1) * (p2 `2))) is complex real ext-real Element of REAL
(p3 `1) * (p1 `2) is complex real ext-real Element of REAL
(p1 `1) * (p3 `2) is complex real ext-real Element of REAL
((p3 `1) * (p1 `2)) - ((p1 `1) * (p3 `2)) is complex real ext-real Element of REAL
((((p1 `1) * (p2 `2)) - ((p2 `1) * (p1 `2))) + (((p2 `1) * (p3 `2)) - ((p3 `1) * (p2 `2)))) + (((p3 `1) * (p1 `2)) - ((p1 `1) * (p3 `2))) is complex real ext-real Element of REAL
(((((p1 `1) * (p2 `2)) - ((p2 `1) * (p1 `2))) + (((p2 `1) * (p3 `2)) - ((p3 `1) * (p2 `2)))) + (((p3 `1) * (p1 `2)) - ((p1 `1) * (p3 `2)))) / 2 is complex real ext-real Element of REAL
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 - p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
- 1 is non empty complex real ext-real non positive negative set
(- 1) * p1 is Relation-like Function-like set
K214((TOP-REAL 2),p2,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
the U5 of (TOP-REAL 2) is Relation-like [: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):] -defined the carrier of (TOP-REAL 2) -valued Function-like total V30([: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2)) Element of bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):]
[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):] is set
[:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is set
bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is set
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p1) is Relation-like Function-like complex-valued set
K251(p2,K280(p1)) is Relation-like Function-like set
|.(p2 - p1).| is complex real ext-real non negative Element of REAL
sqr (p2 - p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p2 - p1),(p2 - p1)) is Relation-like Function-like set
K339((sqr (p2 - p1))) is complex real ext-real Element of REAL
sqrt K339((sqr (p2 - p1))) is complex real ext-real Element of REAL
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p2 is Relation-like Function-like set
K214((TOP-REAL 2),p3,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p2) is Relation-like Function-like complex-valued set
K251(p3,K280(p2)) is Relation-like Function-like set
|.(p3 - p2).| is complex real ext-real non negative Element of REAL
sqr (p3 - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p3 - p2),(p3 - p2)) is Relation-like Function-like set
K339((sqr (p3 - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr (p3 - p2))) is complex real ext-real Element of REAL
|.(p2 - p1).| + |.(p3 - p2).| is complex real ext-real non negative Element of REAL
p1 - p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p3 is Relation-like Function-like set
K214((TOP-REAL 2),p1,(- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p3) is Relation-like Function-like complex-valued set
K251(p1,K280(p3)) is Relation-like Function-like set
|.(p1 - p3).| is complex real ext-real non negative Element of REAL
sqr (p1 - p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p1 - p3),(p1 - p3)) is Relation-like Function-like set
K339((sqr (p1 - p3))) is complex real ext-real Element of REAL
sqrt K339((sqr (p1 - p3))) is complex real ext-real Element of REAL
(|.(p2 - p1).| + |.(p3 - p2).|) + |.(p1 - p3).| is complex real ext-real non negative Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p2 is Relation-like Function-like set
K214((TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p2) is Relation-like Function-like complex-valued set
K251(p1,K280(p2)) is Relation-like Function-like set
|.(p1 - p2).| is complex real ext-real non negative Element of REAL
sqr (p1 - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p1 - p2),(p1 - p2)) is Relation-like Function-like set
K339((sqr (p1 - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr (p1 - p2))) is complex real ext-real Element of REAL
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(p1,p2,p3) is complex real ext-real set
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p1 `1) * (p2 `2) is complex real ext-real Element of REAL
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p2 `1) * (p1 `2) is complex real ext-real Element of REAL
((p1 `1) * (p2 `2)) - ((p2 `1) * (p1 `2)) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p2 `1) * (p3 `2) is complex real ext-real Element of REAL
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
(p3 `1) * (p2 `2) is complex real ext-real Element of REAL
((p2 `1) * (p3 `2)) - ((p3 `1) * (p2 `2)) is complex real ext-real Element of REAL
(((p1 `1) * (p2 `2)) - ((p2 `1) * (p1 `2))) + (((p2 `1) * (p3 `2)) - ((p3 `1) * (p2 `2))) is complex real ext-real Element of REAL
(p3 `1) * (p1 `2) is complex real ext-real Element of REAL
(p1 `1) * (p3 `2) is complex real ext-real Element of REAL
((p3 `1) * (p1 `2)) - ((p1 `1) * (p3 `2)) is complex real ext-real Element of REAL
((((p1 `1) * (p2 `2)) - ((p2 `1) * (p1 `2))) + (((p2 `1) * (p3 `2)) - ((p3 `1) * (p2 `2)))) + (((p3 `1) * (p1 `2)) - ((p1 `1) * (p3 `2))) is complex real ext-real Element of REAL
(((((p1 `1) * (p2 `2)) - ((p2 `1) * (p1 `2))) + (((p2 `1) * (p3 `2)) - ((p3 `1) * (p2 `2)))) + (((p3 `1) * (p1 `2)) - ((p1 `1) * (p3 `2)))) / 2 is complex real ext-real Element of REAL
p3 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p3,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p3,K280(p2)) is Relation-like Function-like set
|.(p3 - p2).| is complex real ext-real non negative Element of REAL
sqr (p3 - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p3 - p2),(p3 - p2)) is Relation-like Function-like set
K339((sqr (p3 - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr (p3 - p2))) is complex real ext-real Element of REAL
|.(p1 - p2).| * |.(p3 - p2).| is complex real ext-real non negative Element of REAL
angle (p3,p2,p1) is complex real ext-real Element of REAL
euc2cpx p3 is complex Element of COMPLEX
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
euc2cpx p2 is complex Element of COMPLEX
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
euc2cpx p1 is complex Element of COMPLEX
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
angle ((euc2cpx p3),(euc2cpx p2),(euc2cpx p1)) is complex real ext-real set
sin (angle (p3,p2,p1)) is complex real ext-real Element of REAL
(|.(p1 - p2).| * |.(p3 - p2).|) * (sin (angle (p3,p2,p1))) is complex real ext-real Element of REAL
((|.(p1 - p2).| * |.(p3 - p2).|) * (sin (angle (p3,p2,p1)))) / 2 is complex real ext-real Element of REAL
|.(0. (TOP-REAL 2)).| is complex real ext-real non negative Element of REAL
sqr (0. (TOP-REAL 2)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((0. (TOP-REAL 2)),(0. (TOP-REAL 2))) is Relation-like Function-like set
K339((sqr (0. (TOP-REAL 2)))) is complex real ext-real Element of REAL
sqrt K339((sqr (0. (TOP-REAL 2)))) is complex real ext-real Element of REAL
|.(0. (TOP-REAL 2)).| is complex real ext-real non negative Element of REAL
sqr (0. (TOP-REAL 2)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((0. (TOP-REAL 2)),(0. (TOP-REAL 2))) is Relation-like Function-like set
K339((sqr (0. (TOP-REAL 2)))) is complex real ext-real Element of REAL
sqrt K339((sqr (0. (TOP-REAL 2)))) is complex real ext-real Element of REAL
euc2cpx (p3 - p2) is complex Element of COMPLEX
(p3 - p2) `1 is complex real ext-real Element of REAL
K367((p3 - p2),1) is complex real ext-real Element of REAL
(p3 - p2) `2 is complex real ext-real Element of REAL
K367((p3 - p2),2) is complex real ext-real Element of REAL
((p3 - p2) `2) * <i> is complex set
((p3 - p2) `1) + (((p3 - p2) `2) * <i>) is complex set
euc2cpx (p1 - p2) is complex Element of COMPLEX
(p1 - p2) `1 is complex real ext-real Element of REAL
K367((p1 - p2),1) is complex real ext-real Element of REAL
(p1 - p2) `2 is complex real ext-real Element of REAL
K367((p1 - p2),2) is complex real ext-real Element of REAL
((p1 - p2) `2) * <i> is complex set
((p1 - p2) `1) + (((p1 - p2) `2) * <i>) is complex set
|.(euc2cpx (p1 - p2)).| is complex real ext-real Element of REAL
Re (euc2cpx (p1 - p2)) is complex real ext-real Element of REAL
(Re (euc2cpx (p1 - p2))) ^2 is complex real ext-real Element of REAL
(Re (euc2cpx (p1 - p2))) * (Re (euc2cpx (p1 - p2))) is complex real ext-real set
Im (euc2cpx (p1 - p2)) is complex real ext-real Element of REAL
(Im (euc2cpx (p1 - p2))) ^2 is complex real ext-real Element of REAL
(Im (euc2cpx (p1 - p2))) * (Im (euc2cpx (p1 - p2))) is complex real ext-real set
((Re (euc2cpx (p1 - p2))) ^2) + ((Im (euc2cpx (p1 - p2))) ^2) is complex real ext-real Element of REAL
sqrt (((Re (euc2cpx (p1 - p2))) ^2) + ((Im (euc2cpx (p1 - p2))) ^2)) is complex real ext-real Element of REAL
|.(euc2cpx (p3 - p2)).| is complex real ext-real Element of REAL
Re (euc2cpx (p3 - p2)) is complex real ext-real Element of REAL
(Re (euc2cpx (p3 - p2))) ^2 is complex real ext-real Element of REAL
(Re (euc2cpx (p3 - p2))) * (Re (euc2cpx (p3 - p2))) is complex real ext-real set
Im (euc2cpx (p3 - p2)) is complex real ext-real Element of REAL
(Im (euc2cpx (p3 - p2))) ^2 is complex real ext-real Element of REAL
(Im (euc2cpx (p3 - p2))) * (Im (euc2cpx (p3 - p2))) is complex real ext-real set
((Re (euc2cpx (p3 - p2))) ^2) + ((Im (euc2cpx (p3 - p2))) ^2) is complex real ext-real Element of REAL
sqrt (((Re (euc2cpx (p3 - p2))) ^2) + ((Im (euc2cpx (p3 - p2))) ^2)) is complex real ext-real Element of REAL
|.(euc2cpx (p1 - p2)).| * |.(euc2cpx (p3 - p2)).| is complex real ext-real Element of REAL
angle (p1,p2,p3) is complex real ext-real Element of REAL
angle ((euc2cpx p1),(euc2cpx p2),(euc2cpx p3)) is complex real ext-real set
sin (angle (p1,p2,p3)) is complex real ext-real Element of REAL
- (sin (angle (p1,p2,p3))) is complex real ext-real Element of REAL
(|.(p1 - p2).| * |.(p3 - p2).|) * (- (sin (angle (p1,p2,p3)))) is complex real ext-real Element of REAL
((|.(p1 - p2).| * |.(p3 - p2).|) * (- (sin (angle (p1,p2,p3))))) / 2 is complex real ext-real Element of REAL
angle ((euc2cpx (p1 - p2)),(euc2cpx (p3 - p2))) is complex real ext-real Element of REAL
sin (angle ((euc2cpx (p1 - p2)),(euc2cpx (p3 - p2)))) is complex real ext-real Element of REAL
- (sin (angle ((euc2cpx (p1 - p2)),(euc2cpx (p3 - p2))))) is complex real ext-real Element of REAL
(|.(p1 - p2).| * |.(p3 - p2).|) * (- (sin (angle ((euc2cpx (p1 - p2)),(euc2cpx (p3 - p2)))))) is complex real ext-real Element of REAL
((|.(p1 - p2).| * |.(p3 - p2).|) * (- (sin (angle ((euc2cpx (p1 - p2)),(euc2cpx (p3 - p2))))))) / 2 is complex real ext-real Element of REAL
(euc2cpx (p1 - p2)) .|. (euc2cpx (p3 - p2)) is complex Element of COMPLEX
Im ((euc2cpx (p1 - p2)) .|. (euc2cpx (p3 - p2))) is complex real ext-real Element of REAL
(Im ((euc2cpx (p1 - p2)) .|. (euc2cpx (p3 - p2)))) / (|.(euc2cpx (p1 - p2)).| * |.(euc2cpx (p3 - p2)).|) is complex real ext-real Element of REAL
- ((Im ((euc2cpx (p1 - p2)) .|. (euc2cpx (p3 - p2)))) / (|.(euc2cpx (p1 - p2)).| * |.(euc2cpx (p3 - p2)).|)) is complex real ext-real Element of REAL
- (- ((Im ((euc2cpx (p1 - p2)) .|. (euc2cpx (p3 - p2)))) / (|.(euc2cpx (p1 - p2)).| * |.(euc2cpx (p3 - p2)).|))) is complex real ext-real Element of REAL
(|.(p1 - p2).| * |.(p3 - p2).|) * (- (- ((Im ((euc2cpx (p1 - p2)) .|. (euc2cpx (p3 - p2)))) / (|.(euc2cpx (p1 - p2)).| * |.(euc2cpx (p3 - p2)).|)))) is complex real ext-real Element of REAL
((|.(p1 - p2).| * |.(p3 - p2).|) * (- (- ((Im ((euc2cpx (p1 - p2)) .|. (euc2cpx (p3 - p2)))) / (|.(euc2cpx (p1 - p2)).| * |.(euc2cpx (p3 - p2)).|))))) / 2 is complex real ext-real Element of REAL
|.(euc2cpx (p1 - p2)).| * |.(p3 - p2).| is complex real ext-real Element of REAL
(|.(euc2cpx (p1 - p2)).| * |.(p3 - p2).|) * ((Im ((euc2cpx (p1 - p2)) .|. (euc2cpx (p3 - p2)))) / (|.(euc2cpx (p1 - p2)).| * |.(euc2cpx (p3 - p2)).|)) is complex real ext-real Element of REAL
((|.(euc2cpx (p1 - p2)).| * |.(p3 - p2).|) * ((Im ((euc2cpx (p1 - p2)) .|. (euc2cpx (p3 - p2)))) / (|.(euc2cpx (p1 - p2)).| * |.(euc2cpx (p3 - p2)).|))) / 2 is complex real ext-real Element of REAL
(|.(euc2cpx (p1 - p2)).| * |.(euc2cpx (p3 - p2)).|) * ((Im ((euc2cpx (p1 - p2)) .|. (euc2cpx (p3 - p2)))) / (|.(euc2cpx (p1 - p2)).| * |.(euc2cpx (p3 - p2)).|)) is complex real ext-real Element of REAL
((|.(euc2cpx (p1 - p2)).| * |.(euc2cpx (p3 - p2)).|) * ((Im ((euc2cpx (p1 - p2)) .|. (euc2cpx (p3 - p2)))) / (|.(euc2cpx (p1 - p2)).| * |.(euc2cpx (p3 - p2)).|))) / 2 is complex real ext-real Element of REAL
(|.(euc2cpx (p1 - p2)).| * |.(euc2cpx (p3 - p2)).|) / (|.(euc2cpx (p1 - p2)).| * |.(euc2cpx (p3 - p2)).|) is complex real ext-real Element of REAL
(Im ((euc2cpx (p1 - p2)) .|. (euc2cpx (p3 - p2)))) / ((|.(euc2cpx (p1 - p2)).| * |.(euc2cpx (p3 - p2)).|) / (|.(euc2cpx (p1 - p2)).| * |.(euc2cpx (p3 - p2)).|)) is complex real ext-real Element of REAL
((Im ((euc2cpx (p1 - p2)) .|. (euc2cpx (p3 - p2)))) / ((|.(euc2cpx (p1 - p2)).| * |.(euc2cpx (p3 - p2)).|) / (|.(euc2cpx (p1 - p2)).| * |.(euc2cpx (p3 - p2)).|))) / 2 is complex real ext-real Element of REAL
(Im ((euc2cpx (p1 - p2)) .|. (euc2cpx (p3 - p2)))) / 1 is complex real ext-real Element of REAL
((Im ((euc2cpx (p1 - p2)) .|. (euc2cpx (p3 - p2)))) / 1) / 2 is complex real ext-real Element of REAL
(p1 `1) - (p2 `1) is complex real ext-real Element of REAL
(p3 `2) - (p2 `2) is complex real ext-real Element of REAL
((p1 `1) - (p2 `1)) * ((p3 `2) - (p2 `2)) is complex real ext-real Element of REAL
- (((p1 `1) - (p2 `1)) * ((p3 `2) - (p2 `2))) is complex real ext-real Element of REAL
(p1 `2) - (p2 `2) is complex real ext-real Element of REAL
(p3 `1) - (p2 `1) is complex real ext-real Element of REAL
((p1 `2) - (p2 `2)) * ((p3 `1) - (p2 `1)) is complex real ext-real Element of REAL
(- (((p1 `1) - (p2 `1)) * ((p3 `2) - (p2 `2)))) + (((p1 `2) - (p2 `2)) * ((p3 `1) - (p2 `1))) is complex real ext-real Element of REAL
((- (((p1 `1) - (p2 `1)) * ((p3 `2) - (p2 `2)))) + (((p1 `2) - (p2 `2)) * ((p3 `1) - (p2 `1)))) / 2 is complex real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 - p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p1 is Relation-like Function-like set
K214((TOP-REAL 2),p3,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p1) is Relation-like Function-like complex-valued set
K251(p3,K280(p1)) is Relation-like Function-like set
|.(p3 - p1).| is complex real ext-real non negative Element of REAL
sqr (p3 - p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p3 - p1),(p3 - p1)) is Relation-like Function-like set
K339((sqr (p3 - p1))) is complex real ext-real Element of REAL
sqrt K339((sqr (p3 - p1))) is complex real ext-real Element of REAL
angle (p3,p1,p2) is complex real ext-real Element of REAL
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
angle ((euc2cpx p3),(euc2cpx p1),(euc2cpx p2)) is complex real ext-real set
sin (angle (p3,p1,p2)) is complex real ext-real Element of REAL
|.(p3 - p1).| * (sin (angle (p3,p1,p2))) is complex real ext-real Element of REAL
p3 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p2 is Relation-like Function-like set
K214((TOP-REAL 2),p3,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p2) is Relation-like Function-like complex-valued set
K251(p3,K280(p2)) is Relation-like Function-like set
|.(p3 - p2).| is complex real ext-real non negative Element of REAL
sqr (p3 - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p3 - p2),(p3 - p2)) is Relation-like Function-like set
K339((sqr (p3 - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr (p3 - p2))) is complex real ext-real Element of REAL
angle (p1,p2,p3) is complex real ext-real Element of REAL
angle ((euc2cpx p1),(euc2cpx p2),(euc2cpx p3)) is complex real ext-real set
sin (angle (p1,p2,p3)) is complex real ext-real Element of REAL
|.(p3 - p2).| * (sin (angle (p1,p2,p3))) is complex real ext-real Element of REAL
(p2,p1,p3) is complex real ext-real set
(p2 `1) * (p1 `2) is complex real ext-real Element of REAL
(p1 `1) * (p2 `2) is complex real ext-real Element of REAL
((p2 `1) * (p1 `2)) - ((p1 `1) * (p2 `2)) is complex real ext-real Element of REAL
(p1 `1) * (p3 `2) is complex real ext-real Element of REAL
(p3 `1) * (p1 `2) is complex real ext-real Element of REAL
((p1 `1) * (p3 `2)) - ((p3 `1) * (p1 `2)) is complex real ext-real Element of REAL
(((p2 `1) * (p1 `2)) - ((p1 `1) * (p2 `2))) + (((p1 `1) * (p3 `2)) - ((p3 `1) * (p1 `2))) is complex real ext-real Element of REAL
(p3 `1) * (p2 `2) is complex real ext-real Element of REAL
(p2 `1) * (p3 `2) is complex real ext-real Element of REAL
((p3 `1) * (p2 `2)) - ((p2 `1) * (p3 `2)) is complex real ext-real Element of REAL
((((p2 `1) * (p1 `2)) - ((p1 `1) * (p2 `2))) + (((p1 `1) * (p3 `2)) - ((p3 `1) * (p1 `2)))) + (((p3 `1) * (p2 `2)) - ((p2 `1) * (p3 `2))) is complex real ext-real Element of REAL
(((((p2 `1) * (p1 `2)) - ((p1 `1) * (p2 `2))) + (((p1 `1) * (p3 `2)) - ((p3 `1) * (p1 `2)))) + (((p3 `1) * (p2 `2)) - ((p2 `1) * (p3 `2)))) / 2 is complex real ext-real Element of REAL
(p3,p2,p1) is complex real ext-real set
(((p3 `1) * (p2 `2)) - ((p2 `1) * (p3 `2))) + (((p2 `1) * (p1 `2)) - ((p1 `1) * (p2 `2))) is complex real ext-real Element of REAL
((((p3 `1) * (p2 `2)) - ((p2 `1) * (p3 `2))) + (((p2 `1) * (p1 `2)) - ((p1 `1) * (p2 `2)))) + (((p1 `1) * (p3 `2)) - ((p3 `1) * (p1 `2))) is complex real ext-real Element of REAL
(((((p3 `1) * (p2 `2)) - ((p2 `1) * (p3 `2))) + (((p2 `1) * (p1 `2)) - ((p1 `1) * (p2 `2)))) + (((p1 `1) * (p3 `2)) - ((p3 `1) * (p1 `2)))) / 2 is complex real ext-real Element of REAL
p2 - p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p2,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p2,K280(p1)) is Relation-like Function-like set
|.(p2 - p1).| is complex real ext-real non negative Element of REAL
sqr (p2 - p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p2 - p1),(p2 - p1)) is Relation-like Function-like set
K339((sqr (p2 - p1))) is complex real ext-real Element of REAL
sqrt K339((sqr (p2 - p1))) is complex real ext-real Element of REAL
|.(p2 - p1).| * |.(p3 - p1).| is complex real ext-real non negative Element of REAL
(|.(p2 - p1).| * |.(p3 - p1).|) * (sin (angle (p3,p1,p2))) is complex real ext-real Element of REAL
((|.(p2 - p1).| * |.(p3 - p1).|) * (sin (angle (p3,p1,p2)))) / 2 is complex real ext-real Element of REAL
p1 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p1,K280(p2)) is Relation-like Function-like set
|.(p1 - p2).| is complex real ext-real non negative Element of REAL
sqr (p1 - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p1 - p2),(p1 - p2)) is Relation-like Function-like set
K339((sqr (p1 - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr (p1 - p2))) is complex real ext-real Element of REAL
|.(p3 - p2).| * |.(p1 - p2).| is complex real ext-real non negative Element of REAL
(|.(p3 - p2).| * |.(p1 - p2).|) * (sin (angle (p1,p2,p3))) is complex real ext-real Element of REAL
((|.(p3 - p2).| * |.(p1 - p2).|) * (sin (angle (p1,p2,p3)))) / 2 is complex real ext-real Element of REAL
|.(p3 - p2).| * |.(p2 - p1).| is complex real ext-real non negative Element of REAL
(|.(p3 - p2).| * |.(p2 - p1).|) * (sin (angle (p1,p2,p3))) is complex real ext-real Element of REAL
(|.(p3 - p1).| * (sin (angle (p3,p1,p2)))) * |.(p2 - p1).| is complex real ext-real Element of REAL
(|.(p3 - p2).| * (sin (angle (p1,p2,p3)))) * |.(p2 - p1).| is complex real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p2 is Relation-like Function-like set
K214((TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p2) is Relation-like Function-like complex-valued set
K251(p1,K280(p2)) is Relation-like Function-like set
|.(p1 - p2).| is complex real ext-real non negative Element of REAL
sqr (p1 - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p1 - p2),(p1 - p2)) is Relation-like Function-like set
K339((sqr (p1 - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr (p1 - p2))) is complex real ext-real Element of REAL
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p3,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p3,K280(p2)) is Relation-like Function-like set
|.(p3 - p2).| is complex real ext-real non negative Element of REAL
sqr (p3 - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p3 - p2),(p3 - p2)) is Relation-like Function-like set
K339((sqr (p3 - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr (p3 - p2))) is complex real ext-real Element of REAL
p3 - p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p1 is Relation-like Function-like set
K214((TOP-REAL 2),p3,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p1) is Relation-like Function-like complex-valued set
K251(p3,K280(p1)) is Relation-like Function-like set
|.(p3 - p1).| is complex real ext-real non negative Element of REAL
sqr (p3 - p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p3 - p1),(p3 - p1)) is Relation-like Function-like set
K339((sqr (p3 - p1))) is complex real ext-real Element of REAL
sqrt K339((sqr (p3 - p1))) is complex real ext-real Element of REAL
angle (p1,p2,p3) is complex real ext-real Element of REAL
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx p2),(euc2cpx p3)) is complex real ext-real set
cos (angle (p1,p2,p3)) is complex real ext-real Element of REAL
p4 is complex real ext-real set
p4 ^2 is complex real ext-real set
p4 * p4 is complex real ext-real set
2 * p4 is complex real ext-real Element of REAL
p is complex real ext-real set
p ^2 is complex real ext-real set
p * p is complex real ext-real set
(p4 ^2) + (p ^2) is complex real ext-real set
(2 * p4) * p is complex real ext-real Element of REAL
((2 * p4) * p) * (cos (angle (p1,p2,p3))) is complex real ext-real Element of REAL
((p4 ^2) + (p ^2)) - (((2 * p4) * p) * (cos (angle (p1,p2,p3)))) is complex real ext-real Element of REAL
a is complex real ext-real set
a ^2 is complex real ext-real set
a * a is complex real ext-real set
|.(0. (TOP-REAL 2)).| is complex real ext-real non negative Element of REAL
sqr (0. (TOP-REAL 2)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((0. (TOP-REAL 2)),(0. (TOP-REAL 2))) is Relation-like Function-like set
K339((sqr (0. (TOP-REAL 2)))) is complex real ext-real Element of REAL
sqrt K339((sqr (0. (TOP-REAL 2)))) is complex real ext-real Element of REAL
|.(0. (TOP-REAL 2)).| is complex real ext-real non negative Element of REAL
sqr (0. (TOP-REAL 2)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((0. (TOP-REAL 2)),(0. (TOP-REAL 2))) is Relation-like Function-like set
K339((sqr (0. (TOP-REAL 2)))) is complex real ext-real Element of REAL
sqrt K339((sqr (0. (TOP-REAL 2)))) is complex real ext-real Element of REAL
|.(p1 - p2).| ^2 is complex real ext-real Element of REAL
|.(p1 - p2).| * |.(p1 - p2).| is complex real ext-real non negative set
|.(p3 - p2).| ^2 is complex real ext-real Element of REAL
|.(p3 - p2).| * |.(p3 - p2).| is complex real ext-real non negative set
(|.(p1 - p2).| ^2) + (|.(p3 - p2).| ^2) is complex real ext-real Element of REAL
2 * |.(p1 - p2).| is complex real ext-real non negative Element of REAL
(2 * |.(p1 - p2).|) * |.(p3 - p2).| is complex real ext-real non negative Element of REAL
((2 * |.(p1 - p2).|) * |.(p3 - p2).|) * (cos (angle (p1,p2,p3))) is complex real ext-real Element of REAL
((|.(p1 - p2).| ^2) + (|.(p3 - p2).| ^2)) - (((2 * |.(p1 - p2).|) * |.(p3 - p2).|) * (cos (angle (p1,p2,p3)))) is complex real ext-real Element of REAL
- (p1 - p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- (p1 - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * (p1 - p2) is Relation-like Function-like set
|.(- (p1 - p2)).| is complex real ext-real non negative Element of REAL
sqr (- (p1 - p2)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((- (p1 - p2)),(- (p1 - p2))) is Relation-like Function-like set
K339((sqr (- (p1 - p2)))) is complex real ext-real Element of REAL
sqrt K339((sqr (- (p1 - p2)))) is complex real ext-real Element of REAL
|.(- (p1 - p2)).| ^2 is complex real ext-real Element of REAL
|.(- (p1 - p2)).| * |.(- (p1 - p2)).| is complex real ext-real non negative set
p2 - p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p2,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p2,K280(p1)) is Relation-like Function-like set
|.(p2 - p1).| is complex real ext-real non negative Element of REAL
sqr (p2 - p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p2 - p1),(p2 - p1)) is Relation-like Function-like set
K339((sqr (p2 - p1))) is complex real ext-real Element of REAL
sqrt K339((sqr (p2 - p1))) is complex real ext-real Element of REAL
|.(p2 - p1).| ^2 is complex real ext-real Element of REAL
|.(p2 - p1).| * |.(p2 - p1).| is complex real ext-real non negative set
euc2cpx (p3 - p2) is complex Element of COMPLEX
(p3 - p2) `1 is complex real ext-real Element of REAL
K367((p3 - p2),1) is complex real ext-real Element of REAL
(p3 - p2) `2 is complex real ext-real Element of REAL
K367((p3 - p2),2) is complex real ext-real Element of REAL
((p3 - p2) `2) * <i> is complex set
((p3 - p2) `1) + (((p3 - p2) `2) * <i>) is complex set
euc2cpx (p1 - p2) is complex Element of COMPLEX
(p1 - p2) `1 is complex real ext-real Element of REAL
K367((p1 - p2),1) is complex real ext-real Element of REAL
(p1 - p2) `2 is complex real ext-real Element of REAL
K367((p1 - p2),2) is complex real ext-real Element of REAL
((p1 - p2) `2) * <i> is complex set
((p1 - p2) `1) + (((p1 - p2) `2) * <i>) is complex set
|.(euc2cpx (p1 - p2)).| is complex real ext-real Element of REAL
Re (euc2cpx (p1 - p2)) is complex real ext-real Element of REAL
(Re (euc2cpx (p1 - p2))) ^2 is complex real ext-real Element of REAL
(Re (euc2cpx (p1 - p2))) * (Re (euc2cpx (p1 - p2))) is complex real ext-real set
Im (euc2cpx (p1 - p2)) is complex real ext-real Element of REAL
(Im (euc2cpx (p1 - p2))) ^2 is complex real ext-real Element of REAL
(Im (euc2cpx (p1 - p2))) * (Im (euc2cpx (p1 - p2))) is complex real ext-real set
((Re (euc2cpx (p1 - p2))) ^2) + ((Im (euc2cpx (p1 - p2))) ^2) is complex real ext-real Element of REAL
sqrt (((Re (euc2cpx (p1 - p2))) ^2) + ((Im (euc2cpx (p1 - p2))) ^2)) is complex real ext-real Element of REAL
|.(euc2cpx (p3 - p2)).| is complex real ext-real Element of REAL
Re (euc2cpx (p3 - p2)) is complex real ext-real Element of REAL
(Re (euc2cpx (p3 - p2))) ^2 is complex real ext-real Element of REAL
(Re (euc2cpx (p3 - p2))) * (Re (euc2cpx (p3 - p2))) is complex real ext-real set
Im (euc2cpx (p3 - p2)) is complex real ext-real Element of REAL
(Im (euc2cpx (p3 - p2))) ^2 is complex real ext-real Element of REAL
(Im (euc2cpx (p3 - p2))) * (Im (euc2cpx (p3 - p2))) is complex real ext-real set
((Re (euc2cpx (p3 - p2))) ^2) + ((Im (euc2cpx (p3 - p2))) ^2) is complex real ext-real Element of REAL
sqrt (((Re (euc2cpx (p3 - p2))) ^2) + ((Im (euc2cpx (p3 - p2))) ^2)) is complex real ext-real Element of REAL
|.(euc2cpx (p1 - p2)).| * |.(euc2cpx (p3 - p2)).| is complex real ext-real Element of REAL
((p4 ^2) + (p ^2)) - (a ^2) is complex real ext-real set
|.p1.| is complex real ext-real non negative Element of REAL
sqr p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt (p1,p1) is Relation-like Function-like set
K339((sqr p1)) is complex real ext-real Element of REAL
sqrt K339((sqr p1)) is complex real ext-real Element of REAL
|.p1.| ^2 is complex real ext-real Element of REAL
|.p1.| * |.p1.| is complex real ext-real non negative set
|(p2,p1)| is complex real ext-real Element of REAL
2 * |(p2,p1)| is complex real ext-real Element of REAL
(|.p1.| ^2) - (2 * |(p2,p1)|) is complex real ext-real Element of REAL
|.p2.| is complex real ext-real non negative Element of REAL
sqr p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt (p2,p2) is Relation-like Function-like set
K339((sqr p2)) is complex real ext-real Element of REAL
sqrt K339((sqr p2)) is complex real ext-real Element of REAL
|.p2.| ^2 is complex real ext-real Element of REAL
|.p2.| * |.p2.| is complex real ext-real non negative set
((|.p1.| ^2) - (2 * |(p2,p1)|)) + (|.p2.| ^2) is complex real ext-real Element of REAL
|.(p3 - p2).| ^2 is complex real ext-real Element of REAL
|.(p3 - p2).| * |.(p3 - p2).| is complex real ext-real non negative set
(((|.p1.| ^2) - (2 * |(p2,p1)|)) + (|.p2.| ^2)) + (|.(p3 - p2).| ^2) is complex real ext-real Element of REAL
|.(p3 - p1).| ^2 is complex real ext-real Element of REAL
|.(p3 - p1).| * |.(p3 - p1).| is complex real ext-real non negative set
((((|.p1.| ^2) - (2 * |(p2,p1)|)) + (|.p2.| ^2)) + (|.(p3 - p2).| ^2)) - (|.(p3 - p1).| ^2) is complex real ext-real Element of REAL
|.p3.| is complex real ext-real non negative Element of REAL
sqr p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt (p3,p3) is Relation-like Function-like set
K339((sqr p3)) is complex real ext-real Element of REAL
sqrt K339((sqr p3)) is complex real ext-real Element of REAL
|.p3.| ^2 is complex real ext-real Element of REAL
|.p3.| * |.p3.| is complex real ext-real non negative set
|(p1,p3)| is complex real ext-real Element of REAL
2 * |(p1,p3)| is complex real ext-real Element of REAL
(|.p3.| ^2) - (2 * |(p1,p3)|) is complex real ext-real Element of REAL
((|.p3.| ^2) - (2 * |(p1,p3)|)) + (|.p1.| ^2) is complex real ext-real Element of REAL
((((|.p1.| ^2) - (2 * |(p2,p1)|)) + (|.p2.| ^2)) + (|.(p3 - p2).| ^2)) - (((|.p3.| ^2) - (2 * |(p1,p3)|)) + (|.p1.| ^2)) is complex real ext-real Element of REAL
- (2 * |(p2,p1)|) is complex real ext-real Element of REAL
(- (2 * |(p2,p1)|)) + (|.p2.| ^2) is complex real ext-real Element of REAL
((- (2 * |(p2,p1)|)) + (|.p2.| ^2)) + (|.(p3 - p2).| ^2) is complex real ext-real Element of REAL
(((- (2 * |(p2,p1)|)) + (|.p2.| ^2)) + (|.(p3 - p2).| ^2)) - (|.p3.| ^2) is complex real ext-real Element of REAL
((((- (2 * |(p2,p1)|)) + (|.p2.| ^2)) + (|.(p3 - p2).| ^2)) - (|.p3.| ^2)) + (2 * |(p1,p3)|) is complex real ext-real Element of REAL
|(p2,p3)| is complex real ext-real Element of REAL
2 * |(p2,p3)| is complex real ext-real Element of REAL
(|.p3.| ^2) - (2 * |(p2,p3)|) is complex real ext-real Element of REAL
((|.p3.| ^2) - (2 * |(p2,p3)|)) + (|.p2.| ^2) is complex real ext-real Element of REAL
((- (2 * |(p2,p1)|)) + (|.p2.| ^2)) + (((|.p3.| ^2) - (2 * |(p2,p3)|)) + (|.p2.| ^2)) is complex real ext-real Element of REAL
(((- (2 * |(p2,p1)|)) + (|.p2.| ^2)) + (((|.p3.| ^2) - (2 * |(p2,p3)|)) + (|.p2.| ^2))) - (|.p3.| ^2) is complex real ext-real Element of REAL
((((- (2 * |(p2,p1)|)) + (|.p2.| ^2)) + (((|.p3.| ^2) - (2 * |(p2,p3)|)) + (|.p2.| ^2))) - (|.p3.| ^2)) + (2 * |(p1,p3)|) is complex real ext-real Element of REAL
- |(p2,p1)| is complex real ext-real Element of REAL
(- |(p2,p1)|) + (|.p2.| ^2) is complex real ext-real Element of REAL
((- |(p2,p1)|) + (|.p2.| ^2)) - |(p2,p3)| is complex real ext-real Element of REAL
(((- |(p2,p1)|) + (|.p2.| ^2)) - |(p2,p3)|) + |(p1,p3)| is complex real ext-real Element of REAL
2 * ((((- |(p2,p1)|) + (|.p2.| ^2)) - |(p2,p3)|) + |(p1,p3)|) is complex real ext-real Element of REAL
|.(p1 - p2).| * |.(p3 - p2).| is complex real ext-real non negative Element of REAL
(|.(p1 - p2).| * |.(p3 - p2).|) * (cos (angle (p1,p2,p3))) is complex real ext-real Element of REAL
angle ((euc2cpx (p1 - p2)),(euc2cpx (p3 - p2))) is complex real ext-real Element of REAL
cos (angle ((euc2cpx (p1 - p2)),(euc2cpx (p3 - p2)))) is complex real ext-real Element of REAL
(|.(p1 - p2).| * |.(p3 - p2).|) * (cos (angle ((euc2cpx (p1 - p2)),(euc2cpx (p3 - p2))))) is complex real ext-real Element of REAL
|.(euc2cpx (p1 - p2)).| * |.(p3 - p2).| is complex real ext-real Element of REAL
(|.(euc2cpx (p1 - p2)).| * |.(p3 - p2).|) * (cos (angle ((euc2cpx (p1 - p2)),(euc2cpx (p3 - p2))))) is complex real ext-real Element of REAL
(|.(euc2cpx (p1 - p2)).| * |.(euc2cpx (p3 - p2)).|) * (cos (angle ((euc2cpx (p1 - p2)),(euc2cpx (p3 - p2))))) is complex real ext-real Element of REAL
(euc2cpx (p1 - p2)) .|. (euc2cpx (p3 - p2)) is complex Element of COMPLEX
Re ((euc2cpx (p1 - p2)) .|. (euc2cpx (p3 - p2))) is complex real ext-real Element of REAL
(Re ((euc2cpx (p1 - p2)) .|. (euc2cpx (p3 - p2)))) / (|.(euc2cpx (p1 - p2)).| * |.(euc2cpx (p3 - p2)).|) is complex real ext-real Element of REAL
(|.(euc2cpx (p1 - p2)).| * |.(euc2cpx (p3 - p2)).|) * ((Re ((euc2cpx (p1 - p2)) .|. (euc2cpx (p3 - p2)))) / (|.(euc2cpx (p1 - p2)).| * |.(euc2cpx (p3 - p2)).|)) is complex real ext-real Element of REAL
(|.(euc2cpx (p1 - p2)).| * |.(euc2cpx (p3 - p2)).|) / (|.(euc2cpx (p1 - p2)).| * |.(euc2cpx (p3 - p2)).|) is complex real ext-real Element of REAL
(Re ((euc2cpx (p1 - p2)) .|. (euc2cpx (p3 - p2)))) / ((|.(euc2cpx (p1 - p2)).| * |.(euc2cpx (p3 - p2)).|) / (|.(euc2cpx (p1 - p2)).| * |.(euc2cpx (p3 - p2)).|)) is complex real ext-real Element of REAL
(Re ((euc2cpx (p1 - p2)) .|. (euc2cpx (p3 - p2)))) / 1 is complex real ext-real Element of REAL
(p1 `1) - (p2 `1) is complex real ext-real Element of REAL
(p3 `1) - (p2 `1) is complex real ext-real Element of REAL
((p1 `1) - (p2 `1)) * ((p3 `1) - (p2 `1)) is complex real ext-real Element of REAL
(p1 `2) - (p2 `2) is complex real ext-real Element of REAL
(p3 `2) - (p2 `2) is complex real ext-real Element of REAL
((p1 `2) - (p2 `2)) * ((p3 `2) - (p2 `2)) is complex real ext-real Element of REAL
(((p1 `1) - (p2 `1)) * ((p3 `1) - (p2 `1))) + (((p1 `2) - (p2 `2)) * ((p3 `2) - (p2 `2))) is complex real ext-real Element of REAL
(p1 `1) * (p3 `1) is complex real ext-real Element of REAL
(p1 `2) * (p3 `2) is complex real ext-real Element of REAL
((p1 `1) * (p3 `1)) + ((p1 `2) * (p3 `2)) is complex real ext-real Element of REAL
(p1 `1) * (p2 `1) is complex real ext-real Element of REAL
(((p1 `1) * (p3 `1)) + ((p1 `2) * (p3 `2))) - ((p1 `1) * (p2 `1)) is complex real ext-real Element of REAL
(p2 `1) * (p3 `1) is complex real ext-real Element of REAL
((((p1 `1) * (p3 `1)) + ((p1 `2) * (p3 `2))) - ((p1 `1) * (p2 `1))) - ((p2 `1) * (p3 `1)) is complex real ext-real Element of REAL
(p2 `1) * (p2 `1) is complex real ext-real Element of REAL
(((((p1 `1) * (p3 `1)) + ((p1 `2) * (p3 `2))) - ((p1 `1) * (p2 `1))) - ((p2 `1) * (p3 `1))) + ((p2 `1) * (p2 `1)) is complex real ext-real Element of REAL
(p1 `2) * (p2 `2) is complex real ext-real Element of REAL
- ((p1 `2) * (p2 `2)) is complex real ext-real Element of REAL
(p2 `2) * (p3 `2) is complex real ext-real Element of REAL
(- ((p1 `2) * (p2 `2))) - ((p2 `2) * (p3 `2)) is complex real ext-real Element of REAL
(p2 `2) * (p2 `2) is complex real ext-real Element of REAL
((- ((p1 `2) * (p2 `2))) - ((p2 `2) * (p3 `2))) + ((p2 `2) * (p2 `2)) is complex real ext-real Element of REAL
((((((p1 `1) * (p3 `1)) + ((p1 `2) * (p3 `2))) - ((p1 `1) * (p2 `1))) - ((p2 `1) * (p3 `1))) + ((p2 `1) * (p2 `1))) + (((- ((p1 `2) * (p2 `2))) - ((p2 `2) * (p3 `2))) + ((p2 `2) * (p2 `2))) is complex real ext-real Element of REAL
|(p1,p3)| - ((p1 `1) * (p2 `1)) is complex real ext-real Element of REAL
(|(p1,p3)| - ((p1 `1) * (p2 `1))) - ((p2 `1) * (p3 `1)) is complex real ext-real Element of REAL
((|(p1,p3)| - ((p1 `1) * (p2 `1))) - ((p2 `1) * (p3 `1))) + ((p2 `1) * (p2 `1)) is complex real ext-real Element of REAL
(((|(p1,p3)| - ((p1 `1) * (p2 `1))) - ((p2 `1) * (p3 `1))) + ((p2 `1) * (p2 `1))) + (((- ((p1 `2) * (p2 `2))) - ((p2 `2) * (p3 `2))) + ((p2 `2) * (p2 `2))) is complex real ext-real Element of REAL
((p1 `1) * (p2 `1)) + ((p1 `2) * (p2 `2)) is complex real ext-real Element of REAL
|(p1,p3)| - (((p1 `1) * (p2 `1)) + ((p1 `2) * (p2 `2))) is complex real ext-real Element of REAL
(|(p1,p3)| - (((p1 `1) * (p2 `1)) + ((p1 `2) * (p2 `2)))) - ((p2 `1) * (p3 `1)) is complex real ext-real Element of REAL
((|(p1,p3)| - (((p1 `1) * (p2 `1)) + ((p1 `2) * (p2 `2)))) - ((p2 `1) * (p3 `1))) + ((p2 `1) * (p2 `1)) is complex real ext-real Element of REAL
- ((p2 `2) * (p3 `2)) is complex real ext-real Element of REAL
(- ((p2 `2) * (p3 `2))) + ((p2 `2) * (p2 `2)) is complex real ext-real Element of REAL
(((|(p1,p3)| - (((p1 `1) * (p2 `1)) + ((p1 `2) * (p2 `2)))) - ((p2 `1) * (p3 `1))) + ((p2 `1) * (p2 `1))) + ((- ((p2 `2) * (p3 `2))) + ((p2 `2) * (p2 `2))) is complex real ext-real Element of REAL
|(p1,p2)| is complex real ext-real Element of REAL
|(p1,p3)| - |(p1,p2)| is complex real ext-real Element of REAL
(|(p1,p3)| - |(p1,p2)|) - ((p2 `1) * (p3 `1)) is complex real ext-real Element of REAL
((|(p1,p3)| - |(p1,p2)|) - ((p2 `1) * (p3 `1))) + ((p2 `1) * (p2 `1)) is complex real ext-real Element of REAL
(((|(p1,p3)| - |(p1,p2)|) - ((p2 `1) * (p3 `1))) + ((p2 `1) * (p2 `1))) + ((- ((p2 `2) * (p3 `2))) + ((p2 `2) * (p2 `2))) is complex real ext-real Element of REAL
((p2 `1) * (p3 `1)) + ((p2 `2) * (p3 `2)) is complex real ext-real Element of REAL
(|(p1,p3)| - |(p1,p2)|) - (((p2 `1) * (p3 `1)) + ((p2 `2) * (p3 `2))) is complex real ext-real Element of REAL
((|(p1,p3)| - |(p1,p2)|) - (((p2 `1) * (p3 `1)) + ((p2 `2) * (p3 `2)))) + ((p2 `1) * (p2 `1)) is complex real ext-real Element of REAL
(((|(p1,p3)| - |(p1,p2)|) - (((p2 `1) * (p3 `1)) + ((p2 `2) * (p3 `2)))) + ((p2 `1) * (p2 `1))) + ((p2 `2) * (p2 `2)) is complex real ext-real Element of REAL
(|(p1,p3)| - |(p1,p2)|) - |(p2,p3)| is complex real ext-real Element of REAL
((|(p1,p3)| - |(p1,p2)|) - |(p2,p3)|) + ((p2 `1) * (p2 `1)) is complex real ext-real Element of REAL
(((|(p1,p3)| - |(p1,p2)|) - |(p2,p3)|) + ((p2 `1) * (p2 `1))) + ((p2 `2) * (p2 `2)) is complex real ext-real Element of REAL
((p2 `1) * (p2 `1)) + ((p2 `2) * (p2 `2)) is complex real ext-real Element of REAL
((|(p1,p3)| - |(p1,p2)|) - |(p2,p3)|) + (((p2 `1) * (p2 `1)) + ((p2 `2) * (p2 `2))) is complex real ext-real Element of REAL
|(p2,p2)| is complex real ext-real Element of REAL
((|(p1,p3)| - |(p1,p2)|) - |(p2,p3)|) + |(p2,p2)| is complex real ext-real Element of REAL
((|(p1,p3)| - |(p1,p2)|) - |(p2,p3)|) + (|.p2.| ^2) is complex real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
LSeg (p2,p3) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p2) + (b1 * p3)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
angle (p2,p1,p3) is complex real ext-real Element of REAL
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
angle ((euc2cpx p2),(euc2cpx p1),(euc2cpx p3)) is complex real ext-real set
p2 - p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p1 is Relation-like Function-like set
K214((TOP-REAL 2),p2,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p1) is Relation-like Function-like complex-valued set
K251(p2,K280(p1)) is Relation-like Function-like set
euc2cpx (p2 - p1) is complex Element of COMPLEX
(p2 - p1) `1 is complex real ext-real Element of REAL
K367((p2 - p1),1) is complex real ext-real Element of REAL
(p2 - p1) `2 is complex real ext-real Element of REAL
K367((p2 - p1),2) is complex real ext-real Element of REAL
((p2 - p1) `2) * <i> is complex set
((p2 - p1) `1) + (((p2 - p1) `2) * <i>) is complex set
p3 - p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p3,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p3,K280(p1)) is Relation-like Function-like set
euc2cpx (p3 - p1) is complex Element of COMPLEX
(p3 - p1) `1 is complex real ext-real Element of REAL
K367((p3 - p1),1) is complex real ext-real Element of REAL
(p3 - p1) `2 is complex real ext-real Element of REAL
K367((p3 - p1),2) is complex real ext-real Element of REAL
((p3 - p1) `2) * <i> is complex set
((p3 - p1) `1) + (((p3 - p1) `2) * <i>) is complex set
a is complex real ext-real Element of REAL
1 - a is complex real ext-real Element of REAL
(1 - a) * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 - a) * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
a * p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
a * p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((1 - a) * p2) + (a * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((1 - a) * p2),(a * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 - a) * p2) + (a * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
- a is complex real ext-real Element of REAL
1 + (- a) is complex real ext-real Element of REAL
(1 + (- a)) * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 + (- a)) * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((1 + (- a)) * p2) + (a * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((1 + (- a)) * p2),(a * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 + (- a)) * p2) + (a * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - (((1 + (- a)) * p2) + (a * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- (((1 + (- a)) * p2) + (a * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- (((1 + (- a)) * p2) + (a * p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * (((1 + (- a)) * p2) + (a * p3)) is Relation-like Function-like set
K214((TOP-REAL 2),p3,(- (((1 + (- a)) * p2) + (a * p3)))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(- (((1 + (- a)) * p2) + (a * p3)))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (- (((1 + (- a)) * p2) + (a * p3))) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - (((1 + (- a)) * p2) + (a * p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280((((1 + (- a)) * p2) + (a * p3))) is Relation-like Function-like complex-valued set
K251(p3,K280((((1 + (- a)) * p2) + (a * p3)))) is Relation-like Function-like set
1 * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
1 * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- a) * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(- a) * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1 * p2) + ((- a) * p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(1 * p2),((- a) * p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 * p2) + ((- a) * p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((1 * p2) + ((- a) * p2)) + (a * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((1 * p2) + ((- a) * p2)),(a * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 * p2) + ((- a) * p2)) + (a * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - (((1 * p2) + ((- a) * p2)) + (a * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- (((1 * p2) + ((- a) * p2)) + (a * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- (((1 * p2) + ((- a) * p2)) + (a * p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * (((1 * p2) + ((- a) * p2)) + (a * p3)) is Relation-like Function-like set
K214((TOP-REAL 2),p3,(- (((1 * p2) + ((- a) * p2)) + (a * p3)))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(- (((1 * p2) + ((- a) * p2)) + (a * p3)))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (- (((1 * p2) + ((- a) * p2)) + (a * p3))) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - (((1 * p2) + ((- a) * p2)) + (a * p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280((((1 * p2) + ((- a) * p2)) + (a * p3))) is Relation-like Function-like complex-valued set
K251(p3,K280((((1 * p2) + ((- a) * p2)) + (a * p3)))) is Relation-like Function-like set
(- 1) * (((1 * p2) + ((- a) * p2)) + (a * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(- 1) * (((1 * p2) + ((- a) * p2)) + (a * p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 + ((- 1) * (((1 * p2) + ((- a) * p2)) + (a * p3))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,((- 1) * (((1 * p2) + ((- a) * p2)) + (a * p3)))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + ((- 1) * (((1 * p2) + ((- a) * p2)) + (a * p3))) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * ((1 * p2) + ((- a) * p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(- 1) * ((1 * p2) + ((- a) * p2)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * (a * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(- 1) * (a * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((- 1) * ((1 * p2) + ((- a) * p2))) + ((- 1) * (a * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((- 1) * ((1 * p2) + ((- a) * p2))),((- 1) * (a * p3))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((- 1) * ((1 * p2) + ((- a) * p2))) + ((- 1) * (a * p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 + (((- 1) * ((1 * p2) + ((- a) * p2))) + ((- 1) * (a * p3))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(((- 1) * ((1 * p2) + ((- a) * p2))) + ((- 1) * (a * p3)))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (((- 1) * ((1 * p2) + ((- a) * p2))) + ((- 1) * (a * p3))) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 + ((- a) * p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,((- a) * p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + ((- a) * p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * (p2 + ((- a) * p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(- 1) * (p2 + ((- a) * p2)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((- 1) * (p2 + ((- a) * p2))) + ((- 1) * (a * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((- 1) * (p2 + ((- a) * p2))),((- 1) * (a * p3))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((- 1) * (p2 + ((- a) * p2))) + ((- 1) * (a * p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 + (((- 1) * (p2 + ((- a) * p2))) + ((- 1) * (a * p3))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(((- 1) * (p2 + ((- a) * p2))) + ((- 1) * (a * p3)))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (((- 1) * (p2 + ((- a) * p2))) + ((- 1) * (a * p3))) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * a is complex real ext-real Element of REAL
((- 1) * a) * p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((- 1) * a) * p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((- 1) * (p2 + ((- a) * p2))) + (((- 1) * a) * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((- 1) * (p2 + ((- a) * p2))),(((- 1) * a) * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((- 1) * (p2 + ((- a) * p2))) + (((- 1) * a) * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 + (((- 1) * (p2 + ((- a) * p2))) + (((- 1) * a) * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(((- 1) * (p2 + ((- a) * p2))) + (((- 1) * a) * p3))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (((- 1) * (p2 + ((- a) * p2))) + (((- 1) * a) * p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(- 1) * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * ((- a) * p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(- 1) * ((- a) * p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((- 1) * p2) + ((- 1) * ((- a) * p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((- 1) * p2),((- 1) * ((- a) * p2))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((- 1) * p2) + ((- 1) * ((- a) * p2)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- a) * p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(- a) * p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(((- 1) * p2) + ((- 1) * ((- a) * p2))) + ((- a) * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(((- 1) * p2) + ((- 1) * ((- a) * p2))),((- a) * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(((- 1) * p2) + ((- 1) * ((- a) * p2))) + ((- a) * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 + ((((- 1) * p2) + ((- 1) * ((- a) * p2))) + ((- a) * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,((((- 1) * p2) + ((- 1) * ((- a) * p2))) + ((- a) * p3))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + ((((- 1) * p2) + ((- 1) * ((- a) * p2))) + ((- a) * p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * (- a) is complex real ext-real Element of REAL
((- 1) * (- a)) * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((- 1) * (- a)) * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((- 1) * p2) + (((- 1) * (- a)) * p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((- 1) * p2),(((- 1) * (- a)) * p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((- 1) * p2) + (((- 1) * (- a)) * p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(((- 1) * p2) + (((- 1) * (- a)) * p2)) + ((- a) * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(((- 1) * p2) + (((- 1) * (- a)) * p2)),((- a) * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(((- 1) * p2) + (((- 1) * (- a)) * p2)) + ((- a) * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 + ((((- 1) * p2) + (((- 1) * (- a)) * p2)) + ((- a) * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,((((- 1) * p2) + (((- 1) * (- a)) * p2)) + ((- a) * p3))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + ((((- 1) * p2) + (((- 1) * (- a)) * p2)) + ((- a) * p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
a * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
a * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(a * p2) + ((- a) * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(a * p2),((- a) * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(a * p2) + ((- a) * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((- 1) * p2) + ((a * p2) + ((- a) * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((- 1) * p2),((a * p2) + ((- a) * p3))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((- 1) * p2) + ((a * p2) + ((- a) * p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 + (((- 1) * p2) + ((a * p2) + ((- a) * p3))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(((- 1) * p2) + ((a * p2) + ((- a) * p3)))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (((- 1) * p2) + ((a * p2) + ((- a) * p3))) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
- p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p2 is Relation-like Function-like set
(- p2) + ((a * p2) + ((- a) * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(- p2),((a * p2) + ((- a) * p3))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(- p2) + ((a * p2) + ((- a) * p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 + ((- p2) + ((a * p2) + ((- a) * p3))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,((- p2) + ((a * p2) + ((- a) * p3)))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + ((- p2) + ((a * p2) + ((- a) * p3))) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- p2) + p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(- p2),p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(- p2) + p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((- p2) + p3) + ((a * p2) + ((- a) * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((- p2) + p3),((a * p2) + ((- a) * p3))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((- p2) + p3) + ((a * p2) + ((- a) * p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
- (- p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * (- p2) is Relation-like Function-like set
a * (- (- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
a * (- (- p2)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(a * (- (- p2))) + ((- a) * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(a * (- (- p2))),((- a) * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(a * (- (- p2))) + ((- a) * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((- p2) + p3) + ((a * (- (- p2))) + ((- a) * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((- p2) + p3),((a * (- (- p2))) + ((- a) * p3))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((- p2) + p3) + ((a * (- (- p2))) + ((- a) * p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * (- p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(- 1) * (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
a * ((- 1) * (- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
a * ((- 1) * (- p2)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(a * ((- 1) * (- p2))) + ((- a) * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(a * ((- 1) * (- p2))),((- a) * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(a * ((- 1) * (- p2))) + ((- a) * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((- p2) + p3) + ((a * ((- 1) * (- p2))) + ((- a) * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((- p2) + p3),((a * ((- 1) * (- p2))) + ((- a) * p3))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((- p2) + p3) + ((a * ((- 1) * (- p2))) + ((- a) * p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
a * (- 1) is complex real ext-real Element of REAL
(a * (- 1)) * (- p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(a * (- 1)) * (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((a * (- 1)) * (- p2)) + ((- a) * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((a * (- 1)) * (- p2)),((- a) * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((a * (- 1)) * (- p2)) + ((- a) * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((- p2) + p3) + (((a * (- 1)) * (- p2)) + ((- a) * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((- p2) + p3),(((a * (- 1)) * (- p2)) + ((- a) * p3))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((- p2) + p3) + (((a * (- 1)) * (- p2)) + ((- a) * p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- a) * ((- p2) + p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(- a) * ((- p2) + p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((- p2) + p3) + ((- a) * ((- p2) + p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((- p2) + p3),((- a) * ((- p2) + p3))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((- p2) + p3) + ((- a) * ((- p2) + p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
1 * ((- p2) + p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
1 * ((- p2) + p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1 * ((- p2) + p3)) + ((- a) * ((- p2) + p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(1 * ((- p2) + p3)),((- a) * ((- p2) + p3))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 * ((- p2) + p3)) + ((- a) * ((- p2) + p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1 + (- a)) * ((- p2) + p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 + (- a)) * ((- p2) + p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1 - a) * ((- p2) + p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 - a) * ((- p2) + p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1 * p2) + (0. (TOP-REAL 2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(1 * p2),(0. (TOP-REAL 2))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 * p2) + (0. (TOP-REAL 2)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
1 * p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
1 * p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(0. (TOP-REAL 2)) + (1 * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(0. (TOP-REAL 2)),(1 * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(0. (TOP-REAL 2)) + (1 * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- a) + 1 is complex real ext-real Element of REAL
(- 1) + 1 is complex real ext-real Element of REAL
- (euc2cpx (p3 - p1)) is complex Element of COMPLEX
|.(p3 - p1).| is complex real ext-real non negative Element of REAL
sqr (p3 - p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p3 - p1),(p3 - p1)) is Relation-like Function-like set
K339((sqr (p3 - p1))) is complex real ext-real Element of REAL
sqrt K339((sqr (p3 - p1))) is complex real ext-real Element of REAL
a / (1 - a) is complex real ext-real Element of REAL
- (a / (1 - a)) is complex real ext-real Element of REAL
p2 - (((1 + (- a)) * p2) + (a * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p2,(- (((1 + (- a)) * p2) + (a * p3)))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- (((1 + (- a)) * p2) + (a * p3)))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- (((1 + (- a)) * p2) + (a * p3))) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - (((1 + (- a)) * p2) + (a * p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p2,K280((((1 + (- a)) * p2) + (a * p3)))) is Relation-like Function-like set
p2 - (((1 * p2) + ((- a) * p2)) + (a * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p2,(- (((1 * p2) + ((- a) * p2)) + (a * p3)))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- (((1 * p2) + ((- a) * p2)) + (a * p3)))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- (((1 * p2) + ((- a) * p2)) + (a * p3))) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - (((1 * p2) + ((- a) * p2)) + (a * p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p2,K280((((1 * p2) + ((- a) * p2)) + (a * p3)))) is Relation-like Function-like set
p2 + ((- 1) * (((1 * p2) + ((- a) * p2)) + (a * p3))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,((- 1) * (((1 * p2) + ((- a) * p2)) + (a * p3)))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + ((- 1) * (((1 * p2) + ((- a) * p2)) + (a * p3))) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 + (((- 1) * ((1 * p2) + ((- a) * p2))) + ((- 1) * (a * p3))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(((- 1) * ((1 * p2) + ((- a) * p2))) + ((- 1) * (a * p3)))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (((- 1) * ((1 * p2) + ((- a) * p2))) + ((- 1) * (a * p3))) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 + (((- 1) * (p2 + ((- a) * p2))) + ((- 1) * (a * p3))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(((- 1) * (p2 + ((- a) * p2))) + ((- 1) * (a * p3)))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (((- 1) * (p2 + ((- a) * p2))) + ((- 1) * (a * p3))) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 + (((- 1) * (p2 + ((- a) * p2))) + (((- 1) * a) * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(((- 1) * (p2 + ((- a) * p2))) + (((- 1) * a) * p3))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (((- 1) * (p2 + ((- a) * p2))) + (((- 1) * a) * p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 + ((((- 1) * p2) + ((- 1) * ((- a) * p2))) + ((- a) * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,((((- 1) * p2) + ((- 1) * ((- a) * p2))) + ((- a) * p3))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + ((((- 1) * p2) + ((- 1) * ((- a) * p2))) + ((- a) * p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 + ((((- 1) * p2) + (((- 1) * (- a)) * p2)) + ((- a) * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,((((- 1) * p2) + (((- 1) * (- a)) * p2)) + ((- a) * p3))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + ((((- 1) * p2) + (((- 1) * (- a)) * p2)) + ((- a) * p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 + (((- 1) * p2) + ((a * p2) + ((- a) * p3))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(((- 1) * p2) + ((a * p2) + ((- a) * p3)))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (((- 1) * p2) + ((a * p2) + ((- a) * p3))) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 + ((- p2) + ((a * p2) + ((- a) * p3))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,((- p2) + ((a * p2) + ((- a) * p3)))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + ((- p2) + ((a * p2) + ((- a) * p3))) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 + (- p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(p2 + (- p2)) + ((a * p2) + ((- a) * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(p2 + (- p2)),((a * p2) + ((- a) * p3))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(p2 + (- p2)) + ((a * p2) + ((- a) * p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(0. (TOP-REAL 2)) + ((a * p2) + ((- a) * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(0. (TOP-REAL 2)),((a * p2) + ((- a) * p3))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(0. (TOP-REAL 2)) + ((a * p2) + ((- a) * p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(a * (- 1)) * p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(a * (- 1)) * p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(a * p2) + ((a * (- 1)) * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(a * p2),((a * (- 1)) * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(a * p2) + ((a * (- 1)) * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(- 1) * p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
a * ((- 1) * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
a * ((- 1) * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(a * p2) + (a * ((- 1) * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(a * p2),(a * ((- 1) * p3))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(a * p2) + (a * ((- 1) * p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
- p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p3 is Relation-like Function-like set
a * (- p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
a * (- p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(a * p2) + (a * (- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(a * p2),(a * (- p3))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(a * p2) + (a * (- p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p2,(- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p3) is Relation-like Function-like complex-valued set
K251(p2,K280(p3)) is Relation-like Function-like set
a * (p2 - p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
a * (p2 - p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(euc2cpx (p3 - p1)) * (- (a / (1 - a))) is complex set
cpx2euc ((euc2cpx (p3 - p1)) * (- (a / (1 - a)))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
Re ((euc2cpx (p3 - p1)) * (- (a / (1 - a)))) is complex real ext-real Element of REAL
Im ((euc2cpx (p3 - p1)) * (- (a / (1 - a)))) is complex real ext-real Element of REAL
|[(Re ((euc2cpx (p3 - p1)) * (- (a / (1 - a))))),(Im ((euc2cpx (p3 - p1)) * (- (a / (1 - a)))))]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
cpx2euc (euc2cpx (p3 - p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
Re (euc2cpx (p3 - p1)) is complex real ext-real Element of REAL
Im (euc2cpx (p3 - p1)) is complex real ext-real Element of REAL
|[(Re (euc2cpx (p3 - p1))),(Im (euc2cpx (p3 - p1)))]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(- (a / (1 - a))) * (cpx2euc (euc2cpx (p3 - p1))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(- (a / (1 - a))) * (cpx2euc (euc2cpx (p3 - p1))) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- (a / (1 - a))) * ((1 - a) * ((- p2) + p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(- (a / (1 - a))) * ((1 - a) * ((- p2) + p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- (a / (1 - a))) * (1 - a) is complex real ext-real Element of REAL
((- (a / (1 - a))) * (1 - a)) * ((- p2) + p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((- (a / (1 - a))) * (1 - a)) * ((- p2) + p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- a) / (1 - a) is complex real ext-real Element of REAL
((- a) / (1 - a)) * (1 - a) is complex real ext-real Element of REAL
(((- a) / (1 - a)) * (1 - a)) * ((- p2) + p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(((- a) / (1 - a)) * (1 - a)) * ((- p2) + p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1 - a) / (1 - a) is complex real ext-real Element of REAL
((1 - a) / (1 - a)) * (- a) is complex real ext-real Element of REAL
(((1 - a) / (1 - a)) * (- a)) * ((- p2) + p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(((1 - a) / (1 - a)) * (- a)) * ((- p2) + p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
1 * (- a) is complex real ext-real Element of REAL
(1 * (- a)) * ((- p2) + p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 * (- a)) * ((- p2) + p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(a * (- 1)) * ((- p2) + p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(a * (- 1)) * ((- p2) + p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * ((- p2) + p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(- 1) * ((- p2) + p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
a * ((- 1) * ((- p2) + p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
a * ((- 1) * ((- p2) + p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((- 1) * (- p2)) + ((- 1) * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((- 1) * (- p2)),((- 1) * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((- 1) * (- p2)) + ((- 1) * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
a * (((- 1) * (- p2)) + ((- 1) * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
a * (((- 1) * (- p2)) + ((- 1) * p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- (- p2)) + ((- 1) * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(- (- p2)),((- 1) * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(- (- p2)) + ((- 1) * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
a * ((- (- p2)) + ((- 1) * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
a * ((- (- p2)) + ((- 1) * p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- (- p2)) + (- p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(- (- p2)),(- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(- (- p2)) + (- p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
a * ((- (- p2)) + (- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
a * ((- (- p2)) + (- p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 + (- p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
a * (p2 + (- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
a * (p2 + (- p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
cpx2euc (euc2cpx (p2 - p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
Re (euc2cpx (p2 - p1)) is complex real ext-real Element of REAL
Im (euc2cpx (p2 - p1)) is complex real ext-real Element of REAL
|[(Re (euc2cpx (p2 - p1))),(Im (euc2cpx (p2 - p1)))]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
Arg (- (euc2cpx (p3 - p1))) is complex real ext-real Element of REAL
Arg (euc2cpx (p2 - p1)) is complex real ext-real Element of REAL
angle ((euc2cpx (p2 - p1)),(- (euc2cpx (p3 - p1)))) is complex real ext-real Element of REAL
(Arg (- (euc2cpx (p3 - p1)))) - (Arg (euc2cpx (p2 - p1))) is complex real ext-real Element of REAL
(Arg (- (euc2cpx (p3 - p1)))) - (Arg (euc2cpx (p2 - p1))) is complex real ext-real Element of REAL
(Arg (- (euc2cpx (p3 - p1)))) - (Arg (euc2cpx (p2 - p1))) is complex real ext-real Element of REAL
- (- (euc2cpx (p3 - p1))) is complex Element of COMPLEX
angle ((euc2cpx (p2 - p1)),(- (- (euc2cpx (p3 - p1))))) is complex real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
LSeg (p2,p3) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p2) + (b1 * p3)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p3,p2,p4) is complex real ext-real Element of REAL
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
euc2cpx p4 is complex Element of COMPLEX
p4 `1 is complex real ext-real Element of REAL
K367(p4,1) is complex real ext-real Element of REAL
p4 `2 is complex real ext-real Element of REAL
K367(p4,2) is complex real ext-real Element of REAL
(p4 `2) * <i> is complex set
(p4 `1) + ((p4 `2) * <i>) is complex set
angle ((euc2cpx p3),(euc2cpx p2),(euc2cpx p4)) is complex real ext-real set
angle (p1,p2,p4) is complex real ext-real Element of REAL
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx p2),(euc2cpx p4)) is complex real ext-real set
p1 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p2 is Relation-like Function-like set
K214((TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p2) is Relation-like Function-like complex-valued set
K251(p1,K280(p2)) is Relation-like Function-like set
euc2cpx (p1 - p2) is complex Element of COMPLEX
(p1 - p2) `1 is complex real ext-real Element of REAL
K367((p1 - p2),1) is complex real ext-real Element of REAL
(p1 - p2) `2 is complex real ext-real Element of REAL
K367((p1 - p2),2) is complex real ext-real Element of REAL
((p1 - p2) `2) * <i> is complex set
((p1 - p2) `1) + (((p1 - p2) `2) * <i>) is complex set
p4 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p4,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p4,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p4 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p4 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p4,K280(p2)) is Relation-like Function-like set
euc2cpx (p4 - p2) is complex Element of COMPLEX
(p4 - p2) `1 is complex real ext-real Element of REAL
K367((p4 - p2),1) is complex real ext-real Element of REAL
(p4 - p2) `2 is complex real ext-real Element of REAL
K367((p4 - p2),2) is complex real ext-real Element of REAL
((p4 - p2) `2) * <i> is complex set
((p4 - p2) `1) + (((p4 - p2) `2) * <i>) is complex set
p3 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p3,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p3,K280(p2)) is Relation-like Function-like set
euc2cpx (p3 - p2) is complex Element of COMPLEX
(p3 - p2) `1 is complex real ext-real Element of REAL
K367((p3 - p2),1) is complex real ext-real Element of REAL
(p3 - p2) `2 is complex real ext-real Element of REAL
K367((p3 - p2),2) is complex real ext-real Element of REAL
((p3 - p2) `2) * <i> is complex set
((p3 - p2) `1) + (((p3 - p2) `2) * <i>) is complex set
r is complex real ext-real Element of REAL
1 - r is complex real ext-real Element of REAL
(1 - r) * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 - r) * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
r * p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
r * p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((1 - r) * p2) + (r * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((1 - r) * p2),(r * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 - r) * p2) + (r * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
- r is complex real ext-real Element of REAL
1 + (- r) is complex real ext-real Element of REAL
(1 + (- r)) * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 + (- r)) * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((1 + (- r)) * p2) + (r * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((1 + (- r)) * p2),(r * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 + (- r)) * p2) + (r * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(((1 + (- r)) * p2) + (r * p3)) - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),(((1 + (- r)) * p2) + (r * p3)),(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(((1 + (- r)) * p2) + (r * p3)),(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(((1 + (- r)) * p2) + (r * p3)) + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(((1 + (- r)) * p2) + (r * p3)) - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251((((1 + (- r)) * p2) + (r * p3)),K280(p2)) is Relation-like Function-like set
1 * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
1 * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- r) * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(- r) * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1 * p2) + ((- r) * p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(1 * p2),((- r) * p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 * p2) + ((- r) * p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((1 * p2) + ((- r) * p2)) + (r * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((1 * p2) + ((- r) * p2)),(r * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 * p2) + ((- r) * p2)) + (r * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(((1 * p2) + ((- r) * p2)) + (r * p3)) - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),(((1 * p2) + ((- r) * p2)) + (r * p3)),(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(((1 * p2) + ((- r) * p2)) + (r * p3)),(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(((1 * p2) + ((- r) * p2)) + (r * p3)) + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(((1 * p2) + ((- r) * p2)) + (r * p3)) - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251((((1 * p2) + ((- r) * p2)) + (r * p3)),K280(p2)) is Relation-like Function-like set
p2 + ((- r) * p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,((- r) * p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + ((- r) * p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(p2 + ((- r) * p2)) + (r * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(p2 + ((- r) * p2)),(r * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(p2 + ((- r) * p2)) + (r * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((p2 + ((- r) * p2)) + (r * p3)) - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),((p2 + ((- r) * p2)) + (r * p3)),(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((p2 + ((- r) * p2)) + (r * p3)),(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((p2 + ((- r) * p2)) + (r * p3)) + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((p2 + ((- r) * p2)) + (r * p3)) - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(((p2 + ((- r) * p2)) + (r * p3)),K280(p2)) is Relation-like Function-like set
(r * p3) + (- p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(r * p3),(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(r * p3) + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(p2 + ((- r) * p2)) + ((r * p3) + (- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(p2 + ((- r) * p2)),((r * p3) + (- p2))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(p2 + ((- r) * p2)) + ((r * p3) + (- p2)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((- r) * p2) + ((r * p3) + (- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((- r) * p2),((r * p3) + (- p2))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((- r) * p2) + ((r * p3) + (- p2)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 + (((- r) * p2) + ((r * p3) + (- p2))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(((- r) * p2) + ((r * p3) + (- p2)))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (((- r) * p2) + ((r * p3) + (- p2))) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((- r) * p2) + (r * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((- r) * p2),(r * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((- r) * p2) + (r * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- p2) + (((- r) * p2) + (r * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(- p2),(((- r) * p2) + (r * p3))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(- p2) + (((- r) * p2) + (r * p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 + ((- p2) + (((- r) * p2) + (r * p3))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,((- p2) + (((- r) * p2) + (r * p3)))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + ((- p2) + (((- r) * p2) + (r * p3))) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 + (- p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(p2 + (- p2)) + (((- r) * p2) + (r * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(p2 + (- p2)),(((- r) * p2) + (r * p3))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(p2 + (- p2)) + (((- r) * p2) + (r * p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(0. (TOP-REAL 2)) + (((- r) * p2) + (r * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(0. (TOP-REAL 2)),(((- r) * p2) + (r * p3))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(0. (TOP-REAL 2)) + (((- r) * p2) + (r * p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
r * (- 1) is complex real ext-real Element of REAL
(r * (- 1)) * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(r * (- 1)) * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((r * (- 1)) * p2) + (r * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((r * (- 1)) * p2),(r * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((r * (- 1)) * p2) + (r * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(- 1) * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
r * ((- 1) * p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
r * ((- 1) * p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(r * ((- 1) * p2)) + (r * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(r * ((- 1) * p2)),(r * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(r * ((- 1) * p2)) + (r * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
r * (- p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
r * (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(r * (- p2)) + (r * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(r * (- p2)),(r * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(r * (- p2)) + (r * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
r * (p3 - p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
r * (p3 - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1 * p2) + (0. (TOP-REAL 2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(1 * p2),(0. (TOP-REAL 2))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 * p2) + (0. (TOP-REAL 2)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(euc2cpx (p3 - p2)) * r is complex set
cpx2euc ((euc2cpx (p3 - p2)) * r) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
Re ((euc2cpx (p3 - p2)) * r) is complex real ext-real Element of REAL
Im ((euc2cpx (p3 - p2)) * r) is complex real ext-real Element of REAL
|[(Re ((euc2cpx (p3 - p2)) * r)),(Im ((euc2cpx (p3 - p2)) * r))]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
cpx2euc (euc2cpx (p3 - p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
Re (euc2cpx (p3 - p2)) is complex real ext-real Element of REAL
Im (euc2cpx (p3 - p2)) is complex real ext-real Element of REAL
|[(Re (euc2cpx (p3 - p2))),(Im (euc2cpx (p3 - p2)))]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
r * (cpx2euc (euc2cpx (p3 - p2))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
r * (cpx2euc (euc2cpx (p3 - p2))) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
cpx2euc (euc2cpx (p1 - p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
Re (euc2cpx (p1 - p2)) is complex real ext-real Element of REAL
Im (euc2cpx (p1 - p2)) is complex real ext-real Element of REAL
|[(Re (euc2cpx (p1 - p2))),(Im (euc2cpx (p1 - p2)))]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
Arg (euc2cpx (p1 - p2)) is complex real ext-real Element of REAL
Arg (euc2cpx (p3 - p2)) is complex real ext-real Element of REAL
angle ((euc2cpx (p3 - p2)),(euc2cpx (p4 - p2))) is complex real ext-real Element of REAL
angle ((euc2cpx (p1 - p2)),(euc2cpx (p4 - p2))) is complex real ext-real Element of REAL
- (Arg (euc2cpx (p3 - p2))) is complex real ext-real Element of REAL
Rotate ((euc2cpx (p4 - p2)),(- (Arg (euc2cpx (p3 - p2))))) is complex Element of COMPLEX
Arg (Rotate ((euc2cpx (p4 - p2)),(- (Arg (euc2cpx (p3 - p2)))))) is complex real ext-real Element of REAL
(2 * PI) - (Arg (euc2cpx (p3 - p2))) is complex real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
LSeg (p2,p3) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p2) + (b1 * p3)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p4,p2,p3) is complex real ext-real Element of REAL
euc2cpx p4 is complex Element of COMPLEX
p4 `1 is complex real ext-real Element of REAL
K367(p4,1) is complex real ext-real Element of REAL
p4 `2 is complex real ext-real Element of REAL
K367(p4,2) is complex real ext-real Element of REAL
(p4 `2) * <i> is complex set
(p4 `1) + ((p4 `2) * <i>) is complex set
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
angle ((euc2cpx p4),(euc2cpx p2),(euc2cpx p3)) is complex real ext-real set
angle (p4,p2,p1) is complex real ext-real Element of REAL
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
angle ((euc2cpx p4),(euc2cpx p2),(euc2cpx p1)) is complex real ext-real set
angle (p3,p2,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p3),(euc2cpx p2),(euc2cpx p4)) is complex real ext-real set
angle (p1,p2,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p1),(euc2cpx p2),(euc2cpx p4)) is complex real ext-real set
(2 * PI) - (angle (p3,p2,p4)) is complex real ext-real Element of REAL
(2 * PI) - (angle (p1,p2,p4)) is complex real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
LSeg (p1,p2) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p1) + (b1 * p2)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
p3 is complex real ext-real set
p4 is complex real ext-real set
p is complex real ext-real set
inside_of_circle (p3,p4,p) is Element of bool the carrier of (TOP-REAL 2)
outside_of_circle (p3,p4,p) is Element of bool the carrier of (TOP-REAL 2)
circle (p3,p4,p) is Element of bool the carrier of (TOP-REAL 2)
(LSeg (p1,p2)) /\ (circle (p3,p4,p)) is Element of bool the carrier of (TOP-REAL 2)
|[p3,p4]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 - |[p3,p4]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- |[p3,p4]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- |[p3,p4]| is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * |[p3,p4]| is Relation-like Function-like set
K214((TOP-REAL 2),p1,(- |[p3,p4]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- |[p3,p4]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- |[p3,p4]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - |[p3,p4]| is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(|[p3,p4]|) is Relation-like Function-like complex-valued set
K251(p1,K280(|[p3,p4]|)) is Relation-like Function-like set
p2 - |[p3,p4]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p2,(- |[p3,p4]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- |[p3,p4]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- |[p3,p4]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - |[p3,p4]| is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p2,K280(|[p3,p4]|)) is Relation-like Function-like set
{ b1 where b1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2) : not p <= |.(b1 - |[p3,p4]|).| } is set
{ b1 where b1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2) : not |.(b1 - |[p3,p4]|).| <= p } is set
LSeg ((p1 - |[p3,p4]|),(p2 - |[p3,p4]|)) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * (p1 - |[p3,p4]|)) + (b1 * (p2 - |[p3,p4]|))) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
(TOP-REAL 2) | (LSeg ((p1 - |[p3,p4]|),(p2 - |[p3,p4]|))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (LSeg ((p1 - |[p3,p4]|),(p2 - |[p3,p4]|)))) is non empty set
[: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg ((p1 - |[p3,p4]|),(p2 - |[p3,p4]|)))):] is set
bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg ((p1 - |[p3,p4]|),(p2 - |[p3,p4]|)))):] is set
p5 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p5 - |[p3,p4]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p5,(- |[p3,p4]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p5,(- |[p3,p4]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p5 + (- |[p3,p4]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p5 - |[p3,p4]| is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p5,K280(|[p3,p4]|)) is Relation-like Function-like set
|.(p5 - |[p3,p4]|).| is complex real ext-real non negative Element of REAL
sqr (p5 - |[p3,p4]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p5 - |[p3,p4]|),(p5 - |[p3,p4]|)) is Relation-like Function-like set
K339((sqr (p5 - |[p3,p4]|))) is complex real ext-real Element of REAL
sqrt K339((sqr (p5 - |[p3,p4]|))) is complex real ext-real Element of REAL
z2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
z2 - |[p3,p4]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),z2,(- |[p3,p4]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),z2,(- |[p3,p4]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
z2 + (- |[p3,p4]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
z2 - |[p3,p4]| is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(z2,K280(|[p3,p4]|)) is Relation-like Function-like set
|.(z2 - |[p3,p4]|).| is complex real ext-real non negative Element of REAL
sqr (z2 - |[p3,p4]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((z2 - |[p3,p4]|),(z2 - |[p3,p4]|)) is Relation-like Function-like set
K339((sqr (z2 - |[p3,p4]|))) is complex real ext-real Element of REAL
sqrt K339((sqr (z2 - |[p3,p4]|))) is complex real ext-real Element of REAL
p5 is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | (LSeg ((p1 - |[p3,p4]|),(p2 - |[p3,p4]|)))) -valued Function-like total V30( the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg ((p1 - |[p3,p4]|),(p2 - |[p3,p4]|))))) Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg ((p1 - |[p3,p4]|),(p2 - |[p3,p4]|)))):]
p5 . 0 is set
p5 . 1 is set
[: the carrier of I[01], the carrier of (TOP-REAL 2):] is set
bool [: the carrier of I[01], the carrier of (TOP-REAL 2):] is set
z2 is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like total V30( the carrier of I[01], the carrier of (TOP-REAL 2)) Element of bool [: the carrier of I[01], the carrier of (TOP-REAL 2):]
dom z2 is set
z2 /. 0 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
z2 /. 1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
r is complex real ext-real Element of REAL
f0 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
f0 - |[p3,p4]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),f0,(- |[p3,p4]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),f0,(- |[p3,p4]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
f0 + (- |[p3,p4]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
f0 - |[p3,p4]| is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(f0,K280(|[p3,p4]|)) is Relation-like Function-like set
|.(f0 - |[p3,p4]|).| is complex real ext-real non negative Element of REAL
sqr (f0 - |[p3,p4]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((f0 - |[p3,p4]|),(f0 - |[p3,p4]|)) is Relation-like Function-like set
K339((sqr (f0 - |[p3,p4]|))) is complex real ext-real Element of REAL
sqrt K339((sqr (f0 - |[p3,p4]|))) is complex real ext-real Element of REAL
d is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
d - |[p3,p4]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),d,(- |[p3,p4]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),d,(- |[p3,p4]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
d + (- |[p3,p4]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
d - |[p3,p4]| is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(d,K280(|[p3,p4]|)) is Relation-like Function-like set
|.(d - |[p3,p4]|).| is complex real ext-real non negative Element of REAL
sqr (d - |[p3,p4]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((d - |[p3,p4]|),(d - |[p3,p4]|)) is Relation-like Function-like set
K339((sqr (d - |[p3,p4]|))) is complex real ext-real Element of REAL
sqrt K339((sqr (d - |[p3,p4]|))) is complex real ext-real Element of REAL
f0 is complex real ext-real Element of the carrier of I[01]
z2 /. f0 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K117( the carrier of I[01], the carrier of (TOP-REAL 2),z2,f0) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
|.(z2 /. f0).| is complex real ext-real non negative Element of REAL
sqr (z2 /. f0) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((z2 /. f0),(z2 /. f0)) is Relation-like Function-like set
K339((sqr (z2 /. f0))) is complex real ext-real Element of REAL
sqrt K339((sqr (z2 /. f0))) is complex real ext-real Element of REAL
{ b1 where b1 is ext-real Element of ExtREAL : ( 0 <= b1 & b1 <= 1 ) } is set
f2 is ext-real Element of ExtREAL
d is complex real ext-real Element of REAL
p5 . d is set
rng z2 is set
z2 . d is set
f6 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
f6 + |[p3,p4]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),f6,|[p3,p4]|) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
f6 + |[p3,p4]| is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
1 - d is complex real ext-real Element of REAL
(1 - d) * (p1 - |[p3,p4]|) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 - d) * (p1 - |[p3,p4]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
d * (p2 - |[p3,p4]|) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
d * (p2 - |[p3,p4]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((1 - d) * (p1 - |[p3,p4]|)) + (d * (p2 - |[p3,p4]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((1 - d) * (p1 - |[p3,p4]|)),(d * (p2 - |[p3,p4]|))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 - d) * (p1 - |[p3,p4]|)) + (d * (p2 - |[p3,p4]|)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1 - d) * p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 - d) * p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1 - d) * |[p3,p4]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 - d) * |[p3,p4]| is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((1 - d) * p1) - ((1 - d) * |[p3,p4]|) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- ((1 - d) * |[p3,p4]|) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- ((1 - d) * |[p3,p4]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * ((1 - d) * |[p3,p4]|) is Relation-like Function-like set
K214((TOP-REAL 2),((1 - d) * p1),(- ((1 - d) * |[p3,p4]|))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((1 - d) * p1),(- ((1 - d) * |[p3,p4]|))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 - d) * p1) + (- ((1 - d) * |[p3,p4]|)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((1 - d) * p1) - ((1 - d) * |[p3,p4]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(((1 - d) * |[p3,p4]|)) is Relation-like Function-like complex-valued set
K251(((1 - d) * p1),K280(((1 - d) * |[p3,p4]|))) is Relation-like Function-like set
(((1 - d) * p1) - ((1 - d) * |[p3,p4]|)) + (d * (p2 - |[p3,p4]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(((1 - d) * p1) - ((1 - d) * |[p3,p4]|)),(d * (p2 - |[p3,p4]|))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(((1 - d) * p1) - ((1 - d) * |[p3,p4]|)) + (d * (p2 - |[p3,p4]|)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
d * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
d * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
d * |[p3,p4]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
d * |[p3,p4]| is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(d * p2) - (d * |[p3,p4]|) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- (d * |[p3,p4]|) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- (d * |[p3,p4]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * (d * |[p3,p4]|) is Relation-like Function-like set
K214((TOP-REAL 2),(d * p2),(- (d * |[p3,p4]|))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(d * p2),(- (d * |[p3,p4]|))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(d * p2) + (- (d * |[p3,p4]|)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(d * p2) - (d * |[p3,p4]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280((d * |[p3,p4]|)) is Relation-like Function-like complex-valued set
K251((d * p2),K280((d * |[p3,p4]|))) is Relation-like Function-like set
(((1 - d) * p1) - ((1 - d) * |[p3,p4]|)) + ((d * p2) - (d * |[p3,p4]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(((1 - d) * p1) - ((1 - d) * |[p3,p4]|)),((d * p2) - (d * |[p3,p4]|))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(((1 - d) * p1) - ((1 - d) * |[p3,p4]|)) + ((d * p2) - (d * |[p3,p4]|)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
- (1 - d) is complex real ext-real Element of REAL
(- (1 - d)) * |[p3,p4]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(- (1 - d)) * |[p3,p4]| is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((1 - d) * p1) + ((- (1 - d)) * |[p3,p4]|) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((1 - d) * p1),((- (1 - d)) * |[p3,p4]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 - d) * p1) + ((- (1 - d)) * |[p3,p4]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(((1 - d) * p1) + ((- (1 - d)) * |[p3,p4]|)) + ((d * p2) - (d * |[p3,p4]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(((1 - d) * p1) + ((- (1 - d)) * |[p3,p4]|)),((d * p2) - (d * |[p3,p4]|))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(((1 - d) * p1) + ((- (1 - d)) * |[p3,p4]|)) + ((d * p2) - (d * |[p3,p4]|)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) + d is complex real ext-real Element of REAL
((- 1) + d) * |[p3,p4]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((- 1) + d) * |[p3,p4]| is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((1 - d) * p1) + (((- 1) + d) * |[p3,p4]|) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((1 - d) * p1),(((- 1) + d) * |[p3,p4]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 - d) * p1) + (((- 1) + d) * |[p3,p4]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(((1 - d) * p1) + (((- 1) + d) * |[p3,p4]|)) + ((d * p2) - (d * |[p3,p4]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(((1 - d) * p1) + (((- 1) + d) * |[p3,p4]|)),((d * p2) - (d * |[p3,p4]|))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(((1 - d) * p1) + (((- 1) + d) * |[p3,p4]|)) + ((d * p2) - (d * |[p3,p4]|)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * |[p3,p4]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(- 1) * |[p3,p4]| is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((- 1) * |[p3,p4]|) + (d * |[p3,p4]|) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((- 1) * |[p3,p4]|),(d * |[p3,p4]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((- 1) * |[p3,p4]|) + (d * |[p3,p4]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((1 - d) * p1) + (((- 1) * |[p3,p4]|) + (d * |[p3,p4]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((1 - d) * p1),(((- 1) * |[p3,p4]|) + (d * |[p3,p4]|))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 - d) * p1) + (((- 1) * |[p3,p4]|) + (d * |[p3,p4]|)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(((1 - d) * p1) + (((- 1) * |[p3,p4]|) + (d * |[p3,p4]|))) + ((d * p2) - (d * |[p3,p4]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(((1 - d) * p1) + (((- 1) * |[p3,p4]|) + (d * |[p3,p4]|))),((d * p2) - (d * |[p3,p4]|))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(((1 - d) * p1) + (((- 1) * |[p3,p4]|) + (d * |[p3,p4]|))) + ((d * p2) - (d * |[p3,p4]|)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((1 - d) * p1) + ((- 1) * |[p3,p4]|) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((1 - d) * p1),((- 1) * |[p3,p4]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 - d) * p1) + ((- 1) * |[p3,p4]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(((1 - d) * p1) + ((- 1) * |[p3,p4]|)) + (d * |[p3,p4]|) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(((1 - d) * p1) + ((- 1) * |[p3,p4]|)),(d * |[p3,p4]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(((1 - d) * p1) + ((- 1) * |[p3,p4]|)) + (d * |[p3,p4]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(d * p2) + (- (d * |[p3,p4]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((((1 - d) * p1) + ((- 1) * |[p3,p4]|)) + (d * |[p3,p4]|)) + ((d * p2) + (- (d * |[p3,p4]|))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((((1 - d) * p1) + ((- 1) * |[p3,p4]|)) + (d * |[p3,p4]|)),((d * p2) + (- (d * |[p3,p4]|)))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((((1 - d) * p1) + ((- 1) * |[p3,p4]|)) + (d * |[p3,p4]|)) + ((d * p2) + (- (d * |[p3,p4]|))) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(d * |[p3,p4]|) + ((d * p2) + (- (d * |[p3,p4]|))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(d * |[p3,p4]|),((d * p2) + (- (d * |[p3,p4]|)))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(d * |[p3,p4]|) + ((d * p2) + (- (d * |[p3,p4]|))) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(((1 - d) * p1) + ((- 1) * |[p3,p4]|)) + ((d * |[p3,p4]|) + ((d * p2) + (- (d * |[p3,p4]|)))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(((1 - d) * p1) + ((- 1) * |[p3,p4]|)),((d * |[p3,p4]|) + ((d * p2) + (- (d * |[p3,p4]|))))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(((1 - d) * p1) + ((- 1) * |[p3,p4]|)) + ((d * |[p3,p4]|) + ((d * p2) + (- (d * |[p3,p4]|)))) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(d * |[p3,p4]|) + (- (d * |[p3,p4]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(d * |[p3,p4]|),(- (d * |[p3,p4]|))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(d * |[p3,p4]|) + (- (d * |[p3,p4]|)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((d * |[p3,p4]|) + (- (d * |[p3,p4]|))) + (d * p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((d * |[p3,p4]|) + (- (d * |[p3,p4]|))),(d * p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((d * |[p3,p4]|) + (- (d * |[p3,p4]|))) + (d * p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(((1 - d) * p1) + ((- 1) * |[p3,p4]|)) + (((d * |[p3,p4]|) + (- (d * |[p3,p4]|))) + (d * p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(((1 - d) * p1) + ((- 1) * |[p3,p4]|)),(((d * |[p3,p4]|) + (- (d * |[p3,p4]|))) + (d * p2))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(((1 - d) * p1) + ((- 1) * |[p3,p4]|)) + (((d * |[p3,p4]|) + (- (d * |[p3,p4]|))) + (d * p2)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
- d is complex real ext-real Element of REAL
(- d) * |[p3,p4]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(- d) * |[p3,p4]| is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(d * |[p3,p4]|) + ((- d) * |[p3,p4]|) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(d * |[p3,p4]|),((- d) * |[p3,p4]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(d * |[p3,p4]|) + ((- d) * |[p3,p4]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((d * |[p3,p4]|) + ((- d) * |[p3,p4]|)) + (d * p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((d * |[p3,p4]|) + ((- d) * |[p3,p4]|)),(d * p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((d * |[p3,p4]|) + ((- d) * |[p3,p4]|)) + (d * p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(((1 - d) * p1) + ((- 1) * |[p3,p4]|)) + (((d * |[p3,p4]|) + ((- d) * |[p3,p4]|)) + (d * p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(((1 - d) * p1) + ((- 1) * |[p3,p4]|)),(((d * |[p3,p4]|) + ((- d) * |[p3,p4]|)) + (d * p2))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(((1 - d) * p1) + ((- 1) * |[p3,p4]|)) + (((d * |[p3,p4]|) + ((- d) * |[p3,p4]|)) + (d * p2)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
d + (- d) is complex real ext-real Element of REAL
(d + (- d)) * |[p3,p4]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(d + (- d)) * |[p3,p4]| is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((d + (- d)) * |[p3,p4]|) + (d * p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((d + (- d)) * |[p3,p4]|),(d * p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((d + (- d)) * |[p3,p4]|) + (d * p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(((1 - d) * p1) + ((- 1) * |[p3,p4]|)) + (((d + (- d)) * |[p3,p4]|) + (d * p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(((1 - d) * p1) + ((- 1) * |[p3,p4]|)),(((d + (- d)) * |[p3,p4]|) + (d * p2))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(((1 - d) * p1) + ((- 1) * |[p3,p4]|)) + (((d + (- d)) * |[p3,p4]|) + (d * p2)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(0. (TOP-REAL 2)) + (d * p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(0. (TOP-REAL 2)),(d * p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(0. (TOP-REAL 2)) + (d * p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(((1 - d) * p1) + ((- 1) * |[p3,p4]|)) + ((0. (TOP-REAL 2)) + (d * p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(((1 - d) * p1) + ((- 1) * |[p3,p4]|)),((0. (TOP-REAL 2)) + (d * p2))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(((1 - d) * p1) + ((- 1) * |[p3,p4]|)) + ((0. (TOP-REAL 2)) + (d * p2)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(((1 - d) * p1) + ((- 1) * |[p3,p4]|)) + (d * p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(((1 - d) * p1) + ((- 1) * |[p3,p4]|)),(d * p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(((1 - d) * p1) + ((- 1) * |[p3,p4]|)) + (d * p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((1 - d) * p1) + (d * p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((1 - d) * p1),(d * p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 - d) * p1) + (d * p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(((1 - d) * p1) + (d * p2)) + ((- 1) * |[p3,p4]|) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(((1 - d) * p1) + (d * p2)),((- 1) * |[p3,p4]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(((1 - d) * p1) + (d * p2)) + ((- 1) * |[p3,p4]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((((1 - d) * p1) + (d * p2)) + ((- 1) * |[p3,p4]|)) + |[p3,p4]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((((1 - d) * p1) + (d * p2)) + ((- 1) * |[p3,p4]|)),|[p3,p4]|) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((((1 - d) * p1) + (d * p2)) + ((- 1) * |[p3,p4]|)) + |[p3,p4]| is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(((1 - d) * p1) + (d * p2)) + (- |[p3,p4]|) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(((1 - d) * p1) + (d * p2)),(- |[p3,p4]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(((1 - d) * p1) + (d * p2)) + (- |[p3,p4]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((((1 - d) * p1) + (d * p2)) + (- |[p3,p4]|)) + |[p3,p4]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((((1 - d) * p1) + (d * p2)) + (- |[p3,p4]|)),|[p3,p4]|) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((((1 - d) * p1) + (d * p2)) + (- |[p3,p4]|)) + |[p3,p4]| is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- |[p3,p4]|) + |[p3,p4]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(- |[p3,p4]|),|[p3,p4]|) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(- |[p3,p4]|) + |[p3,p4]| is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(((1 - d) * p1) + (d * p2)) + ((- |[p3,p4]|) + |[p3,p4]|) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(((1 - d) * p1) + (d * p2)),((- |[p3,p4]|) + |[p3,p4]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(((1 - d) * p1) + (d * p2)) + ((- |[p3,p4]|) + |[p3,p4]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(((1 - d) * p1) + (d * p2)) + (0. (TOP-REAL 2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(((1 - d) * p1) + (d * p2)),(0. (TOP-REAL 2))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(((1 - d) * p1) + (d * p2)) + (0. (TOP-REAL 2)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
f6 + (0. (TOP-REAL 2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),f6,(0. (TOP-REAL 2))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
f6 + (0. (TOP-REAL 2)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
|.(f6 + (0. (TOP-REAL 2))).| is complex real ext-real non negative Element of REAL
sqr (f6 + (0. (TOP-REAL 2))) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((f6 + (0. (TOP-REAL 2))),(f6 + (0. (TOP-REAL 2)))) is Relation-like Function-like set
K339((sqr (f6 + (0. (TOP-REAL 2))))) is complex real ext-real Element of REAL
sqrt K339((sqr (f6 + (0. (TOP-REAL 2))))) is complex real ext-real Element of REAL
|[p3,p4]| - |[p3,p4]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),|[p3,p4]|,(- |[p3,p4]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),|[p3,p4]|,(- |[p3,p4]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
|[p3,p4]| + (- |[p3,p4]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
|[p3,p4]| - |[p3,p4]| is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(|[p3,p4]|,K280(|[p3,p4]|)) is Relation-like Function-like set
f6 + (|[p3,p4]| - |[p3,p4]|) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),f6,(|[p3,p4]| - |[p3,p4]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
f6 + (|[p3,p4]| - |[p3,p4]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
|.(f6 + (|[p3,p4]| - |[p3,p4]|)).| is complex real ext-real non negative Element of REAL
sqr (f6 + (|[p3,p4]| - |[p3,p4]|)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((f6 + (|[p3,p4]| - |[p3,p4]|)),(f6 + (|[p3,p4]| - |[p3,p4]|))) is Relation-like Function-like set
K339((sqr (f6 + (|[p3,p4]| - |[p3,p4]|)))) is complex real ext-real Element of REAL
sqrt K339((sqr (f6 + (|[p3,p4]| - |[p3,p4]|)))) is complex real ext-real Element of REAL
(f6 + |[p3,p4]|) + (- |[p3,p4]|) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(f6 + |[p3,p4]|),(- |[p3,p4]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(f6 + |[p3,p4]|) + (- |[p3,p4]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
|.((f6 + |[p3,p4]|) + (- |[p3,p4]|)).| is complex real ext-real non negative Element of REAL
sqr ((f6 + |[p3,p4]|) + (- |[p3,p4]|)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt (((f6 + |[p3,p4]|) + (- |[p3,p4]|)),((f6 + |[p3,p4]|) + (- |[p3,p4]|))) is Relation-like Function-like set
K339((sqr ((f6 + |[p3,p4]|) + (- |[p3,p4]|)))) is complex real ext-real Element of REAL
sqrt K339((sqr ((f6 + |[p3,p4]|) + (- |[p3,p4]|)))) is complex real ext-real Element of REAL
(f6 + |[p3,p4]|) - |[p3,p4]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),(f6 + |[p3,p4]|),(- |[p3,p4]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(f6 + |[p3,p4]|) - |[p3,p4]| is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251((f6 + |[p3,p4]|),K280(|[p3,p4]|)) is Relation-like Function-like set
|.((f6 + |[p3,p4]|) - |[p3,p4]|).| is complex real ext-real non negative Element of REAL
sqr ((f6 + |[p3,p4]|) - |[p3,p4]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt (((f6 + |[p3,p4]|) - |[p3,p4]|),((f6 + |[p3,p4]|) - |[p3,p4]|)) is Relation-like Function-like set
K339((sqr ((f6 + |[p3,p4]|) - |[p3,p4]|))) is complex real ext-real Element of REAL
sqrt K339((sqr ((f6 + |[p3,p4]|) - |[p3,p4]|))) is complex real ext-real Element of REAL
{ b1 where b1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2) : |.(b1 - |[p3,p4]|).| = p } is set
f22 is ext-real Element of ExtREAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p1,p2,p3) is complex real ext-real Element of REAL
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx p2),(euc2cpx p3)) is complex real ext-real set
LSeg (p1,p3) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p1) + (b1 * p3)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
p2 - p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p1 is Relation-like Function-like set
K214((TOP-REAL 2),p2,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p1) is Relation-like Function-like complex-valued set
K251(p2,K280(p1)) is Relation-like Function-like set
|.(p2 - p1).| is complex real ext-real non negative Element of REAL
sqr (p2 - p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p2 - p1),(p2 - p1)) is Relation-like Function-like set
K339((sqr (p2 - p1))) is complex real ext-real Element of REAL
sqrt K339((sqr (p2 - p1))) is complex real ext-real Element of REAL
|[(p1 `1),(p1 `2)]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 - p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p3,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p3,K280(p1)) is Relation-like Function-like set
|.(p3 - p1).| is complex real ext-real non negative Element of REAL
sqr (p3 - p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p3 - p1),(p3 - p1)) is Relation-like Function-like set
K339((sqr (p3 - p1))) is complex real ext-real Element of REAL
sqrt K339((sqr (p3 - p1))) is complex real ext-real Element of REAL
|.(p3 - p1).| ^2 is complex real ext-real Element of REAL
|.(p3 - p1).| * |.(p3 - p1).| is complex real ext-real non negative set
p1 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p2 is Relation-like Function-like set
K214((TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p2) is Relation-like Function-like complex-valued set
K251(p1,K280(p2)) is Relation-like Function-like set
|.(p1 - p2).| is complex real ext-real non negative Element of REAL
sqr (p1 - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p1 - p2),(p1 - p2)) is Relation-like Function-like set
K339((sqr (p1 - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr (p1 - p2))) is complex real ext-real Element of REAL
|.(p1 - p2).| ^2 is complex real ext-real Element of REAL
|.(p1 - p2).| * |.(p1 - p2).| is complex real ext-real non negative set
p3 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p3,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p3,K280(p2)) is Relation-like Function-like set
|.(p3 - p2).| is complex real ext-real non negative Element of REAL
sqr (p3 - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p3 - p2),(p3 - p2)) is Relation-like Function-like set
K339((sqr (p3 - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr (p3 - p2))) is complex real ext-real Element of REAL
|.(p3 - p2).| ^2 is complex real ext-real Element of REAL
|.(p3 - p2).| * |.(p3 - p2).| is complex real ext-real non negative set
(|.(p1 - p2).| ^2) + (|.(p3 - p2).| ^2) is complex real ext-real Element of REAL
2 * |.(p1 - p2).| is complex real ext-real non negative Element of REAL
(2 * |.(p1 - p2).|) * |.(p3 - p2).| is complex real ext-real non negative Element of REAL
((2 * |.(p1 - p2).|) * |.(p3 - p2).|) * (- 1) is complex real ext-real non positive Element of REAL
((|.(p1 - p2).| ^2) + (|.(p3 - p2).| ^2)) - (((2 * |.(p1 - p2).|) * |.(p3 - p2).|) * (- 1)) is complex real ext-real Element of REAL
|.(p1 - p2).| + |.(p3 - p2).| is complex real ext-real non negative Element of REAL
(|.(p1 - p2).| + |.(p3 - p2).|) ^2 is complex real ext-real Element of REAL
(|.(p1 - p2).| + |.(p3 - p2).|) * (|.(p1 - p2).| + |.(p3 - p2).|) is complex real ext-real non negative set
|.(p2 - p1).| ^2 is complex real ext-real Element of REAL
|.(p2 - p1).| * |.(p2 - p1).| is complex real ext-real non negative set
|.(p2 - p1).| + |.(p3 - p2).| is complex real ext-real non negative Element of REAL
(|.(p2 - p1).| + |.(p3 - p2).|) ^2 is complex real ext-real Element of REAL
(|.(p2 - p1).| + |.(p3 - p2).|) * (|.(p2 - p1).| + |.(p3 - p2).|) is complex real ext-real non negative set
2 * |.(p2 - p1).| is complex real ext-real non negative Element of REAL
(2 * |.(p2 - p1).|) * |.(p3 - p2).| is complex real ext-real non negative Element of REAL
(|.(p2 - p1).| ^2) + ((2 * |.(p2 - p1).|) * |.(p3 - p2).|) is complex real ext-real Element of REAL
((|.(p2 - p1).| ^2) + ((2 * |.(p2 - p1).|) * |.(p3 - p2).|)) + (|.(p3 - p2).| ^2) is complex real ext-real Element of REAL
(((|.(p2 - p1).| ^2) + ((2 * |.(p2 - p1).|) * |.(p3 - p2).|)) + (|.(p3 - p2).| ^2)) - (|.(p2 - p1).| ^2) is complex real ext-real Element of REAL
(|.(p2 - p1).| ^2) - (|.(p2 - p1).| ^2) is complex real ext-real Element of REAL
(2 * |.(p2 - p1).|) + |.(p3 - p2).| is complex real ext-real non negative Element of REAL
((2 * |.(p2 - p1).|) + |.(p3 - p2).|) * |.(p3 - p2).| is complex real ext-real non negative Element of REAL
{ b1 where b1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2) : not |.(b1 - |[(p1 `1),(p1 `2)]|).| <= |.(p2 - p1).| } is set
outside_of_circle ((p1 `1),(p1 `2),|.(p2 - p1).|) is Element of bool the carrier of (TOP-REAL 2)
p1 - |[(p1 `1),(p1 `2)]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- |[(p1 `1),(p1 `2)]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- |[(p1 `1),(p1 `2)]| is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * |[(p1 `1),(p1 `2)]| is Relation-like Function-like set
K214((TOP-REAL 2),p1,(- |[(p1 `1),(p1 `2)]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- |[(p1 `1),(p1 `2)]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- |[(p1 `1),(p1 `2)]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - |[(p1 `1),(p1 `2)]| is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(|[(p1 `1),(p1 `2)]|) is Relation-like Function-like complex-valued set
K251(p1,K280(|[(p1 `1),(p1 `2)]|)) is Relation-like Function-like set
|.(p1 - |[(p1 `1),(p1 `2)]|).| is complex real ext-real non negative Element of REAL
sqr (p1 - |[(p1 `1),(p1 `2)]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p1 - |[(p1 `1),(p1 `2)]|),(p1 - |[(p1 `1),(p1 `2)]|)) is Relation-like Function-like set
K339((sqr (p1 - |[(p1 `1),(p1 `2)]|))) is complex real ext-real Element of REAL
sqrt K339((sqr (p1 - |[(p1 `1),(p1 `2)]|))) is complex real ext-real Element of REAL
{ b1 where b1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2) : not |.(p2 - p1).| <= |.(b1 - |[(p1 `1),(p1 `2)]|).| } is set
inside_of_circle ((p1 `1),(p1 `2),|.(p2 - p1).|) is Element of bool the carrier of (TOP-REAL 2)
circle ((p1 `1),(p1 `2),|.(p2 - p1).|) is Element of bool the carrier of (TOP-REAL 2)
(LSeg (p1,p3)) /\ (circle ((p1 `1),(p1 `2),|.(p2 - p1).|)) is Element of bool the carrier of (TOP-REAL 2)
b is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p2,p1,p3) is complex real ext-real Element of REAL
angle ((euc2cpx p2),(euc2cpx p1),(euc2cpx p3)) is complex real ext-real set
angle (p1,p3,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p1),(euc2cpx p3),(euc2cpx p2)) is complex real ext-real set
(angle (p2,p1,p3)) + (angle (p1,p3,p2)) is complex real ext-real Element of REAL
angle (p3,p2,p1) is complex real ext-real Element of REAL
angle ((euc2cpx p3),(euc2cpx p2),(euc2cpx p1)) is complex real ext-real set
((angle (p2,p1,p3)) + (angle (p1,p3,p2))) + (angle (p3,p2,p1)) is complex real ext-real Element of REAL
((angle (p2,p1,p3)) + (angle (p1,p3,p2))) + PI is complex real ext-real Element of REAL
angle (p1,p3,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p1),(euc2cpx p3),(euc2cpx p2)) is complex real ext-real set
(angle (p2,p1,p3)) + (angle (p1,p3,p2)) is complex real ext-real Element of REAL
angle (p3,p2,p1) is complex real ext-real Element of REAL
angle ((euc2cpx p3),(euc2cpx p2),(euc2cpx p1)) is complex real ext-real set
((angle (p2,p1,p3)) + (angle (p1,p3,p2))) + (angle (p3,p2,p1)) is complex real ext-real Element of REAL
(2 * PI) + (2 * PI) is non empty complex real ext-real positive non negative Element of REAL
((angle (p2,p1,p3)) + (angle (p1,p3,p2))) + PI is complex real ext-real Element of REAL
angle (p1,p3,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p1),(euc2cpx p3),(euc2cpx p2)) is complex real ext-real set
(angle (p2,p1,p3)) + (angle (p1,p3,p2)) is complex real ext-real Element of REAL
angle (p3,p2,p1) is complex real ext-real Element of REAL
angle ((euc2cpx p3),(euc2cpx p2),(euc2cpx p1)) is complex real ext-real set
((angle (p2,p1,p3)) + (angle (p1,p3,p2))) + (angle (p3,p2,p1)) is complex real ext-real Element of REAL
{ b1 where b1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2) : |.(b1 - |[(p1 `1),(p1 `2)]|).| = |.(p2 - p1).| } is set
b - p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),b,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),b,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
b + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
b - p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(b,K280(p1)) is Relation-like Function-like set
|.(b - p1).| is complex real ext-real non negative Element of REAL
sqr (b - p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((b - p1),(b - p1)) is Relation-like Function-like set
K339((sqr (b - p1))) is complex real ext-real Element of REAL
sqrt K339((sqr (b - p1))) is complex real ext-real Element of REAL
r is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
r - |[(p1 `1),(p1 `2)]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),r,(- |[(p1 `1),(p1 `2)]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),r,(- |[(p1 `1),(p1 `2)]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
r + (- |[(p1 `1),(p1 `2)]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
r - |[(p1 `1),(p1 `2)]| is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(r,K280(|[(p1 `1),(p1 `2)]|)) is Relation-like Function-like set
|.(r - |[(p1 `1),(p1 `2)]|).| is complex real ext-real non negative Element of REAL
sqr (r - |[(p1 `1),(p1 `2)]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((r - |[(p1 `1),(p1 `2)]|),(r - |[(p1 `1),(p1 `2)]|)) is Relation-like Function-like set
K339((sqr (r - |[(p1 `1),(p1 `2)]|))) is complex real ext-real Element of REAL
sqrt K339((sqr (r - |[(p1 `1),(p1 `2)]|))) is complex real ext-real Element of REAL
r is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
r - |[(p1 `1),(p1 `2)]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),r,(- |[(p1 `1),(p1 `2)]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),r,(- |[(p1 `1),(p1 `2)]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
r + (- |[(p1 `1),(p1 `2)]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
r - |[(p1 `1),(p1 `2)]| is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(r,K280(|[(p1 `1),(p1 `2)]|)) is Relation-like Function-like set
|.(r - |[(p1 `1),(p1 `2)]|).| is complex real ext-real non negative Element of REAL
sqr (r - |[(p1 `1),(p1 `2)]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((r - |[(p1 `1),(p1 `2)]|),(r - |[(p1 `1),(p1 `2)]|)) is Relation-like Function-like set
K339((sqr (r - |[(p1 `1),(p1 `2)]|))) is complex real ext-real Element of REAL
sqrt K339((sqr (r - |[(p1 `1),(p1 `2)]|))) is complex real ext-real Element of REAL
b - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),b,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),b,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
b + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
b - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(b,K280(p2)) is Relation-like Function-like set
|.(b - p2).| is complex real ext-real non negative Element of REAL
sqr (b - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((b - p2),(b - p2)) is Relation-like Function-like set
K339((sqr (b - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr (b - p2))) is complex real ext-real Element of REAL
|.(b - p2).| ^2 is complex real ext-real Element of REAL
|.(b - p2).| * |.(b - p2).| is complex real ext-real non negative set
|.(p2 - p1).| ^2 is complex real ext-real Element of REAL
|.(p2 - p1).| * |.(p2 - p1).| is complex real ext-real non negative set
|.(b - p1).| ^2 is complex real ext-real Element of REAL
|.(b - p1).| * |.(b - p1).| is complex real ext-real non negative set
(|.(p2 - p1).| ^2) + (|.(b - p1).| ^2) is complex real ext-real Element of REAL
2 * |.(p2 - p1).| is complex real ext-real non negative Element of REAL
(2 * |.(p2 - p1).|) * |.(b - p1).| is complex real ext-real non negative Element of REAL
angle (p2,p1,b) is complex real ext-real Element of REAL
euc2cpx b is complex Element of COMPLEX
b `1 is complex real ext-real Element of REAL
K367(b,1) is complex real ext-real Element of REAL
b `2 is complex real ext-real Element of REAL
K367(b,2) is complex real ext-real Element of REAL
(b `2) * <i> is complex set
(b `1) + ((b `2) * <i>) is complex set
angle ((euc2cpx p2),(euc2cpx p1),(euc2cpx b)) is complex real ext-real set
cos (angle (p2,p1,b)) is complex real ext-real Element of REAL
((2 * |.(p2 - p1).|) * |.(b - p1).|) * (cos (angle (p2,p1,b))) is complex real ext-real Element of REAL
((|.(p2 - p1).| ^2) + (|.(b - p1).| ^2)) - (((2 * |.(p2 - p1).|) * |.(b - p1).|) * (cos (angle (p2,p1,b)))) is complex real ext-real Element of REAL
(|.(p2 - p1).| ^2) + (|.(p2 - p1).| ^2) is complex real ext-real Element of REAL
(2 * |.(p2 - p1).|) * |.(p2 - p1).| is complex real ext-real non negative Element of REAL
((2 * |.(p2 - p1).|) * |.(p2 - p1).|) * (cos 0) is complex real ext-real Element of REAL
((|.(p2 - p1).| ^2) + (|.(p2 - p1).| ^2)) - (((2 * |.(p2 - p1).|) * |.(p2 - p1).|) * (cos 0)) is complex real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
LSeg (p2,p3) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p2) + (b1 * p3)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
LSeg (p2,p4) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p2) + (b1 * p4)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
p is complex real ext-real Element of REAL
1 - p is complex real ext-real Element of REAL
(1 - p) * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 - p) * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p * p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p * p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((1 - p) * p2) + (p * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((1 - p) * p2),(p * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 - p) * p2) + (p * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
a is complex real ext-real Element of REAL
1 - a is complex real ext-real Element of REAL
(1 - a) * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 - a) * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
a * p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
a * p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((1 - a) * p2) + (a * p4) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((1 - a) * p2),(a * p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 - a) * p2) + (a * p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
- p is complex real ext-real Element of REAL
1 + (- p) is complex real ext-real Element of REAL
(1 + (- p)) * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 + (- p)) * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((1 + (- p)) * p2) + (p * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((1 + (- p)) * p2),(p * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 + (- p)) * p2) + (p * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
- a is complex real ext-real Element of REAL
1 + (- a) is complex real ext-real Element of REAL
(1 + (- a)) * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 + (- a)) * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((1 + (- a)) * p2) + (a * p4) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((1 + (- a)) * p2),(a * p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 + (- a)) * p2) + (a * p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
1 * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
1 * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- p) * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(- p) * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1 * p2) + ((- p) * p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(1 * p2),((- p) * p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 * p2) + ((- p) * p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((1 * p2) + ((- p) * p2)) + (p * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((1 * p2) + ((- p) * p2)),(p * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 * p2) + ((- p) * p2)) + (p * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- a) * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(- a) * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1 * p2) + ((- a) * p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(1 * p2),((- a) * p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 * p2) + ((- a) * p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((1 * p2) + ((- a) * p2)) + (a * p4) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((1 * p2) + ((- a) * p2)),(a * p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 * p2) + ((- a) * p2)) + (a * p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 + ((- p) * p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,((- p) * p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + ((- p) * p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(p2 + ((- p) * p2)) + (p * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(p2 + ((- p) * p2)),(p * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(p2 + ((- p) * p2)) + (p * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 + ((- a) * p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,((- a) * p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + ((- a) * p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(p2 + ((- a) * p2)) + (a * p4) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(p2 + ((- a) * p2)),(a * p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(p2 + ((- a) * p2)) + (a * p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
- p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p2 is Relation-like Function-like set
((- p) * p2) + (p * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((- p) * p2),(p * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((- p) * p2) + (p * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 + (((- p) * p2) + (p * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(((- p) * p2) + (p * p3))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (((- p) * p2) + (p * p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- p2) + (p2 + (((- p) * p2) + (p * p3))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(- p2),(p2 + (((- p) * p2) + (p * p3)))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(- p2) + (p2 + (((- p) * p2) + (p * p3))) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- p2) + ((p2 + ((- a) * p2)) + (a * p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(- p2),((p2 + ((- a) * p2)) + (a * p4))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(- p2) + ((p2 + ((- a) * p2)) + (a * p4)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- p2) + p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(- p2),p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(- p2) + p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((- p2) + p2) + (((- p) * p2) + (p * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((- p2) + p2),(((- p) * p2) + (p * p3))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((- p2) + p2) + (((- p) * p2) + (p * p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(0. (TOP-REAL 2)) + (((- p) * p2) + (p * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(0. (TOP-REAL 2)),(((- p) * p2) + (p * p3))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(0. (TOP-REAL 2)) + (((- p) * p2) + (p * p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((- a) * p2) + (a * p4) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((- a) * p2),(a * p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((- a) * p2) + (a * p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 + (((- a) * p2) + (a * p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(((- a) * p2) + (a * p4))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (((- a) * p2) + (a * p4)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- p2) + (p2 + (((- a) * p2) + (a * p4))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(- p2),(p2 + (((- a) * p2) + (a * p4)))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(- p2) + (p2 + (((- a) * p2) + (a * p4))) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((- p2) + p2) + (((- a) * p2) + (a * p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((- p2) + p2),(((- a) * p2) + (a * p4))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((- p2) + p2) + (((- a) * p2) + (a * p4)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(0. (TOP-REAL 2)) + (((- a) * p2) + (a * p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(0. (TOP-REAL 2)),(((- a) * p2) + (a * p4))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(0. (TOP-REAL 2)) + (((- a) * p2) + (a * p4)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
1 / a is complex real ext-real Element of REAL
(1 / a) * ((- p) * p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 / a) * ((- p) * p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1 / a) * (p * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 / a) * (p * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((1 / a) * ((- p) * p2)) + ((1 / a) * (p * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((1 / a) * ((- p) * p2)),((1 / a) * (p * p3))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 / a) * ((- p) * p2)) + ((1 / a) * (p * p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1 / a) * (((- a) * p2) + (a * p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 / a) * (((- a) * p2) + (a * p4)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1 / a) * (- p) is complex real ext-real Element of REAL
((1 / a) * (- p)) * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 / a) * (- p)) * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(((1 / a) * (- p)) * p2) + ((1 / a) * (p * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(((1 / a) * (- p)) * p2),((1 / a) * (p * p3))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(((1 / a) * (- p)) * p2) + ((1 / a) * (p * p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1 / a) * p is complex real ext-real Element of REAL
(- 1) * ((1 / a) * p) is complex real ext-real Element of REAL
((- 1) * ((1 / a) * p)) * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((- 1) * ((1 / a) * p)) * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((1 / a) * p) * p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 / a) * p) * p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(((- 1) * ((1 / a) * p)) * p2) + (((1 / a) * p) * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(((- 1) * ((1 / a) * p)) * p2),(((1 / a) * p) * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(((- 1) * ((1 / a) * p)) * p2) + (((1 / a) * p) * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p / a is complex real ext-real Element of REAL
(p / a) * 1 is complex real ext-real Element of REAL
(- 1) * ((p / a) * 1) is complex real ext-real Element of REAL
((- 1) * ((p / a) * 1)) * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((- 1) * ((p / a) * 1)) * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(((- 1) * ((p / a) * 1)) * p2) + (((1 / a) * p) * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(((- 1) * ((p / a) * 1)) * p2),(((1 / a) * p) * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(((- 1) * ((p / a) * 1)) * p2) + (((1 / a) * p) * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
- (p / a) is complex real ext-real Element of REAL
(- (p / a)) * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(- (p / a)) * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((p / a) * 1) * p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((p / a) * 1) * p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((- (p / a)) * p2) + (((p / a) * 1) * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((- (p / a)) * p2),(((p / a) * 1) * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((- (p / a)) * p2) + (((p / a) * 1) * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(p / a) * p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(p / a) * p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((- (p / a)) * p2) + ((p / a) * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((- (p / a)) * p2),((p / a) * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((- (p / a)) * p2) + ((p / a) * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1 / a) * ((- a) * p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 / a) * ((- a) * p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1 / a) * (a * p4) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 / a) * (a * p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((1 / a) * ((- a) * p2)) + ((1 / a) * (a * p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((1 / a) * ((- a) * p2)),((1 / a) * (a * p4))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 / a) * ((- a) * p2)) + ((1 / a) * (a * p4)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1 / a) * (- a) is complex real ext-real Element of REAL
((1 / a) * (- a)) * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 / a) * (- a)) * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(((1 / a) * (- a)) * p2) + ((1 / a) * (a * p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(((1 / a) * (- a)) * p2),((1 / a) * (a * p4))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(((1 / a) * (- a)) * p2) + ((1 / a) * (a * p4)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1 / a) * a is complex real ext-real Element of REAL
(- 1) * ((1 / a) * a) is complex real ext-real Element of REAL
((- 1) * ((1 / a) * a)) * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((- 1) * ((1 / a) * a)) * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((1 / a) * a) * p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 / a) * a) * p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(((- 1) * ((1 / a) * a)) * p2) + (((1 / a) * a) * p4) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(((- 1) * ((1 / a) * a)) * p2),(((1 / a) * a) * p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(((- 1) * ((1 / a) * a)) * p2) + (((1 / a) * a) * p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
a / a is complex real ext-real Element of REAL
(a / a) * 1 is complex real ext-real Element of REAL
(- 1) * ((a / a) * 1) is complex real ext-real Element of REAL
((- 1) * ((a / a) * 1)) * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((- 1) * ((a / a) * 1)) * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(((- 1) * ((a / a) * 1)) * p2) + (((1 / a) * a) * p4) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(((- 1) * ((a / a) * 1)) * p2),(((1 / a) * a) * p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(((- 1) * ((a / a) * 1)) * p2) + (((1 / a) * a) * p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * (a / a) is complex real ext-real Element of REAL
((- 1) * (a / a)) * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((- 1) * (a / a)) * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((a / a) * 1) * p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((a / a) * 1) * p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(((- 1) * (a / a)) * p2) + (((a / a) * 1) * p4) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(((- 1) * (a / a)) * p2),(((a / a) * 1) * p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(((- 1) * (a / a)) * p2) + (((a / a) * 1) * p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * 1 is non empty complex real ext-real non positive negative Element of REAL
((- 1) * 1) * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((- 1) * 1) * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(a / a) * p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(a / a) * p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(((- 1) * 1) * p2) + ((a / a) * p4) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(((- 1) * 1) * p2),((a / a) * p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(((- 1) * 1) * p2) + ((a / a) * p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(- 1) * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
1 * p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
1 * p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((- 1) * p2) + (1 * p4) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((- 1) * p2),(1 * p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((- 1) * p2) + (1 * p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- p2) + (1 * p4) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(- p2),(1 * p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(- p2) + (1 * p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p4 + (- p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p4,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p4 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p4 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p4,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p4 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p2) is Relation-like Function-like complex-valued set
K251(p4,K280(p2)) is Relation-like Function-like set
(p4 - p2) + p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(p4 - p2),p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(p4 - p2) + p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 + ((- (p / a)) * p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,((- (p / a)) * p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + ((- (p / a)) * p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(p2 + ((- (p / a)) * p2)) + ((p / a) * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(p2 + ((- (p / a)) * p2)),((p / a) * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(p2 + ((- (p / a)) * p2)) + ((p / a) * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1 * p2) + ((- (p / a)) * p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(1 * p2),((- (p / a)) * p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 * p2) + ((- (p / a)) * p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((1 * p2) + ((- (p / a)) * p2)) + ((p / a) * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((1 * p2) + ((- (p / a)) * p2)),((p / a) * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 * p2) + ((- (p / a)) * p2)) + ((p / a) * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
1 + (- (p / a)) is complex real ext-real Element of REAL
(1 + (- (p / a))) * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 + (- (p / a))) * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((1 + (- (p / a))) * p2) + ((p / a) * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((1 + (- (p / a))) * p2),((p / a) * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 + (- (p / a))) * p2) + ((p / a) * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
1 - (p / a) is complex real ext-real Element of REAL
(1 - (p / a)) * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 - (p / a)) * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((1 - (p / a)) * p2) + ((p / a) * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((1 - (p / a)) * p2),((p / a) * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 - (p / a)) * p2) + ((p / a) * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(p * p2) + ((- p) * p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(p * p2),((- p) * p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(p * p2) + ((- p) * p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((p * p2) + ((- p) * p2)) + (p * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((p * p2) + ((- p) * p2)),(p * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((p * p2) + ((- p) * p2)) + (p * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p * p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p * p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((- p) * p2) + (p * p4) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((- p) * p2),(p * p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((- p) * p2) + (p * p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(p * p2) + (((- p) * p2) + (p * p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(p * p2),(((- p) * p2) + (p * p4))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(p * p2) + (((- p) * p2) + (p * p4)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p + (- p) is complex real ext-real Element of REAL
(p + (- p)) * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(p + (- p)) * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((p + (- p)) * p2) + (p * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((p + (- p)) * p2),(p * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((p + (- p)) * p2) + (p * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(0. (TOP-REAL 2)) + (p * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(0. (TOP-REAL 2)),(p * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(0. (TOP-REAL 2)) + (p * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((p * p2) + ((- p) * p2)) + (p * p4) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((p * p2) + ((- p) * p2)),(p * p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((p * p2) + ((- p) * p2)) + (p * p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((p + (- p)) * p2) + (p * p4) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((p + (- p)) * p2),(p * p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((p + (- p)) * p2) + (p * p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(0. (TOP-REAL 2)) + (p * p4) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(0. (TOP-REAL 2)),(p * p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(0. (TOP-REAL 2)) + (p * p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
0 * p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
0 * p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 + (0 * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(0 * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (0 * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 + (0. (TOP-REAL 2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(0. (TOP-REAL 2))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (0. (TOP-REAL 2)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
1 / p is complex real ext-real Element of REAL
(1 / p) * ((- p) * p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 / p) * ((- p) * p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1 / p) * (p * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 / p) * (p * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((1 / p) * ((- p) * p2)) + ((1 / p) * (p * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((1 / p) * ((- p) * p2)),((1 / p) * (p * p3))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 / p) * ((- p) * p2)) + ((1 / p) * (p * p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1 / p) * (((- a) * p2) + (a * p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 / p) * (((- a) * p2) + (a * p4)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1 / p) * (- p) is complex real ext-real Element of REAL
((1 / p) * (- p)) * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 / p) * (- p)) * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(((1 / p) * (- p)) * p2) + ((1 / p) * (p * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(((1 / p) * (- p)) * p2),((1 / p) * (p * p3))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(((1 / p) * (- p)) * p2) + ((1 / p) * (p * p3)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1 / p) * p is complex real ext-real Element of REAL
(- 1) * ((1 / p) * p) is complex real ext-real Element of REAL
((- 1) * ((1 / p) * p)) * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((- 1) * ((1 / p) * p)) * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((1 / p) * p) * p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 / p) * p) * p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(((- 1) * ((1 / p) * p)) * p2) + (((1 / p) * p) * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(((- 1) * ((1 / p) * p)) * p2),(((1 / p) * p) * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(((- 1) * ((1 / p) * p)) * p2) + (((1 / p) * p) * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p / p is complex real ext-real Element of REAL
(p / p) * 1 is complex real ext-real Element of REAL
(- 1) * ((p / p) * 1) is complex real ext-real Element of REAL
((- 1) * ((p / p) * 1)) * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((- 1) * ((p / p) * 1)) * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(((- 1) * ((p / p) * 1)) * p2) + (((1 / p) * p) * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(((- 1) * ((p / p) * 1)) * p2),(((1 / p) * p) * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(((- 1) * ((p / p) * 1)) * p2) + (((1 / p) * p) * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
- (p / p) is complex real ext-real Element of REAL
(- (p / p)) * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(- (p / p)) * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((p / p) * 1) * p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((p / p) * 1) * p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((- (p / p)) * p2) + (((p / p) * 1) * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((- (p / p)) * p2),(((p / p) * 1) * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((- (p / p)) * p2) + (((p / p) * 1) * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(- 1) * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((- 1) * p2) + (((p / p) * 1) * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((- 1) * p2),(((p / p) * 1) * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((- 1) * p2) + (((p / p) * 1) * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
1 * p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
1 * p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1 * p3) + ((- 1) * p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(1 * p3),((- 1) * p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 * p3) + ((- 1) * p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1 * p3) + (- p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(1 * p3),(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 * p3) + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 + (- p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p3,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p2) is Relation-like Function-like complex-valued set
K251(p3,K280(p2)) is Relation-like Function-like set
(1 / p) * ((- a) * p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 / p) * ((- a) * p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1 / p) * (a * p4) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 / p) * (a * p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((1 / p) * ((- a) * p2)) + ((1 / p) * (a * p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((1 / p) * ((- a) * p2)),((1 / p) * (a * p4))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 / p) * ((- a) * p2)) + ((1 / p) * (a * p4)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1 / p) * (- a) is complex real ext-real Element of REAL
((1 / p) * (- a)) * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 / p) * (- a)) * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(((1 / p) * (- a)) * p2) + ((1 / p) * (a * p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(((1 / p) * (- a)) * p2),((1 / p) * (a * p4))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(((1 / p) * (- a)) * p2) + ((1 / p) * (a * p4)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1 / p) * a is complex real ext-real Element of REAL
(- 1) * ((1 / p) * a) is complex real ext-real Element of REAL
((- 1) * ((1 / p) * a)) * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((- 1) * ((1 / p) * a)) * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((1 / p) * a) * p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 / p) * a) * p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(((- 1) * ((1 / p) * a)) * p2) + (((1 / p) * a) * p4) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(((- 1) * ((1 / p) * a)) * p2),(((1 / p) * a) * p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(((- 1) * ((1 / p) * a)) * p2) + (((1 / p) * a) * p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
a / p is complex real ext-real Element of REAL
(a / p) * 1 is complex real ext-real Element of REAL
(- 1) * ((a / p) * 1) is complex real ext-real Element of REAL
((- 1) * ((a / p) * 1)) * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((- 1) * ((a / p) * 1)) * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(((- 1) * ((a / p) * 1)) * p2) + (((1 / p) * a) * p4) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(((- 1) * ((a / p) * 1)) * p2),(((1 / p) * a) * p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(((- 1) * ((a / p) * 1)) * p2) + (((1 / p) * a) * p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(p3 - p2) + p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(p3 - p2),p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(p3 - p2) + p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
- (a / p) is complex real ext-real Element of REAL
(- (a / p)) * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(- (a / p)) * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(a / p) * p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(a / p) * p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((- (a / p)) * p2) + ((a / p) * p4) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((- (a / p)) * p2),((a / p) * p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((- (a / p)) * p2) + ((a / p) * p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(((- (a / p)) * p2) + ((a / p) * p4)) + p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(((- (a / p)) * p2) + ((a / p) * p4)),p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(((- (a / p)) * p2) + ((a / p) * p4)) + p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 + ((- (a / p)) * p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,((- (a / p)) * p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + ((- (a / p)) * p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(p2 + ((- (a / p)) * p2)) + ((a / p) * p4) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(p2 + ((- (a / p)) * p2)),((a / p) * p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(p2 + ((- (a / p)) * p2)) + ((a / p) * p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1 * p2) + ((- (a / p)) * p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(1 * p2),((- (a / p)) * p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 * p2) + ((- (a / p)) * p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((1 * p2) + ((- (a / p)) * p2)) + ((a / p) * p4) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((1 * p2) + ((- (a / p)) * p2)),((a / p) * p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 * p2) + ((- (a / p)) * p2)) + ((a / p) * p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
1 + (- (a / p)) is complex real ext-real Element of REAL
(1 + (- (a / p))) * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 + (- (a / p))) * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((1 + (- (a / p))) * p2) + ((a / p) * p4) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((1 + (- (a / p))) * p2),((a / p) * p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 + (- (a / p))) * p2) + ((a / p) * p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
1 - (a / p) is complex real ext-real Element of REAL
(1 - (a / p)) * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 - (a / p)) * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((1 - (a / p)) * p2) + ((a / p) * p4) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((1 - (a / p)) * p2),((a / p) * p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 - (a / p)) * p2) + ((a / p) * p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
3 * PI is non empty complex real ext-real positive non negative Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
LSeg (p2,p3) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p2) + (b1 * p3)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p2,p1,p4) is complex real ext-real Element of REAL
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
euc2cpx p4 is complex Element of COMPLEX
p4 `1 is complex real ext-real Element of REAL
K367(p4,1) is complex real ext-real Element of REAL
p4 `2 is complex real ext-real Element of REAL
K367(p4,2) is complex real ext-real Element of REAL
(p4 `2) * <i> is complex set
(p4 `1) + ((p4 `2) * <i>) is complex set
angle ((euc2cpx p2),(euc2cpx p1),(euc2cpx p4)) is complex real ext-real set
angle (p4,p1,p3) is complex real ext-real Element of REAL
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
angle ((euc2cpx p4),(euc2cpx p1),(euc2cpx p3)) is complex real ext-real set
(angle (p2,p1,p4)) + (angle (p4,p1,p3)) is complex real ext-real Element of REAL
angle (p2,p1,p3) is complex real ext-real Element of REAL
angle ((euc2cpx p2),(euc2cpx p1),(euc2cpx p3)) is complex real ext-real set
(angle (p2,p1,p3)) + (2 * PI) is complex real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
LSeg (p2,p3) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p2) + (b1 * p3)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p4,p1,p2) is complex real ext-real Element of REAL
euc2cpx p4 is complex Element of COMPLEX
p4 `1 is complex real ext-real Element of REAL
K367(p4,1) is complex real ext-real Element of REAL
p4 `2 is complex real ext-real Element of REAL
K367(p4,2) is complex real ext-real Element of REAL
(p4 `2) * <i> is complex set
(p4 `1) + ((p4 `2) * <i>) is complex set
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
angle ((euc2cpx p4),(euc2cpx p1),(euc2cpx p2)) is complex real ext-real set
angle (p2,p1,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p2),(euc2cpx p1),(euc2cpx p4)) is complex real ext-real set
angle (p4,p1,p3) is complex real ext-real Element of REAL
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
angle ((euc2cpx p4),(euc2cpx p1),(euc2cpx p3)) is complex real ext-real set
angle (p3,p1,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p3),(euc2cpx p1),(euc2cpx p4)) is complex real ext-real set
(angle (p3,p1,p4)) + (angle (p4,p1,p2)) is complex real ext-real Element of REAL
(angle (p3,p1,p4)) + (angle (p4,p1,p2)) is complex real ext-real Element of REAL
0 / 2 is empty complex real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() Element of REAL
- PI is non empty complex real ext-real non positive negative Element of REAL
(- PI) / 2 is non empty complex real ext-real non positive negative Element of REAL
(angle (p3,p1,p4)) + (angle (p4,p1,p2)) is complex real ext-real Element of REAL
(PI / 2) + (2 * PI) is non empty complex real ext-real positive non negative Element of REAL
0 + (2 * PI) is non empty complex real ext-real positive non negative Element of REAL
(angle (p3,p1,p4)) + (angle (p4,p1,p2)) is complex real ext-real Element of REAL
(2 * PI) - (angle (p4,p1,p2)) is complex real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
LSeg (p2,p3) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p2) + (b1 * p3)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p2,p1,p4) is complex real ext-real Element of REAL
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
euc2cpx p4 is complex Element of COMPLEX
p4 `1 is complex real ext-real Element of REAL
K367(p4,1) is complex real ext-real Element of REAL
p4 `2 is complex real ext-real Element of REAL
K367(p4,2) is complex real ext-real Element of REAL
(p4 `2) * <i> is complex set
(p4 `1) + ((p4 `2) * <i>) is complex set
angle ((euc2cpx p2),(euc2cpx p1),(euc2cpx p4)) is complex real ext-real set
p is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
LSeg (p4,p) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p4) + (b1 * p)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
angle (p3,p1,p) is complex real ext-real Element of REAL
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
euc2cpx p is complex Element of COMPLEX
p `1 is complex real ext-real Element of REAL
K367(p,1) is complex real ext-real Element of REAL
p `2 is complex real ext-real Element of REAL
K367(p,2) is complex real ext-real Element of REAL
(p `2) * <i> is complex set
(p `1) + ((p `2) * <i>) is complex set
angle ((euc2cpx p3),(euc2cpx p1),(euc2cpx p)) is complex real ext-real set
angle (p4,p1,p3) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx p1),(euc2cpx p3)) is complex real ext-real set
(angle (p2,p1,p4)) + (angle (p4,p1,p3)) is complex real ext-real Element of REAL
(angle (p4,p1,p3)) + (angle (p3,p1,p)) is complex real ext-real Element of REAL
angle (p4,p1,p3) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx p1),(euc2cpx p3)) is complex real ext-real set
(angle (p2,p1,p4)) + (angle (p4,p1,p3)) is complex real ext-real Element of REAL
(angle (p4,p1,p3)) + (angle (p3,p1,p)) is complex real ext-real Element of REAL
0 + (2 * PI) is non empty complex real ext-real positive non negative Element of REAL
(angle (p3,p1,p)) + (2 * PI) is complex real ext-real Element of REAL
angle (p4,p1,p3) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx p1),(euc2cpx p3)) is complex real ext-real set
(angle (p2,p1,p4)) + (angle (p4,p1,p3)) is complex real ext-real Element of REAL
(angle (p4,p1,p3)) + (angle (p3,p1,p)) is complex real ext-real Element of REAL
(2 * PI) - (2 * PI) is complex real ext-real Element of REAL
(angle (p3,p1,p)) - (2 * PI) is complex real ext-real Element of REAL
angle (p4,p1,p3) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx p1),(euc2cpx p3)) is complex real ext-real set
(angle (p2,p1,p4)) + (angle (p4,p1,p3)) is complex real ext-real Element of REAL
(angle (p4,p1,p3)) + (angle (p3,p1,p)) is complex real ext-real Element of REAL
angle (p4,p1,p3) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx p1),(euc2cpx p3)) is complex real ext-real set
(angle (p2,p1,p4)) + (angle (p4,p1,p3)) is complex real ext-real Element of REAL
(angle (p4,p1,p3)) + (angle (p3,p1,p)) is complex real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p2 is Relation-like Function-like set
K214((TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p2) is Relation-like Function-like complex-valued set
K251(p1,K280(p2)) is Relation-like Function-like set
|.(p1 - p2).| is complex real ext-real non negative Element of REAL
sqr (p1 - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p1 - p2),(p1 - p2)) is Relation-like Function-like set
K339((sqr (p1 - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr (p1 - p2))) is complex real ext-real Element of REAL
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 - p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p1 is Relation-like Function-like set
K214((TOP-REAL 2),p3,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p1) is Relation-like Function-like complex-valued set
K251(p3,K280(p1)) is Relation-like Function-like set
|.(p3 - p1).| is complex real ext-real non negative Element of REAL
sqr (p3 - p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p3 - p1),(p3 - p1)) is Relation-like Function-like set
K339((sqr (p3 - p1))) is complex real ext-real Element of REAL
sqrt K339((sqr (p3 - p1))) is complex real ext-real Element of REAL
angle (p1,p2,p3) is complex real ext-real Element of REAL
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx p2),(euc2cpx p3)) is complex real ext-real set
angle (p2,p3,p1) is complex real ext-real Element of REAL
angle ((euc2cpx p2),(euc2cpx p3),(euc2cpx p1)) is complex real ext-real set
|.(p1 - p2).| ^2 is complex real ext-real Element of REAL
|.(p1 - p2).| * |.(p1 - p2).| is complex real ext-real non negative set
p2 - p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p3 is Relation-like Function-like set
K214((TOP-REAL 2),p2,(- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p3) is Relation-like Function-like complex-valued set
K251(p2,K280(p3)) is Relation-like Function-like set
|.(p2 - p3).| is complex real ext-real non negative Element of REAL
sqr (p2 - p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p2 - p3),(p2 - p3)) is Relation-like Function-like set
K339((sqr (p2 - p3))) is complex real ext-real Element of REAL
sqrt K339((sqr (p2 - p3))) is complex real ext-real Element of REAL
|.(p2 - p3).| ^2 is complex real ext-real Element of REAL
|.(p2 - p3).| * |.(p2 - p3).| is complex real ext-real non negative set
p1 - p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p1,(- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p1,K280(p3)) is Relation-like Function-like set
|.(p1 - p3).| is complex real ext-real non negative Element of REAL
sqr (p1 - p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p1 - p3),(p1 - p3)) is Relation-like Function-like set
K339((sqr (p1 - p3))) is complex real ext-real Element of REAL
sqrt K339((sqr (p1 - p3))) is complex real ext-real Element of REAL
|.(p1 - p3).| ^2 is complex real ext-real Element of REAL
|.(p1 - p3).| * |.(p1 - p3).| is complex real ext-real non negative set
(|.(p2 - p3).| ^2) + (|.(p1 - p3).| ^2) is complex real ext-real Element of REAL
2 * |.(p2 - p3).| is complex real ext-real non negative Element of REAL
(2 * |.(p2 - p3).|) * |.(p1 - p3).| is complex real ext-real non negative Element of REAL
cos (angle (p2,p3,p1)) is complex real ext-real Element of REAL
((2 * |.(p2 - p3).|) * |.(p1 - p3).|) * (cos (angle (p2,p3,p1))) is complex real ext-real Element of REAL
((|.(p2 - p3).| ^2) + (|.(p1 - p3).| ^2)) - (((2 * |.(p2 - p3).|) * |.(p1 - p3).|) * (cos (angle (p2,p3,p1)))) is complex real ext-real Element of REAL
p3 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p3,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p3,K280(p2)) is Relation-like Function-like set
|.(p3 - p2).| is complex real ext-real non negative Element of REAL
sqr (p3 - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p3 - p2),(p3 - p2)) is Relation-like Function-like set
K339((sqr (p3 - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr (p3 - p2))) is complex real ext-real Element of REAL
|.(p3 - p2).| ^2 is complex real ext-real Element of REAL
|.(p3 - p2).| * |.(p3 - p2).| is complex real ext-real non negative set
(|.(p1 - p2).| ^2) + (|.(p3 - p2).| ^2) is complex real ext-real Element of REAL
2 * |.(p1 - p2).| is complex real ext-real non negative Element of REAL
(2 * |.(p1 - p2).|) * |.(p3 - p2).| is complex real ext-real non negative Element of REAL
cos (angle (p1,p2,p3)) is complex real ext-real Element of REAL
((2 * |.(p1 - p2).|) * |.(p3 - p2).|) * (cos (angle (p1,p2,p3))) is complex real ext-real Element of REAL
((|.(p1 - p2).| ^2) + (|.(p3 - p2).| ^2)) - (((2 * |.(p1 - p2).|) * |.(p3 - p2).|) * (cos (angle (p1,p2,p3)))) is complex real ext-real Element of REAL
(|.(p1 - p3).| ^2) - (((2 * |.(p2 - p3).|) * |.(p1 - p3).|) * (cos (angle (p2,p3,p1)))) is complex real ext-real Element of REAL
((|.(p1 - p3).| ^2) - (((2 * |.(p2 - p3).|) * |.(p1 - p3).|) * (cos (angle (p2,p3,p1))))) + (|.(p2 - p3).| ^2) is complex real ext-real Element of REAL
(|.(p1 - p2).| ^2) - (((2 * |.(p1 - p2).|) * |.(p3 - p2).|) * (cos (angle (p1,p2,p3)))) is complex real ext-real Element of REAL
((|.(p1 - p2).| ^2) - (((2 * |.(p1 - p2).|) * |.(p3 - p2).|) * (cos (angle (p1,p2,p3))))) + (|.(p3 - p2).| ^2) is complex real ext-real Element of REAL
((|.(p1 - p2).| ^2) - (((2 * |.(p1 - p2).|) * |.(p3 - p2).|) * (cos (angle (p1,p2,p3))))) + (|.(p2 - p3).| ^2) is complex real ext-real Element of REAL
- (((2 * |.(p2 - p3).|) * |.(p1 - p3).|) * (cos (angle (p2,p3,p1)))) is complex real ext-real Element of REAL
(- (((2 * |.(p2 - p3).|) * |.(p1 - p3).|) * (cos (angle (p2,p3,p1))))) + (|.(p1 - p3).| ^2) is complex real ext-real Element of REAL
2 * |.(p3 - p1).| is complex real ext-real non negative Element of REAL
(2 * |.(p3 - p1).|) * |.(p3 - p2).| is complex real ext-real non negative Element of REAL
((2 * |.(p3 - p1).|) * |.(p3 - p2).|) * (cos (angle (p1,p2,p3))) is complex real ext-real Element of REAL
- (((2 * |.(p3 - p1).|) * |.(p3 - p2).|) * (cos (angle (p1,p2,p3)))) is complex real ext-real Element of REAL
|.(p3 - p1).| ^2 is complex real ext-real Element of REAL
|.(p3 - p1).| * |.(p3 - p1).| is complex real ext-real non negative set
(- (((2 * |.(p3 - p1).|) * |.(p3 - p2).|) * (cos (angle (p1,p2,p3))))) + (|.(p3 - p1).| ^2) is complex real ext-real Element of REAL
(- (((2 * |.(p3 - p1).|) * |.(p3 - p2).|) * (cos (angle (p1,p2,p3))))) + (|.(p1 - p3).| ^2) is complex real ext-real Element of REAL
|.(p2 - p3).| * |.(p1 - p3).| is complex real ext-real non negative Element of REAL
(|.(p2 - p3).| * |.(p1 - p3).|) * (cos (angle (p2,p3,p1))) is complex real ext-real Element of REAL
|.(p3 - p1).| * |.(p3 - p2).| is complex real ext-real non negative Element of REAL
(|.(p3 - p1).| * |.(p3 - p2).|) * (cos (angle (p1,p2,p3))) is complex real ext-real Element of REAL
|.(p3 - p1).| * |.(p2 - p3).| is complex real ext-real non negative Element of REAL
(|.(p3 - p1).| * |.(p2 - p3).|) * (cos (angle (p1,p2,p3))) is complex real ext-real Element of REAL
|.(p1 - p3).| * (cos (angle (p2,p3,p1))) is complex real ext-real Element of REAL
(|.(p1 - p3).| * (cos (angle (p2,p3,p1)))) * |.(p2 - p3).| is complex real ext-real Element of REAL
|.(p3 - p1).| * (cos (angle (p1,p2,p3))) is complex real ext-real Element of REAL
(|.(p3 - p1).| * (cos (angle (p1,p2,p3)))) * |.(p2 - p3).| is complex real ext-real Element of REAL
|.(p3 - p1).| * (cos (angle (p2,p3,p1))) is complex real ext-real Element of REAL
sin (angle (p1,p2,p3)) is complex real ext-real Element of REAL
|.(p1 - p2).| * (sin (angle (p1,p2,p3))) is complex real ext-real Element of REAL
sin (angle (p2,p3,p1)) is complex real ext-real Element of REAL
|.(p1 - p3).| * (sin (angle (p2,p3,p1))) is complex real ext-real Element of REAL
|.(p1 - p2).| * (sin (angle (p2,p3,p1))) is complex real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
LSeg (p1,p2) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p1) + (b1 * p2)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
p2 - p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p1 is Relation-like Function-like set
K214((TOP-REAL 2),p2,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p1) is Relation-like Function-like complex-valued set
K251(p2,K280(p1)) is Relation-like Function-like set
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 - p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p4 is Relation-like Function-like set
K214((TOP-REAL 2),p3,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (- p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p4) is Relation-like Function-like complex-valued set
K251(p3,K280(p4)) is Relation-like Function-like set
|((p3 - p4),(p2 - p1))| is complex real ext-real Element of REAL
p2 - p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p2,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p2,K280(p4)) is Relation-like Function-like set
|((p3 - p4),(p2 - p4))| is complex real ext-real Element of REAL
LSeg (p2,p1) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p2) + (b1 * p1)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
p is complex real ext-real Element of REAL
1 - p is complex real ext-real Element of REAL
(1 - p) * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 - p) * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p * p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p * p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((1 - p) * p2) + (p * p1) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((1 - p) * p2),(p * p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 - p) * p2) + (p * p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - ((1 - p) * p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- ((1 - p) * p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- ((1 - p) * p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * ((1 - p) * p2) is Relation-like Function-like set
K214((TOP-REAL 2),p2,(- ((1 - p) * p2))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- ((1 - p) * p2))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- ((1 - p) * p2)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - ((1 - p) * p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(((1 - p) * p2)) is Relation-like Function-like complex-valued set
K251(p2,K280(((1 - p) * p2))) is Relation-like Function-like set
(p2 - ((1 - p) * p2)) - (p * p1) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- (p * p1) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- (p * p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * (p * p1) is Relation-like Function-like set
K214((TOP-REAL 2),(p2 - ((1 - p) * p2)),(- (p * p1))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(p2 - ((1 - p) * p2)),(- (p * p1))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(p2 - ((1 - p) * p2)) + (- (p * p1)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(p2 - ((1 - p) * p2)) - (p * p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280((p * p1)) is Relation-like Function-like complex-valued set
K251((p2 - ((1 - p) * p2)),K280((p * p1))) is Relation-like Function-like set
1 * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
1 * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1 * p2) - (p * p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- (p * p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- (p * p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * (p * p2) is Relation-like Function-like set
K214((TOP-REAL 2),(1 * p2),(- (p * p2))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(1 * p2),(- (p * p2))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 * p2) + (- (p * p2)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1 * p2) - (p * p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280((p * p2)) is Relation-like Function-like complex-valued set
K251((1 * p2),K280((p * p2))) is Relation-like Function-like set
p2 - ((1 * p2) - (p * p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- ((1 * p2) - (p * p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- ((1 * p2) - (p * p2)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * ((1 * p2) - (p * p2)) is Relation-like Function-like set
K214((TOP-REAL 2),p2,(- ((1 * p2) - (p * p2)))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- ((1 * p2) - (p * p2)))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- ((1 * p2) - (p * p2))) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - ((1 * p2) - (p * p2)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(((1 * p2) - (p * p2))) is Relation-like Function-like complex-valued set
K251(p2,K280(((1 * p2) - (p * p2)))) is Relation-like Function-like set
(p2 - ((1 * p2) - (p * p2))) - (p * p1) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),(p2 - ((1 * p2) - (p * p2))),(- (p * p1))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(p2 - ((1 * p2) - (p * p2))),(- (p * p1))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(p2 - ((1 * p2) - (p * p2))) + (- (p * p1)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(p2 - ((1 * p2) - (p * p2))) - (p * p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251((p2 - ((1 * p2) - (p * p2))),K280((p * p1))) is Relation-like Function-like set
p2 - (p * p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p2,(- (p * p2))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- (p * p2))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- (p * p2)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - (p * p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p2,K280((p * p2))) is Relation-like Function-like set
p2 - (p2 - (p * p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- (p2 - (p * p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- (p2 - (p * p2)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * (p2 - (p * p2)) is Relation-like Function-like set
K214((TOP-REAL 2),p2,(- (p2 - (p * p2)))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- (p2 - (p * p2)))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- (p2 - (p * p2))) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - (p2 - (p * p2)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280((p2 - (p * p2))) is Relation-like Function-like complex-valued set
K251(p2,K280((p2 - (p * p2)))) is Relation-like Function-like set
(p2 - (p2 - (p * p2))) - (p * p1) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),(p2 - (p2 - (p * p2))),(- (p * p1))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(p2 - (p2 - (p * p2))),(- (p * p1))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(p2 - (p2 - (p * p2))) + (- (p * p1)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(p2 - (p2 - (p * p2))) - (p * p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251((p2 - (p2 - (p * p2))),K280((p * p1))) is Relation-like Function-like set
p2 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p2 is Relation-like Function-like set
K214((TOP-REAL 2),p2,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p2) is Relation-like Function-like complex-valued set
K251(p2,K280(p2)) is Relation-like Function-like set
(p2 - p2) + (p * p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(p2 - p2),(p * p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(p2 - p2) + (p * p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((p2 - p2) + (p * p2)) - (p * p1) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),((p2 - p2) + (p * p2)),(- (p * p1))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((p2 - p2) + (p * p2)),(- (p * p1))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((p2 - p2) + (p * p2)) + (- (p * p1)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((p2 - p2) + (p * p2)) - (p * p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(((p2 - p2) + (p * p2)),K280((p * p1))) is Relation-like Function-like set
(0. (TOP-REAL 2)) + (p * p2) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(0. (TOP-REAL 2)),(p * p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(0. (TOP-REAL 2)) + (p * p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((0. (TOP-REAL 2)) + (p * p2)) - (p * p1) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),((0. (TOP-REAL 2)) + (p * p2)),(- (p * p1))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((0. (TOP-REAL 2)) + (p * p2)),(- (p * p1))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((0. (TOP-REAL 2)) + (p * p2)) + (- (p * p1)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((0. (TOP-REAL 2)) + (p * p2)) - (p * p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(((0. (TOP-REAL 2)) + (p * p2)),K280((p * p1))) is Relation-like Function-like set
(p * p2) - (p * p1) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),(p * p2),(- (p * p1))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(p * p2),(- (p * p1))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(p * p2) + (- (p * p1)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(p * p2) - (p * p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251((p * p2),K280((p * p1))) is Relation-like Function-like set
p * (p2 - p1) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p * (p2 - p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p * |((p3 - p4),(p2 - p1))| is complex real ext-real Element of REAL
(1 * p2) + (0. (TOP-REAL 2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(1 * p2),(0. (TOP-REAL 2))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 * p2) + (0. (TOP-REAL 2)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p2 is Relation-like Function-like set
K214((TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p2) is Relation-like Function-like complex-valued set
K251(p1,K280(p2)) is Relation-like Function-like set
|.(p1 - p2).| is complex real ext-real non negative Element of REAL
sqr (p1 - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p1 - p2),(p1 - p2)) is Relation-like Function-like set
K339((sqr (p1 - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr (p1 - p2))) is complex real ext-real Element of REAL
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p3,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p3,K280(p2)) is Relation-like Function-like set
|.(p3 - p2).| is complex real ext-real non negative Element of REAL
sqr (p3 - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p3 - p2),(p3 - p2)) is Relation-like Function-like set
K339((sqr (p3 - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr (p3 - p2))) is complex real ext-real Element of REAL
LSeg (p1,p3) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p1) + (b1 * p3)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p2,p4,p1) is complex real ext-real Element of REAL
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
euc2cpx p4 is complex Element of COMPLEX
p4 `1 is complex real ext-real Element of REAL
K367(p4,1) is complex real ext-real Element of REAL
p4 `2 is complex real ext-real Element of REAL
K367(p4,2) is complex real ext-real Element of REAL
(p4 `2) * <i> is complex set
(p4 `1) + ((p4 `2) * <i>) is complex set
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
angle ((euc2cpx p2),(euc2cpx p4),(euc2cpx p1)) is complex real ext-real set
angle (p1,p2,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p1),(euc2cpx p2),(euc2cpx p4)) is complex real ext-real set
angle (p4,p2,p3) is complex real ext-real Element of REAL
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
angle ((euc2cpx p4),(euc2cpx p2),(euc2cpx p3)) is complex real ext-real set
p2 - p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p1 is Relation-like Function-like set
K214((TOP-REAL 2),p2,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p1) is Relation-like Function-like complex-valued set
K251(p2,K280(p1)) is Relation-like Function-like set
|.(p2 - p1).| is complex real ext-real non negative Element of REAL
sqr (p2 - p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p2 - p1),(p2 - p1)) is Relation-like Function-like set
K339((sqr (p2 - p1))) is complex real ext-real Element of REAL
sqrt K339((sqr (p2 - p1))) is complex real ext-real Element of REAL
{p1} is non empty set
angle (p1,p4,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p1),(euc2cpx p4),(euc2cpx p2)) is complex real ext-real set
angle (p2,p4,p3) is complex real ext-real Element of REAL
angle ((euc2cpx p2),(euc2cpx p4),(euc2cpx p3)) is complex real ext-real set
angle (p2,p1,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p2),(euc2cpx p1),(euc2cpx p4)) is complex real ext-real set
angle (p2,p1,p3) is complex real ext-real Element of REAL
angle ((euc2cpx p2),(euc2cpx p1),(euc2cpx p3)) is complex real ext-real set
angle (p1,p3,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p1),(euc2cpx p3),(euc2cpx p2)) is complex real ext-real set
angle (p4,p3,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx p3),(euc2cpx p2)) is complex real ext-real set
angle (p4,p2,p1) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx p2),(euc2cpx p1)) is complex real ext-real set
angle (p3,p2,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p3),(euc2cpx p2),(euc2cpx p4)) is complex real ext-real set
(angle (p4,p3,p2)) + (angle (p4,p2,p1)) is complex real ext-real Element of REAL
((angle (p4,p3,p2)) + (angle (p4,p2,p1))) + (angle (p2,p4,p3)) is complex real ext-real Element of REAL
(angle (p4,p3,p2)) + (angle (p3,p2,p4)) is complex real ext-real Element of REAL
((angle (p4,p3,p2)) + (angle (p3,p2,p4))) + (angle (p2,p4,p3)) is complex real ext-real Element of REAL
(angle (p4,p3,p2)) + (angle (p4,p2,p1)) is complex real ext-real Element of REAL
((angle (p4,p3,p2)) + (angle (p4,p2,p1))) + (angle (p2,p4,p3)) is complex real ext-real Element of REAL
(angle (p4,p3,p2)) + (angle (p3,p2,p4)) is complex real ext-real Element of REAL
((angle (p4,p3,p2)) + (angle (p3,p2,p4))) + (angle (p2,p4,p3)) is complex real ext-real Element of REAL
(2 * PI) - 0 is non empty complex real ext-real positive non negative Element of REAL
(angle (p3,p2,p4)) - (angle (p4,p2,p1)) is complex real ext-real Element of REAL
(angle (p4,p3,p2)) + (angle (p4,p2,p1)) is complex real ext-real Element of REAL
((angle (p4,p3,p2)) + (angle (p4,p2,p1))) + (angle (p2,p4,p3)) is complex real ext-real Element of REAL
(angle (p4,p3,p2)) + (angle (p3,p2,p4)) is complex real ext-real Element of REAL
((angle (p4,p3,p2)) + (angle (p3,p2,p4))) + (angle (p2,p4,p3)) is complex real ext-real Element of REAL
(2 * PI) - 0 is non empty complex real ext-real positive non negative Element of REAL
(angle (p4,p2,p1)) - (angle (p3,p2,p4)) is complex real ext-real Element of REAL
(angle (p4,p3,p2)) + (angle (p4,p2,p1)) is complex real ext-real Element of REAL
((angle (p4,p3,p2)) + (angle (p4,p2,p1))) + (angle (p2,p4,p3)) is complex real ext-real Element of REAL
(angle (p4,p3,p2)) + (angle (p3,p2,p4)) is complex real ext-real Element of REAL
((angle (p4,p3,p2)) + (angle (p3,p2,p4))) + (angle (p2,p4,p3)) is complex real ext-real Element of REAL
(2 * PI) - (angle (p4,p2,p1)) is complex real ext-real Element of REAL
p4 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p4,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p4,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p4 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p4 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p4,K280(p2)) is Relation-like Function-like set
|.(p4 - p2).| is complex real ext-real non negative Element of REAL
sqr (p4 - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p4 - p2),(p4 - p2)) is Relation-like Function-like set
K339((sqr (p4 - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr (p4 - p2))) is complex real ext-real Element of REAL
p2 - p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p4 is Relation-like Function-like set
K214((TOP-REAL 2),p2,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p4) is Relation-like Function-like complex-valued set
K251(p2,K280(p4)) is Relation-like Function-like set
|.(p2 - p4).| is complex real ext-real non negative Element of REAL
sqr (p2 - p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p2 - p4),(p2 - p4)) is Relation-like Function-like set
K339((sqr (p2 - p4))) is complex real ext-real Element of REAL
sqrt K339((sqr (p2 - p4))) is complex real ext-real Element of REAL
|.(p2 - p1).| ^2 is complex real ext-real Element of REAL
|.(p2 - p1).| * |.(p2 - p1).| is complex real ext-real non negative set
p1 - p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p1,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p1,K280(p4)) is Relation-like Function-like set
|.(p1 - p4).| is complex real ext-real non negative Element of REAL
sqr (p1 - p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p1 - p4),(p1 - p4)) is Relation-like Function-like set
K339((sqr (p1 - p4))) is complex real ext-real Element of REAL
sqrt K339((sqr (p1 - p4))) is complex real ext-real Element of REAL
|.(p1 - p4).| ^2 is complex real ext-real Element of REAL
|.(p1 - p4).| * |.(p1 - p4).| is complex real ext-real non negative set
(|.(p2 - p1).| ^2) + (|.(p1 - p4).| ^2) is complex real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
LSeg (p1,p2) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p1) + (b1 * p2)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
p2 - p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p1 is Relation-like Function-like set
K214((TOP-REAL 2),p2,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p1) is Relation-like Function-like complex-valued set
K251(p2,K280(p1)) is Relation-like Function-like set
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 - p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p3 is Relation-like Function-like set
K214((TOP-REAL 2),p1,(- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p3) is Relation-like Function-like complex-valued set
K251(p1,K280(p3)) is Relation-like Function-like set
|.(p1 - p3).| is complex real ext-real non negative Element of REAL
sqr (p1 - p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p1 - p3),(p1 - p3)) is Relation-like Function-like set
K339((sqr (p1 - p3))) is complex real ext-real Element of REAL
sqrt K339((sqr (p1 - p3))) is complex real ext-real Element of REAL
p2 - p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p2,(- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p2,K280(p3)) is Relation-like Function-like set
|.(p2 - p3).| is complex real ext-real non negative Element of REAL
sqr (p2 - p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p2 - p3),(p2 - p3)) is Relation-like Function-like set
K339((sqr (p2 - p3))) is complex real ext-real Element of REAL
sqrt K339((sqr (p2 - p3))) is complex real ext-real Element of REAL
p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p1,p3,p4) is complex real ext-real Element of REAL
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
euc2cpx p4 is complex Element of COMPLEX
p4 `1 is complex real ext-real Element of REAL
K367(p4,1) is complex real ext-real Element of REAL
p4 `2 is complex real ext-real Element of REAL
K367(p4,2) is complex real ext-real Element of REAL
(p4 `2) * <i> is complex set
(p4 `1) + ((p4 `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx p3),(euc2cpx p4)) is complex real ext-real set
angle (p4,p3,p2) is complex real ext-real Element of REAL
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
angle ((euc2cpx p4),(euc2cpx p3),(euc2cpx p2)) is complex real ext-real set
p1 - p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p4 is Relation-like Function-like set
K214((TOP-REAL 2),p1,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p4) is Relation-like Function-like complex-valued set
K251(p1,K280(p4)) is Relation-like Function-like set
|.(p1 - p4).| is complex real ext-real non negative Element of REAL
sqr (p1 - p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p1 - p4),(p1 - p4)) is Relation-like Function-like set
K339((sqr (p1 - p4))) is complex real ext-real Element of REAL
sqrt K339((sqr (p1 - p4))) is complex real ext-real Element of REAL
p4 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p2 is Relation-like Function-like set
K214((TOP-REAL 2),p4,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p4,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p4 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p4 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p2) is Relation-like Function-like complex-valued set
K251(p4,K280(p2)) is Relation-like Function-like set
|.(p4 - p2).| is complex real ext-real non negative Element of REAL
sqr (p4 - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p4 - p2),(p4 - p2)) is Relation-like Function-like set
K339((sqr (p4 - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr (p4 - p2))) is complex real ext-real Element of REAL
p3 - p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p3,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (- p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p3,K280(p4)) is Relation-like Function-like set
|((p3 - p4),(p2 - p1))| is complex real ext-real Element of REAL
p4 - p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p4,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p4,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p4 + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p4 - p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p4,K280(p1)) is Relation-like Function-like set
|.(p4 - p1).| is complex real ext-real non negative Element of REAL
sqr (p4 - p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p4 - p1),(p4 - p1)) is Relation-like Function-like set
K339((sqr (p4 - p1))) is complex real ext-real Element of REAL
sqrt K339((sqr (p4 - p1))) is complex real ext-real Element of REAL
|.(p4 - p1).| ^2 is complex real ext-real Element of REAL
|.(p4 - p1).| * |.(p4 - p1).| is complex real ext-real non negative set
|.(p1 - p3).| ^2 is complex real ext-real Element of REAL
|.(p1 - p3).| * |.(p1 - p3).| is complex real ext-real non negative set
p4 - p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p4,(- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p4,(- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p4 + (- p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p4 - p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p4,K280(p3)) is Relation-like Function-like set
|.(p4 - p3).| is complex real ext-real non negative Element of REAL
sqr (p4 - p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p4 - p3),(p4 - p3)) is Relation-like Function-like set
K339((sqr (p4 - p3))) is complex real ext-real Element of REAL
sqrt K339((sqr (p4 - p3))) is complex real ext-real Element of REAL
|.(p4 - p3).| ^2 is complex real ext-real Element of REAL
|.(p4 - p3).| * |.(p4 - p3).| is complex real ext-real non negative set
(|.(p1 - p3).| ^2) + (|.(p4 - p3).| ^2) is complex real ext-real Element of REAL
2 * |.(p1 - p3).| is complex real ext-real non negative Element of REAL
(2 * |.(p1 - p3).|) * |.(p4 - p3).| is complex real ext-real non negative Element of REAL
cos (angle (p1,p3,p4)) is complex real ext-real Element of REAL
((2 * |.(p1 - p3).|) * |.(p4 - p3).|) * (cos (angle (p1,p3,p4))) is complex real ext-real Element of REAL
((|.(p1 - p3).| ^2) + (|.(p4 - p3).| ^2)) - (((2 * |.(p1 - p3).|) * |.(p4 - p3).|) * (cos (angle (p1,p3,p4)))) is complex real ext-real Element of REAL
|.(p2 - p3).| ^2 is complex real ext-real Element of REAL
|.(p2 - p3).| * |.(p2 - p3).| is complex real ext-real non negative set
(|.(p4 - p3).| ^2) + (|.(p2 - p3).| ^2) is complex real ext-real Element of REAL
2 * |.(p4 - p3).| is complex real ext-real non negative Element of REAL
(2 * |.(p4 - p3).|) * |.(p2 - p3).| is complex real ext-real non negative Element of REAL
cos (angle (p4,p3,p2)) is complex real ext-real Element of REAL
((2 * |.(p4 - p3).|) * |.(p2 - p3).|) * (cos (angle (p4,p3,p2))) is complex real ext-real Element of REAL
((|.(p4 - p3).| ^2) + (|.(p2 - p3).| ^2)) - (((2 * |.(p4 - p3).|) * |.(p2 - p3).|) * (cos (angle (p4,p3,p2)))) is complex real ext-real Element of REAL
p2 - p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p2,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p2,K280(p4)) is Relation-like Function-like set
|.(p2 - p4).| is complex real ext-real non negative Element of REAL
sqr (p2 - p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p2 - p4),(p2 - p4)) is Relation-like Function-like set
K339((sqr (p2 - p4))) is complex real ext-real Element of REAL
sqrt K339((sqr (p2 - p4))) is complex real ext-real Element of REAL
|.(p2 - p4).| ^2 is complex real ext-real Element of REAL
|.(p2 - p4).| * |.(p2 - p4).| is complex real ext-real non negative set
sqrt (|.(p2 - p4).| ^2) is complex real ext-real Element of REAL
p4 - p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p4,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p4,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p4 + (- p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p4 - p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p4,K280(p4)) is Relation-like Function-like set
|((p3 - p4),(p4 - p4))| is complex real ext-real Element of REAL
|((p3 - p4),(0. (TOP-REAL 2)))| is complex real ext-real Element of REAL
angle (p1,p4,p3) is complex real ext-real Element of REAL
angle ((euc2cpx p1),(euc2cpx p4),(euc2cpx p3)) is complex real ext-real set
cos (angle (p1,p4,p3)) is complex real ext-real Element of REAL
angle (p3,p4,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p3),(euc2cpx p4),(euc2cpx p2)) is complex real ext-real set
cos (angle (p3,p4,p2)) is complex real ext-real Element of REAL
- (cos (angle (p3,p4,p2))) is complex real ext-real Element of REAL
(angle (p1,p4,p3)) + (angle (p3,p4,p2)) is complex real ext-real Element of REAL
- (angle (p3,p4,p2)) is complex real ext-real Element of REAL
PI + (- (angle (p3,p4,p2))) is complex real ext-real Element of REAL
cos (PI + (- (angle (p3,p4,p2)))) is complex real ext-real Element of REAL
cos (- (angle (p3,p4,p2))) is complex real ext-real Element of REAL
- (cos (- (angle (p3,p4,p2)))) is complex real ext-real Element of REAL
(angle (p1,p4,p3)) + (angle (p3,p4,p2)) is complex real ext-real Element of REAL
PI - (angle (p3,p4,p2)) is complex real ext-real Element of REAL
(PI - (angle (p3,p4,p2))) + (2 * PI) is complex real ext-real Element of REAL
cos ((PI - (angle (p3,p4,p2))) + (2 * PI)) is complex real ext-real Element of REAL
- (angle (p3,p4,p2)) is complex real ext-real Element of REAL
PI + (- (angle (p3,p4,p2))) is complex real ext-real Element of REAL
cos (PI + (- (angle (p3,p4,p2)))) is complex real ext-real Element of REAL
cos (- (angle (p3,p4,p2))) is complex real ext-real Element of REAL
- (cos (- (angle (p3,p4,p2)))) is complex real ext-real Element of REAL
(angle (p1,p4,p3)) + (angle (p3,p4,p2)) is complex real ext-real Element of REAL
p3 - p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p3,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p3,K280(p1)) is Relation-like Function-like set
|.(p3 - p1).| is complex real ext-real non negative Element of REAL
sqr (p3 - p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p3 - p1),(p3 - p1)) is Relation-like Function-like set
K339((sqr (p3 - p1))) is complex real ext-real Element of REAL
sqrt K339((sqr (p3 - p1))) is complex real ext-real Element of REAL
|.(p3 - p1).| ^2 is complex real ext-real Element of REAL
|.(p3 - p1).| * |.(p3 - p1).| is complex real ext-real non negative set
|.(p1 - p4).| ^2 is complex real ext-real Element of REAL
|.(p1 - p4).| * |.(p1 - p4).| is complex real ext-real non negative set
|.(p3 - p4).| is complex real ext-real non negative Element of REAL
sqr (p3 - p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p3 - p4),(p3 - p4)) is Relation-like Function-like set
K339((sqr (p3 - p4))) is complex real ext-real Element of REAL
sqrt K339((sqr (p3 - p4))) is complex real ext-real Element of REAL
|.(p3 - p4).| ^2 is complex real ext-real Element of REAL
|.(p3 - p4).| * |.(p3 - p4).| is complex real ext-real non negative set
(|.(p1 - p4).| ^2) + (|.(p3 - p4).| ^2) is complex real ext-real Element of REAL
2 * |.(p1 - p4).| is complex real ext-real non negative Element of REAL
(2 * |.(p1 - p4).|) * |.(p3 - p4).| is complex real ext-real non negative Element of REAL
((2 * |.(p1 - p4).|) * |.(p3 - p4).|) * (cos (angle (p1,p4,p3))) is complex real ext-real Element of REAL
((|.(p1 - p4).| ^2) + (|.(p3 - p4).| ^2)) - (((2 * |.(p1 - p4).|) * |.(p3 - p4).|) * (cos (angle (p1,p4,p3)))) is complex real ext-real Element of REAL
|.(p2 - p3).| ^2 is complex real ext-real Element of REAL
|.(p2 - p3).| * |.(p2 - p3).| is complex real ext-real non negative set
p2 - p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p2,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p2,K280(p4)) is Relation-like Function-like set
|.(p2 - p4).| is complex real ext-real non negative Element of REAL
sqr (p2 - p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p2 - p4),(p2 - p4)) is Relation-like Function-like set
K339((sqr (p2 - p4))) is complex real ext-real Element of REAL
sqrt K339((sqr (p2 - p4))) is complex real ext-real Element of REAL
|.(p2 - p4).| ^2 is complex real ext-real Element of REAL
|.(p2 - p4).| * |.(p2 - p4).| is complex real ext-real non negative set
(|.(p3 - p4).| ^2) + (|.(p2 - p4).| ^2) is complex real ext-real Element of REAL
2 * |.(p3 - p4).| is complex real ext-real non negative Element of REAL
(2 * |.(p3 - p4).|) * |.(p2 - p4).| is complex real ext-real non negative Element of REAL
((2 * |.(p3 - p4).|) * |.(p2 - p4).|) * (cos (angle (p3,p4,p2))) is complex real ext-real Element of REAL
((|.(p3 - p4).| ^2) + (|.(p2 - p4).| ^2)) - (((2 * |.(p3 - p4).|) * |.(p2 - p4).|) * (cos (angle (p3,p4,p2)))) is complex real ext-real Element of REAL
(2 * |.(p1 - p4).|) * (cos (angle (p1,p4,p3))) is complex real ext-real Element of REAL
((2 * |.(p1 - p4).|) * (cos (angle (p1,p4,p3)))) * |.(p3 - p4).| is complex real ext-real Element of REAL
2 * |.(p2 - p4).| is complex real ext-real non negative Element of REAL
(2 * |.(p2 - p4).|) * (cos (angle (p3,p4,p2))) is complex real ext-real Element of REAL
((2 * |.(p2 - p4).|) * (cos (angle (p3,p4,p2)))) * |.(p3 - p4).| is complex real ext-real Element of REAL
2 * (cos (angle (p1,p4,p3))) is complex real ext-real Element of REAL
(2 * (cos (angle (p1,p4,p3)))) * |.(p2 - p4).| is complex real ext-real Element of REAL
2 * (cos (angle (p3,p4,p2))) is complex real ext-real Element of REAL
(2 * (cos (angle (p3,p4,p2)))) * |.(p2 - p4).| is complex real ext-real Element of REAL
|((p3 - p4),(p2 - p4))| is complex real ext-real Element of REAL
- |((p3 - p4),(p2 - p1))| is complex real ext-real Element of REAL
- (p2 - p1) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- (p2 - p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * (p2 - p1) is Relation-like Function-like set
|((p3 - p4),(- (p2 - p1)))| is complex real ext-real Element of REAL
p1 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p1,K280(p2)) is Relation-like Function-like set
|((p3 - p4),(p1 - p2))| is complex real ext-real Element of REAL
|((p3 - p4),(p1 - p4))| is complex real ext-real Element of REAL
angle (p3,p4,p1) is complex real ext-real Element of REAL
angle ((euc2cpx p3),(euc2cpx p4),(euc2cpx p1)) is complex real ext-real set
p2 - p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p2,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p2,K280(p4)) is Relation-like Function-like set
|((p3 - p4),(p2 - p4))| is complex real ext-real Element of REAL
angle (p3,p4,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p3),(euc2cpx p4),(euc2cpx p2)) is complex real ext-real set
angle (p2,p3,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p2),(euc2cpx p3),(euc2cpx p4)) is complex real ext-real set
angle (p4,p3,p1) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx p3),(euc2cpx p1)) is complex real ext-real set
(2 * PI) - (angle (p2,p3,p4)) is complex real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p1,p2,p3) is complex real ext-real Element of REAL
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx p2),(euc2cpx p3)) is complex real ext-real set
angle (p2,p3,p1) is complex real ext-real Element of REAL
angle ((euc2cpx p2),(euc2cpx p3),(euc2cpx p1)) is complex real ext-real set
angle (p3,p1,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p3),(euc2cpx p1),(euc2cpx p2)) is complex real ext-real set
LSeg (p3,p1) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p3) + (b1 * p1)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
LSeg (p2,p3) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p2) + (b1 * p3)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
LSeg (p1,p2) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p1) + (b1 * p2)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
LSeg (p2,p1) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p2) + (b1 * p1)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
LSeg (p3,p2) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p3) + (b1 * p2)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
LSeg (p1,p3) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p1) + (b1 * p3)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p2 is Relation-like Function-like set
K214((TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p2) is Relation-like Function-like complex-valued set
K251(p1,K280(p2)) is Relation-like Function-like set
|.(p1 - p2).| is complex real ext-real non negative Element of REAL
sqr (p1 - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p1 - p2),(p1 - p2)) is Relation-like Function-like set
K339((sqr (p1 - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr (p1 - p2))) is complex real ext-real Element of REAL
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p3,p2,p1) is complex real ext-real Element of REAL
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
angle ((euc2cpx p3),(euc2cpx p2),(euc2cpx p1)) is complex real ext-real set
angle (p2,p1,p3) is complex real ext-real Element of REAL
angle ((euc2cpx p2),(euc2cpx p1),(euc2cpx p3)) is complex real ext-real set
angle (p1,p3,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p1),(euc2cpx p3),(euc2cpx p2)) is complex real ext-real set
p3 - p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p1 is Relation-like Function-like set
K214((TOP-REAL 2),p3,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p1) is Relation-like Function-like complex-valued set
K251(p3,K280(p1)) is Relation-like Function-like set
|.(p3 - p1).| is complex real ext-real non negative Element of REAL
sqr (p3 - p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p3 - p1),(p3 - p1)) is Relation-like Function-like set
K339((sqr (p3 - p1))) is complex real ext-real Element of REAL
sqrt K339((sqr (p3 - p1))) is complex real ext-real Element of REAL
p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p - p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p4 is Relation-like Function-like set
K214((TOP-REAL 2),p,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p + (- p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p - p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p4) is Relation-like Function-like complex-valued set
K251(p,K280(p4)) is Relation-like Function-like set
|.(p - p4).| is complex real ext-real non negative Element of REAL
sqr (p - p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p - p4),(p - p4)) is Relation-like Function-like set
K339((sqr (p - p4))) is complex real ext-real Element of REAL
sqrt K339((sqr (p - p4))) is complex real ext-real Element of REAL
|.(p3 - p1).| * |.(p - p4).| is complex real ext-real non negative Element of REAL
a is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (a,p4,p) is complex real ext-real Element of REAL
euc2cpx a is complex Element of COMPLEX
a `1 is complex real ext-real Element of REAL
K367(a,1) is complex real ext-real Element of REAL
a `2 is complex real ext-real Element of REAL
K367(a,2) is complex real ext-real Element of REAL
(a `2) * <i> is complex set
(a `1) + ((a `2) * <i>) is complex set
euc2cpx p4 is complex Element of COMPLEX
p4 `1 is complex real ext-real Element of REAL
K367(p4,1) is complex real ext-real Element of REAL
p4 `2 is complex real ext-real Element of REAL
K367(p4,2) is complex real ext-real Element of REAL
(p4 `2) * <i> is complex set
(p4 `1) + ((p4 `2) * <i>) is complex set
euc2cpx p is complex Element of COMPLEX
p `1 is complex real ext-real Element of REAL
K367(p,1) is complex real ext-real Element of REAL
p `2 is complex real ext-real Element of REAL
K367(p,2) is complex real ext-real Element of REAL
(p `2) * <i> is complex set
(p `1) + ((p `2) * <i>) is complex set
angle ((euc2cpx a),(euc2cpx p4),(euc2cpx p)) is complex real ext-real set
angle (p4,p,a) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx p),(euc2cpx a)) is complex real ext-real set
angle (p,a,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p),(euc2cpx a),(euc2cpx p4)) is complex real ext-real set
a - p is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p is Relation-like Function-like set
K214((TOP-REAL 2),a,(- p)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),a,(- p)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
a + (- p) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
a - p is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p) is Relation-like Function-like complex-valued set
K251(a,K280(p)) is Relation-like Function-like set
|.(a - p).| is complex real ext-real non negative Element of REAL
sqr (a - p) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((a - p),(a - p)) is Relation-like Function-like set
K339((sqr (a - p))) is complex real ext-real Element of REAL
sqrt K339((sqr (a - p))) is complex real ext-real Element of REAL
|.(p1 - p2).| * |.(a - p).| is complex real ext-real non negative Element of REAL
angle (p2,p3,p1) is complex real ext-real Element of REAL
angle ((euc2cpx p2),(euc2cpx p3),(euc2cpx p1)) is complex real ext-real set
sin (angle (p2,p3,p1)) is complex real ext-real Element of REAL
angle (p,p4,a) is complex real ext-real Element of REAL
angle ((euc2cpx p),(euc2cpx p4),(euc2cpx a)) is complex real ext-real set
sin (angle (p,p4,a)) is complex real ext-real Element of REAL
(sin (angle (p2,p3,p1))) * (sin (angle (p,p4,a))) is complex real ext-real Element of REAL
sin (angle (p3,p2,p1)) is complex real ext-real Element of REAL
- (sin (angle (p3,p2,p1))) is complex real ext-real Element of REAL
(sin (angle (p2,p3,p1))) * (- (sin (angle (p3,p2,p1)))) is complex real ext-real Element of REAL
sin (angle (p,a,p4)) is complex real ext-real Element of REAL
- (sin (angle (p,a,p4))) is complex real ext-real Element of REAL
(- (sin (angle (p,a,p4)))) * (- (sin (angle (p3,p2,p1)))) is complex real ext-real Element of REAL
angle (p4,a,p) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx a),(euc2cpx p)) is complex real ext-real set
sin (angle (p4,a,p)) is complex real ext-real Element of REAL
(sin (angle (p4,a,p))) * (- (sin (angle (p3,p2,p1)))) is complex real ext-real Element of REAL
angle (p1,p2,p3) is complex real ext-real Element of REAL
angle ((euc2cpx p1),(euc2cpx p2),(euc2cpx p3)) is complex real ext-real set
sin (angle (p1,p2,p3)) is complex real ext-real Element of REAL
(sin (angle (p1,p2,p3))) * (sin (angle (p4,a,p))) is complex real ext-real Element of REAL
(|.(p1 - p2).| * |.(a - p).|) * (sin (angle (p1,p2,p3))) is complex real ext-real Element of REAL
((|.(p1 - p2).| * |.(a - p).|) * (sin (angle (p1,p2,p3)))) * (sin (angle (p4,a,p))) is complex real ext-real Element of REAL
|.(p1 - p2).| * (sin (angle (p1,p2,p3))) is complex real ext-real Element of REAL
|.(a - p).| * (sin (angle (p4,a,p))) is complex real ext-real Element of REAL
(|.(p1 - p2).| * (sin (angle (p1,p2,p3)))) * (|.(a - p).| * (sin (angle (p4,a,p)))) is complex real ext-real Element of REAL
p1 - p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p3 is Relation-like Function-like set
K214((TOP-REAL 2),p1,(- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p3) is Relation-like Function-like complex-valued set
K251(p1,K280(p3)) is Relation-like Function-like set
|.(p1 - p3).| is complex real ext-real non negative Element of REAL
sqr (p1 - p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p1 - p3),(p1 - p3)) is Relation-like Function-like set
K339((sqr (p1 - p3))) is complex real ext-real Element of REAL
sqrt K339((sqr (p1 - p3))) is complex real ext-real Element of REAL
|.(p1 - p3).| * (sin (angle (p2,p3,p1))) is complex real ext-real Element of REAL
(|.(p1 - p3).| * (sin (angle (p2,p3,p1)))) * (|.(a - p).| * (sin (angle (p4,a,p)))) is complex real ext-real Element of REAL
p - a is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- a is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- a is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * a is Relation-like Function-like set
K214((TOP-REAL 2),p,(- a)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p,(- a)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p + (- a) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p - a is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(a) is Relation-like Function-like complex-valued set
K251(p,K280(a)) is Relation-like Function-like set
|.(p - a).| is complex real ext-real non negative Element of REAL
sqr (p - a) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p - a),(p - a)) is Relation-like Function-like set
K339((sqr (p - a))) is complex real ext-real Element of REAL
sqrt K339((sqr (p - a))) is complex real ext-real Element of REAL
|.(p - a).| * (sin (angle (p4,a,p))) is complex real ext-real Element of REAL
(|.(p1 - p3).| * (sin (angle (p2,p3,p1)))) * (|.(p - a).| * (sin (angle (p4,a,p)))) is complex real ext-real Element of REAL
|.(p - p4).| * (sin (angle (p,p4,a))) is complex real ext-real Element of REAL
(|.(p1 - p3).| * (sin (angle (p2,p3,p1)))) * (|.(p - p4).| * (sin (angle (p,p4,a)))) is complex real ext-real Element of REAL
|.(p1 - p3).| * |.(p - p4).| is complex real ext-real non negative Element of REAL
(|.(p1 - p3).| * |.(p - p4).|) * (sin (angle (p2,p3,p1))) is complex real ext-real Element of REAL
((|.(p1 - p3).| * |.(p - p4).|) * (sin (angle (p2,p3,p1)))) * (sin (angle (p,p4,a))) is complex real ext-real Element of REAL
(|.(p1 - p2).| * |.(a - p).|) * ((sin (angle (p1,p2,p3))) * (sin (angle (p4,a,p)))) is complex real ext-real Element of REAL
((|.(p1 - p2).| * |.(a - p).|) * ((sin (angle (p1,p2,p3))) * (sin (angle (p4,a,p))))) / ((sin (angle (p1,p2,p3))) * (sin (angle (p4,a,p)))) is complex real ext-real Element of REAL
(|.(p1 - p3).| * |.(p - p4).|) * ((sin (angle (p2,p3,p1))) * (sin (angle (p,p4,a)))) is complex real ext-real Element of REAL
((|.(p1 - p3).| * |.(p - p4).|) * ((sin (angle (p2,p3,p1))) * (sin (angle (p,p4,a))))) / ((sin (angle (p1,p2,p3))) * (sin (angle (p4,a,p)))) is complex real ext-real Element of REAL
(2 * PI) * 0 is empty complex real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() Element of REAL
(2 * PI) + ((2 * PI) * 0) is non empty complex real ext-real positive non negative Element of REAL
PI + ((2 * PI) * 0) is non empty complex real ext-real positive non negative Element of REAL
(2 * PI) * 0 is empty complex real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() Element of REAL
(2 * PI) + ((2 * PI) * 0) is non empty complex real ext-real positive non negative Element of REAL
PI + ((2 * PI) * 0) is non empty complex real ext-real positive non negative Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 - p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p1 is Relation-like Function-like set
K214((TOP-REAL 2),p2,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p1) is Relation-like Function-like complex-valued set
K251(p2,K280(p1)) is Relation-like Function-like set
|.(p2 - p1).| is complex real ext-real non negative Element of REAL
sqr (p2 - p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p2 - p1),(p2 - p1)) is Relation-like Function-like set
K339((sqr (p2 - p1))) is complex real ext-real Element of REAL
sqrt K339((sqr (p2 - p1))) is complex real ext-real Element of REAL
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p1,p2,p3) is complex real ext-real Element of REAL
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx p2),(euc2cpx p3)) is complex real ext-real set
angle (p3,p1,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p3),(euc2cpx p1),(euc2cpx p2)) is complex real ext-real set
p3 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p2 is Relation-like Function-like set
K214((TOP-REAL 2),p3,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p2) is Relation-like Function-like complex-valued set
K251(p3,K280(p2)) is Relation-like Function-like set
|.(p3 - p2).| is complex real ext-real non negative Element of REAL
sqr (p3 - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p3 - p2),(p3 - p2)) is Relation-like Function-like set
K339((sqr (p3 - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr (p3 - p2))) is complex real ext-real Element of REAL
p1 - p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p3 is Relation-like Function-like set
K214((TOP-REAL 2),p1,(- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p3) is Relation-like Function-like complex-valued set
K251(p1,K280(p3)) is Relation-like Function-like set
|.(p1 - p3).| is complex real ext-real non negative Element of REAL
sqr (p1 - p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p1 - p3),(p1 - p3)) is Relation-like Function-like set
K339((sqr (p1 - p3))) is complex real ext-real Element of REAL
sqrt K339((sqr (p1 - p3))) is complex real ext-real Element of REAL
p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p - p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p4 is Relation-like Function-like set
K214((TOP-REAL 2),p,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p + (- p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p - p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p4) is Relation-like Function-like complex-valued set
K251(p,K280(p4)) is Relation-like Function-like set
|.(p - p4).| is complex real ext-real non negative Element of REAL
sqr (p - p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p - p4),(p - p4)) is Relation-like Function-like set
K339((sqr (p - p4))) is complex real ext-real Element of REAL
sqrt K339((sqr (p - p4))) is complex real ext-real Element of REAL
|.(p3 - p2).| * |.(p - p4).| is complex real ext-real non negative Element of REAL
|.(p1 - p3).| * |.(p - p4).| is complex real ext-real non negative Element of REAL
a is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p4,p,a) is complex real ext-real Element of REAL
euc2cpx p4 is complex Element of COMPLEX
p4 `1 is complex real ext-real Element of REAL
K367(p4,1) is complex real ext-real Element of REAL
p4 `2 is complex real ext-real Element of REAL
K367(p4,2) is complex real ext-real Element of REAL
(p4 `2) * <i> is complex set
(p4 `1) + ((p4 `2) * <i>) is complex set
euc2cpx p is complex Element of COMPLEX
p `1 is complex real ext-real Element of REAL
K367(p,1) is complex real ext-real Element of REAL
p `2 is complex real ext-real Element of REAL
K367(p,2) is complex real ext-real Element of REAL
(p `2) * <i> is complex set
(p `1) + ((p `2) * <i>) is complex set
euc2cpx a is complex Element of COMPLEX
a `1 is complex real ext-real Element of REAL
K367(a,1) is complex real ext-real Element of REAL
a `2 is complex real ext-real Element of REAL
K367(a,2) is complex real ext-real Element of REAL
(a `2) * <i> is complex set
(a `1) + ((a `2) * <i>) is complex set
angle ((euc2cpx p4),(euc2cpx p),(euc2cpx a)) is complex real ext-real set
angle (a,p4,p) is complex real ext-real Element of REAL
angle ((euc2cpx a),(euc2cpx p4),(euc2cpx p)) is complex real ext-real set
p4 - a is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- a is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- a is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * a is Relation-like Function-like set
K214((TOP-REAL 2),p4,(- a)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p4,(- a)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p4 + (- a) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p4 - a is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(a) is Relation-like Function-like complex-valued set
K251(p4,K280(a)) is Relation-like Function-like set
|.(p4 - a).| is complex real ext-real non negative Element of REAL
sqr (p4 - a) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p4 - a),(p4 - a)) is Relation-like Function-like set
K339((sqr (p4 - a))) is complex real ext-real Element of REAL
sqrt K339((sqr (p4 - a))) is complex real ext-real Element of REAL
|.(p3 - p2).| * |.(p4 - a).| is complex real ext-real non negative Element of REAL
a - p is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p is Relation-like Function-like set
K214((TOP-REAL 2),a,(- p)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),a,(- p)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
a + (- p) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
a - p is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p) is Relation-like Function-like complex-valued set
K251(a,K280(p)) is Relation-like Function-like set
|.(a - p).| is complex real ext-real non negative Element of REAL
sqr (a - p) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((a - p),(a - p)) is Relation-like Function-like set
K339((sqr (a - p))) is complex real ext-real Element of REAL
sqrt K339((sqr (a - p))) is complex real ext-real Element of REAL
|.(p1 - p3).| * |.(a - p).| is complex real ext-real non negative Element of REAL
|.(p2 - p1).| * |.(a - p).| is complex real ext-real non negative Element of REAL
|.(p2 - p1).| * |.(p4 - a).| is complex real ext-real non negative Element of REAL
angle (p,a,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p),(euc2cpx a),(euc2cpx p4)) is complex real ext-real set
angle (p2,p3,p1) is complex real ext-real Element of REAL
angle ((euc2cpx p2),(euc2cpx p3),(euc2cpx p1)) is complex real ext-real set
(angle (p3,p1,p2)) + (angle (p1,p2,p3)) is complex real ext-real Element of REAL
((angle (p3,p1,p2)) + (angle (p1,p2,p3))) + (angle (p2,p3,p1)) is complex real ext-real Element of REAL
(angle (a,p4,p)) + (angle (p4,p,a)) is complex real ext-real Element of REAL
((angle (a,p4,p)) + (angle (p4,p,a))) + (angle (p,a,p4)) is complex real ext-real Element of REAL
(angle (p3,p1,p2)) + (angle (p1,p2,p3)) is complex real ext-real Element of REAL
((angle (p3,p1,p2)) + (angle (p1,p2,p3))) + (angle (p2,p3,p1)) is complex real ext-real Element of REAL
(angle (a,p4,p)) + (angle (p4,p,a)) is complex real ext-real Element of REAL
((angle (a,p4,p)) + (angle (p4,p,a))) + (angle (p,a,p4)) is complex real ext-real Element of REAL
(angle (p3,p1,p2)) + (angle (p1,p2,p3)) is complex real ext-real Element of REAL
((angle (p3,p1,p2)) + (angle (p1,p2,p3))) + (angle (p2,p3,p1)) is complex real ext-real Element of REAL
(angle (a,p4,p)) + (angle (p4,p,a)) is complex real ext-real Element of REAL
((angle (a,p4,p)) + (angle (p4,p,a))) + (angle (p,a,p4)) is complex real ext-real Element of REAL
- (angle (p,a,p4)) is complex real ext-real Element of REAL
- (2 * PI) is non empty complex real ext-real non positive negative Element of REAL
(angle (p2,p3,p1)) + (- (angle (p,a,p4))) is complex real ext-real Element of REAL
0 + (- (2 * PI)) is non empty complex real ext-real non positive negative Element of REAL
(angle (p2,p3,p1)) - (angle (p,a,p4)) is complex real ext-real Element of REAL
- (4 * PI) is non empty complex real ext-real non positive negative Element of REAL
(2 * PI) / PI is non empty complex real ext-real positive non negative Element of REAL
(4 * PI) / PI is non empty complex real ext-real positive non negative Element of REAL
(angle (p3,p1,p2)) + (angle (p1,p2,p3)) is complex real ext-real Element of REAL
((angle (p3,p1,p2)) + (angle (p1,p2,p3))) + (angle (p2,p3,p1)) is complex real ext-real Element of REAL
(angle (a,p4,p)) + (angle (p4,p,a)) is complex real ext-real Element of REAL
((angle (a,p4,p)) + (angle (p4,p,a))) + (angle (p,a,p4)) is complex real ext-real Element of REAL
- 0 is empty complex real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() Element of REAL
(2 * PI) + (- 0) is non empty complex real ext-real positive non negative Element of REAL
- (angle (p,a,p4)) is complex real ext-real Element of REAL
(angle (p2,p3,p1)) + (- (angle (p,a,p4))) is complex real ext-real Element of REAL
(2 * PI) / PI is non empty complex real ext-real positive non negative Element of REAL
(4 * PI) / PI is non empty complex real ext-real positive non negative Element of REAL
(angle (p3,p1,p2)) + (angle (p1,p2,p3)) is complex real ext-real Element of REAL
((angle (p3,p1,p2)) + (angle (p1,p2,p3))) + (angle (p2,p3,p1)) is complex real ext-real Element of REAL
(angle (a,p4,p)) + (angle (p4,p,a)) is complex real ext-real Element of REAL
((angle (a,p4,p)) + (angle (p4,p,a))) + (angle (p,a,p4)) is complex real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 - p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p1 is Relation-like Function-like set
K214((TOP-REAL 2),p2,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p1) is Relation-like Function-like complex-valued set
K251(p2,K280(p1)) is Relation-like Function-like set
|.(p2 - p1).| is complex real ext-real non negative Element of REAL
sqr (p2 - p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p2 - p1),(p2 - p1)) is Relation-like Function-like set
K339((sqr (p2 - p1))) is complex real ext-real Element of REAL
sqrt K339((sqr (p2 - p1))) is complex real ext-real Element of REAL
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p3,p2,p1) is complex real ext-real Element of REAL
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
angle ((euc2cpx p3),(euc2cpx p2),(euc2cpx p1)) is complex real ext-real set
angle (p2,p1,p3) is complex real ext-real Element of REAL
angle ((euc2cpx p2),(euc2cpx p1),(euc2cpx p3)) is complex real ext-real set
angle (p1,p3,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p1),(euc2cpx p3),(euc2cpx p2)) is complex real ext-real set
p1 - p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p3 is Relation-like Function-like set
K214((TOP-REAL 2),p1,(- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p3) is Relation-like Function-like complex-valued set
K251(p1,K280(p3)) is Relation-like Function-like set
|.(p1 - p3).| is complex real ext-real non negative Element of REAL
sqr (p1 - p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p1 - p3),(p1 - p3)) is Relation-like Function-like set
K339((sqr (p1 - p3))) is complex real ext-real Element of REAL
sqrt K339((sqr (p1 - p3))) is complex real ext-real Element of REAL
p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p - p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p4 is Relation-like Function-like set
K214((TOP-REAL 2),p,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p + (- p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p - p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p4) is Relation-like Function-like complex-valued set
K251(p,K280(p4)) is Relation-like Function-like set
|.(p - p4).| is complex real ext-real non negative Element of REAL
sqr (p - p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p - p4),(p - p4)) is Relation-like Function-like set
K339((sqr (p - p4))) is complex real ext-real Element of REAL
sqrt K339((sqr (p - p4))) is complex real ext-real Element of REAL
|.(p1 - p3).| * |.(p - p4).| is complex real ext-real non negative Element of REAL
a is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p4,p,a) is complex real ext-real Element of REAL
euc2cpx p4 is complex Element of COMPLEX
p4 `1 is complex real ext-real Element of REAL
K367(p4,1) is complex real ext-real Element of REAL
p4 `2 is complex real ext-real Element of REAL
K367(p4,2) is complex real ext-real Element of REAL
(p4 `2) * <i> is complex set
(p4 `1) + ((p4 `2) * <i>) is complex set
euc2cpx p is complex Element of COMPLEX
p `1 is complex real ext-real Element of REAL
K367(p,1) is complex real ext-real Element of REAL
p `2 is complex real ext-real Element of REAL
K367(p,2) is complex real ext-real Element of REAL
(p `2) * <i> is complex set
(p `1) + ((p `2) * <i>) is complex set
euc2cpx a is complex Element of COMPLEX
a `1 is complex real ext-real Element of REAL
K367(a,1) is complex real ext-real Element of REAL
a `2 is complex real ext-real Element of REAL
K367(a,2) is complex real ext-real Element of REAL
(a `2) * <i> is complex set
(a `1) + ((a `2) * <i>) is complex set
angle ((euc2cpx p4),(euc2cpx p),(euc2cpx a)) is complex real ext-real set
angle (p,a,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p),(euc2cpx a),(euc2cpx p4)) is complex real ext-real set
angle (a,p4,p) is complex real ext-real Element of REAL
angle ((euc2cpx a),(euc2cpx p4),(euc2cpx p)) is complex real ext-real set
p4 - a is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- a is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- a is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * a is Relation-like Function-like set
K214((TOP-REAL 2),p4,(- a)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p4,(- a)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p4 + (- a) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p4 - a is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(a) is Relation-like Function-like complex-valued set
K251(p4,K280(a)) is Relation-like Function-like set
|.(p4 - a).| is complex real ext-real non negative Element of REAL
sqr (p4 - a) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p4 - a),(p4 - a)) is Relation-like Function-like set
K339((sqr (p4 - a))) is complex real ext-real Element of REAL
sqrt K339((sqr (p4 - a))) is complex real ext-real Element of REAL
|.(p2 - p1).| * |.(p4 - a).| is complex real ext-real non negative Element of REAL
sin (angle (p3,p2,p1)) is complex real ext-real Element of REAL
angle (p4,a,p) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx a),(euc2cpx p)) is complex real ext-real set
sin (angle (p4,a,p)) is complex real ext-real Element of REAL
(sin (angle (p3,p2,p1))) * (sin (angle (p4,a,p))) is complex real ext-real Element of REAL
sin (angle (p4,p,a)) is complex real ext-real Element of REAL
sin (angle (p,a,p4)) is complex real ext-real Element of REAL
- (sin (angle (p,a,p4))) is complex real ext-real Element of REAL
(sin (angle (p4,p,a))) * (- (sin (angle (p,a,p4)))) is complex real ext-real Element of REAL
angle (a,p,p4) is complex real ext-real Element of REAL
angle ((euc2cpx a),(euc2cpx p),(euc2cpx p4)) is complex real ext-real set
sin (angle (a,p,p4)) is complex real ext-real Element of REAL
- (sin (angle (a,p,p4))) is complex real ext-real Element of REAL
sin (angle (p1,p3,p2)) is complex real ext-real Element of REAL
- (sin (angle (p1,p3,p2))) is complex real ext-real Element of REAL
(- (sin (angle (a,p,p4)))) * (- (sin (angle (p1,p3,p2)))) is complex real ext-real Element of REAL
(sin (angle (a,p,p4))) * (sin (angle (p1,p3,p2))) is complex real ext-real Element of REAL
p4 - p is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p is Relation-like Function-like set
K214((TOP-REAL 2),p4,(- p)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p4,(- p)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p4 + (- p) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p4 - p is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p) is Relation-like Function-like complex-valued set
K251(p4,K280(p)) is Relation-like Function-like set
|.(p4 - p).| is complex real ext-real non negative Element of REAL
sqr (p4 - p) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p4 - p),(p4 - p)) is Relation-like Function-like set
K339((sqr (p4 - p))) is complex real ext-real Element of REAL
sqrt K339((sqr (p4 - p))) is complex real ext-real Element of REAL
|.(p4 - p).| * (sin (angle (a,p,p4))) is complex real ext-real Element of REAL
|.(p4 - a).| * (sin (angle (p4,a,p))) is complex real ext-real Element of REAL
p1 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p2 is Relation-like Function-like set
K214((TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p2) is Relation-like Function-like complex-valued set
K251(p1,K280(p2)) is Relation-like Function-like set
|.(p1 - p2).| is complex real ext-real non negative Element of REAL
sqr (p1 - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p1 - p2),(p1 - p2)) is Relation-like Function-like set
K339((sqr (p1 - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr (p1 - p2))) is complex real ext-real Element of REAL
|.(p1 - p2).| * |.(p4 - a).| is complex real ext-real non negative Element of REAL
(|.(p1 - p2).| * |.(p4 - a).|) * (sin (angle (p3,p2,p1))) is complex real ext-real Element of REAL
((|.(p1 - p2).| * |.(p4 - a).|) * (sin (angle (p3,p2,p1)))) * (sin (angle (p4,a,p))) is complex real ext-real Element of REAL
|.(p1 - p2).| * (sin (angle (p3,p2,p1))) is complex real ext-real Element of REAL
(|.(p1 - p2).| * (sin (angle (p3,p2,p1)))) * (|.(p4 - a).| * (sin (angle (p4,a,p)))) is complex real ext-real Element of REAL
|.(p1 - p3).| * (sin (angle (p1,p3,p2))) is complex real ext-real Element of REAL
(|.(p1 - p3).| * (sin (angle (p1,p3,p2)))) * (|.(p4 - p).| * (sin (angle (a,p,p4)))) is complex real ext-real Element of REAL
|.(p1 - p3).| * |.(p4 - p).| is complex real ext-real non negative Element of REAL
(|.(p1 - p3).| * |.(p4 - p).|) * (sin (angle (a,p,p4))) is complex real ext-real Element of REAL
((|.(p1 - p3).| * |.(p4 - p).|) * (sin (angle (a,p,p4)))) * (sin (angle (p1,p3,p2))) is complex real ext-real Element of REAL
(|.(p1 - p2).| * |.(p4 - a).|) * ((sin (angle (p3,p2,p1))) * (sin (angle (p4,a,p)))) is complex real ext-real Element of REAL
((|.(p1 - p2).| * |.(p4 - a).|) * ((sin (angle (p3,p2,p1))) * (sin (angle (p4,a,p))))) / ((sin (angle (p3,p2,p1))) * (sin (angle (p4,a,p)))) is complex real ext-real Element of REAL
(|.(p1 - p3).| * |.(p4 - p).|) * ((sin (angle (a,p,p4))) * (sin (angle (p1,p3,p2)))) is complex real ext-real Element of REAL
((|.(p1 - p3).| * |.(p4 - p).|) * ((sin (angle (a,p,p4))) * (sin (angle (p1,p3,p2))))) / ((sin (angle (a,p,p4))) * (sin (angle (p1,p3,p2)))) is complex real ext-real Element of REAL
(2 * PI) * 0 is empty complex real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() Element of REAL
(2 * PI) + ((2 * PI) * 0) is non empty complex real ext-real positive non negative Element of REAL
PI + ((2 * PI) * 0) is non empty complex real ext-real positive non negative Element of REAL
(2 * PI) * 0 is empty complex real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() Element of REAL
(2 * PI) + ((2 * PI) * 0) is non empty complex real ext-real positive non negative Element of REAL
PI + ((2 * PI) * 0) is non empty complex real ext-real positive non negative Element of REAL
angle (p,p4,a) is complex real ext-real Element of REAL
angle ((euc2cpx p),(euc2cpx p4),(euc2cpx a)) is complex real ext-real set
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p2 is Relation-like Function-like set
K214((TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p2) is Relation-like Function-like complex-valued set
K251(p1,K280(p2)) is Relation-like Function-like set
|.(p1 - p2).| is complex real ext-real non negative Element of REAL
sqr (p1 - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p1 - p2),(p1 - p2)) is Relation-like Function-like set
K339((sqr (p1 - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr (p1 - p2))) is complex real ext-real Element of REAL
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p1,p2,p3) is complex real ext-real Element of REAL
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx p2),(euc2cpx p3)) is complex real ext-real set
angle (p3,p1,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p3),(euc2cpx p1),(euc2cpx p2)) is complex real ext-real set
p2 - p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p3 is Relation-like Function-like set
K214((TOP-REAL 2),p2,(- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p3) is Relation-like Function-like complex-valued set
K251(p2,K280(p3)) is Relation-like Function-like set
|.(p2 - p3).| is complex real ext-real non negative Element of REAL
sqr (p2 - p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p2 - p3),(p2 - p3)) is Relation-like Function-like set
K339((sqr (p2 - p3))) is complex real ext-real Element of REAL
sqrt K339((sqr (p2 - p3))) is complex real ext-real Element of REAL
p3 - p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p1 is Relation-like Function-like set
K214((TOP-REAL 2),p3,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p1) is Relation-like Function-like complex-valued set
K251(p3,K280(p1)) is Relation-like Function-like set
|.(p3 - p1).| is complex real ext-real non negative Element of REAL
sqr (p3 - p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p3 - p1),(p3 - p1)) is Relation-like Function-like set
K339((sqr (p3 - p1))) is complex real ext-real Element of REAL
sqrt K339((sqr (p3 - p1))) is complex real ext-real Element of REAL
p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p - p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p4 is Relation-like Function-like set
K214((TOP-REAL 2),p,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p + (- p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p - p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p4) is Relation-like Function-like complex-valued set
K251(p,K280(p4)) is Relation-like Function-like set
|.(p - p4).| is complex real ext-real non negative Element of REAL
sqr (p - p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p - p4),(p - p4)) is Relation-like Function-like set
K339((sqr (p - p4))) is complex real ext-real Element of REAL
sqrt K339((sqr (p - p4))) is complex real ext-real Element of REAL
|.(p3 - p1).| * |.(p - p4).| is complex real ext-real non negative Element of REAL
|.(p1 - p2).| * |.(p - p4).| is complex real ext-real non negative Element of REAL
a is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p4,p,a) is complex real ext-real Element of REAL
euc2cpx p4 is complex Element of COMPLEX
p4 `1 is complex real ext-real Element of REAL
K367(p4,1) is complex real ext-real Element of REAL
p4 `2 is complex real ext-real Element of REAL
K367(p4,2) is complex real ext-real Element of REAL
(p4 `2) * <i> is complex set
(p4 `1) + ((p4 `2) * <i>) is complex set
euc2cpx p is complex Element of COMPLEX
p `1 is complex real ext-real Element of REAL
K367(p,1) is complex real ext-real Element of REAL
p `2 is complex real ext-real Element of REAL
K367(p,2) is complex real ext-real Element of REAL
(p `2) * <i> is complex set
(p `1) + ((p `2) * <i>) is complex set
euc2cpx a is complex Element of COMPLEX
a `1 is complex real ext-real Element of REAL
K367(a,1) is complex real ext-real Element of REAL
a `2 is complex real ext-real Element of REAL
K367(a,2) is complex real ext-real Element of REAL
(a `2) * <i> is complex set
(a `1) + ((a `2) * <i>) is complex set
angle ((euc2cpx p4),(euc2cpx p),(euc2cpx a)) is complex real ext-real set
angle (p,a,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p),(euc2cpx a),(euc2cpx p4)) is complex real ext-real set
p4 - a is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- a is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- a is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * a is Relation-like Function-like set
K214((TOP-REAL 2),p4,(- a)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p4,(- a)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p4 + (- a) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p4 - a is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(a) is Relation-like Function-like complex-valued set
K251(p4,K280(a)) is Relation-like Function-like set
|.(p4 - a).| is complex real ext-real non negative Element of REAL
sqr (p4 - a) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p4 - a),(p4 - a)) is Relation-like Function-like set
K339((sqr (p4 - a))) is complex real ext-real Element of REAL
sqrt K339((sqr (p4 - a))) is complex real ext-real Element of REAL
|.(p2 - p3).| * |.(p4 - a).| is complex real ext-real non negative Element of REAL
a - p is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p is Relation-like Function-like set
K214((TOP-REAL 2),a,(- p)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),a,(- p)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
a + (- p) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
a - p is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p) is Relation-like Function-like complex-valued set
K251(a,K280(p)) is Relation-like Function-like set
|.(a - p).| is complex real ext-real non negative Element of REAL
sqr (a - p) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((a - p),(a - p)) is Relation-like Function-like set
K339((sqr (a - p))) is complex real ext-real Element of REAL
sqrt K339((sqr (a - p))) is complex real ext-real Element of REAL
|.(p2 - p3).| * |.(a - p).| is complex real ext-real non negative Element of REAL
|.(p3 - p1).| * |.(a - p).| is complex real ext-real non negative Element of REAL
|.(p1 - p2).| * |.(p4 - a).| is complex real ext-real non negative Element of REAL
angle (a,p4,p) is complex real ext-real Element of REAL
angle ((euc2cpx a),(euc2cpx p4),(euc2cpx p)) is complex real ext-real set
angle (p2,p3,p1) is complex real ext-real Element of REAL
angle ((euc2cpx p2),(euc2cpx p3),(euc2cpx p1)) is complex real ext-real set
(angle (p3,p1,p2)) + (angle (p1,p2,p3)) is complex real ext-real Element of REAL
((angle (p3,p1,p2)) + (angle (p1,p2,p3))) + (angle (p2,p3,p1)) is complex real ext-real Element of REAL
(angle (p,a,p4)) + (angle (a,p4,p)) is complex real ext-real Element of REAL
((angle (p,a,p4)) + (angle (a,p4,p))) + (angle (p4,p,a)) is complex real ext-real Element of REAL
(angle (p3,p1,p2)) + (angle (p1,p2,p3)) is complex real ext-real Element of REAL
((angle (p3,p1,p2)) + (angle (p1,p2,p3))) + (angle (p2,p3,p1)) is complex real ext-real Element of REAL
(angle (p,a,p4)) + (angle (a,p4,p)) is complex real ext-real Element of REAL
((angle (p,a,p4)) + (angle (a,p4,p))) + (angle (p4,p,a)) is complex real ext-real Element of REAL
(angle (p3,p1,p2)) + (angle (p1,p2,p3)) is complex real ext-real Element of REAL
((angle (p3,p1,p2)) + (angle (p1,p2,p3))) + (angle (p2,p3,p1)) is complex real ext-real Element of REAL
(angle (p,a,p4)) + (angle (a,p4,p)) is complex real ext-real Element of REAL
((angle (p,a,p4)) + (angle (a,p4,p))) + (angle (p4,p,a)) is complex real ext-real Element of REAL
- (angle (a,p4,p)) is complex real ext-real Element of REAL
- (2 * PI) is non empty complex real ext-real non positive negative Element of REAL
(angle (p2,p3,p1)) + (- (angle (a,p4,p))) is complex real ext-real Element of REAL
0 + (- (2 * PI)) is non empty complex real ext-real non positive negative Element of REAL
(angle (p2,p3,p1)) - (angle (a,p4,p)) is complex real ext-real Element of REAL
- (4 * PI) is non empty complex real ext-real non positive negative Element of REAL
(2 * PI) / PI is non empty complex real ext-real positive non negative Element of REAL
(4 * PI) / PI is non empty complex real ext-real positive non negative Element of REAL
(angle (p3,p1,p2)) + (angle (p1,p2,p3)) is complex real ext-real Element of REAL
((angle (p3,p1,p2)) + (angle (p1,p2,p3))) + (angle (p2,p3,p1)) is complex real ext-real Element of REAL
(angle (p,a,p4)) + (angle (a,p4,p)) is complex real ext-real Element of REAL
((angle (p,a,p4)) + (angle (a,p4,p))) + (angle (p4,p,a)) is complex real ext-real Element of REAL
- 0 is empty complex real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() Element of REAL
(2 * PI) + (- 0) is non empty complex real ext-real positive non negative Element of REAL
- (angle (a,p4,p)) is complex real ext-real Element of REAL
(angle (p2,p3,p1)) + (- (angle (a,p4,p))) is complex real ext-real Element of REAL
(2 * PI) / PI is non empty complex real ext-real positive non negative Element of REAL
(4 * PI) / PI is non empty complex real ext-real positive non negative Element of REAL
(angle (p3,p1,p2)) + (angle (p1,p2,p3)) is complex real ext-real Element of REAL
((angle (p3,p1,p2)) + (angle (p1,p2,p3))) + (angle (p2,p3,p1)) is complex real ext-real Element of REAL
(angle (p,a,p4)) + (angle (a,p4,p)) is complex real ext-real Element of REAL
((angle (p,a,p4)) + (angle (a,p4,p))) + (angle (p4,p,a)) is complex real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p1,p2,p3) is complex real ext-real Element of REAL
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx p2),(euc2cpx p3)) is complex real ext-real set
angle (p2,p3,p1) is complex real ext-real Element of REAL
angle ((euc2cpx p2),(euc2cpx p3),(euc2cpx p1)) is complex real ext-real set
angle (p3,p1,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p3),(euc2cpx p1),(euc2cpx p2)) is complex real ext-real set
(angle (p1,p2,p3)) + (angle (p2,p3,p1)) is complex real ext-real Element of REAL
((angle (p1,p2,p3)) + (angle (p2,p3,p1))) + (angle (p3,p1,p2)) is complex real ext-real Element of REAL
(2 * PI) + (2 * PI) is non empty complex real ext-real positive non negative Element of REAL
(angle (p2,p3,p1)) + (angle (p3,p1,p2)) is complex real ext-real Element of REAL
PI + (4 * PI) is non empty complex real ext-real positive non negative Element of REAL
(angle (p1,p2,p3)) + ((angle (p2,p3,p1)) + (angle (p3,p1,p2))) is complex real ext-real Element of REAL
0 + PI is non empty complex real ext-real positive non negative Element of REAL
0 + PI is non empty complex real ext-real positive non negative Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p1,p2,p3) is complex real ext-real Element of REAL
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx p2),(euc2cpx p3)) is complex real ext-real set
angle (p2,p3,p1) is complex real ext-real Element of REAL
angle ((euc2cpx p2),(euc2cpx p3),(euc2cpx p1)) is complex real ext-real set
angle (p3,p1,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p3),(euc2cpx p1),(euc2cpx p2)) is complex real ext-real set
p1 is natural complex real ext-real V33() V34() V126() V127() V128() V129() V130() V131() Element of NAT
TOP-REAL p1 is non empty V73() V138() V139() TopSpace-like V186() V187() V188() V189() V190() V191() V192() strict RLTopStruct
the carrier of (TOP-REAL p1) is non empty set
[: the carrier of (TOP-REAL p1), the carrier of R^1:] is complex-valued ext-real-valued real-valued set
bool [: the carrier of (TOP-REAL p1), the carrier of R^1:] is set
p2 is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
p3 is non empty Relation-like the carrier of (TOP-REAL p1) -defined the carrier of R^1 -valued Function-like total V30( the carrier of (TOP-REAL p1), the carrier of R^1) complex-valued ext-real-valued real-valued Element of bool [: the carrier of (TOP-REAL p1), the carrier of R^1:]
the topology of (TOP-REAL p1) is non empty Element of bool (bool the carrier of (TOP-REAL p1))
bool the carrier of (TOP-REAL p1) is set
bool (bool the carrier of (TOP-REAL p1)) is set
TopStruct(# the carrier of (TOP-REAL p1), the topology of (TOP-REAL p1) #) is non empty strict TopSpace-like TopStruct
Euclid p1 is non empty strict Reflexive discerning V180() triangle Discerning MetrStruct
REAL p1 is non empty FinSequence-membered M10( REAL )
K318(p1,REAL) is FinSequence-membered M10( REAL )
Pitag_dist p1 is Relation-like [:(REAL p1),(REAL p1):] -defined REAL -valued Function-like total V30([:(REAL p1),(REAL p1):], REAL ) complex-valued ext-real-valued real-valued Element of bool [:[:(REAL p1),(REAL p1):],REAL:]
[:(REAL p1),(REAL p1):] is set
[:[:(REAL p1),(REAL p1):],REAL:] is complex-valued ext-real-valued real-valued set
bool [:[:(REAL p1),(REAL p1):],REAL:] is set
MetrStruct(# (REAL p1),(Pitag_dist p1) #) is strict MetrStruct
TopSpaceMetr (Euclid p1) is TopStruct
the carrier of (TopSpaceMetr (Euclid p1)) is set
the carrier of (TopSpaceMetr RealSpace) is set
[: the carrier of (TopSpaceMetr (Euclid p1)), the carrier of (TopSpaceMetr RealSpace):] is set
bool [: the carrier of (TopSpaceMetr (Euclid p1)), the carrier of (TopSpaceMetr RealSpace):] is set
the carrier of (Euclid p1) is non empty set
the carrier of RealSpace is non empty V126() V127() V128() set
p is complex real ext-real set
b is complex real ext-real Element of the carrier of RealSpace
p4 is Relation-like the carrier of (TopSpaceMetr (Euclid p1)) -defined the carrier of (TopSpaceMetr RealSpace) -valued Function-like V30( the carrier of (TopSpaceMetr (Euclid p1)), the carrier of (TopSpaceMetr RealSpace)) Element of bool [: the carrier of (TopSpaceMetr (Euclid p1)), the carrier of (TopSpaceMetr RealSpace):]
a is Element of the carrier of (Euclid p1)
p4 . a is set
p5 is Element of the carrier of (Euclid p1)
p4 . p5 is set
dist (a,p5) is complex real ext-real Element of REAL
z2 is complex real ext-real Element of the carrier of RealSpace
dist (b,z2) is complex real ext-real Element of REAL
the distance of RealSpace is Relation-like [: the carrier of RealSpace, the carrier of RealSpace:] -defined REAL -valued Function-like total V30([: the carrier of RealSpace, the carrier of RealSpace:], REAL ) complex-valued ext-real-valued real-valued Element of bool [:[: the carrier of RealSpace, the carrier of RealSpace:],REAL:]
[: the carrier of RealSpace, the carrier of RealSpace:] is complex-valued ext-real-valued real-valued set
[:[: the carrier of RealSpace, the carrier of RealSpace:],REAL:] is complex-valued ext-real-valued real-valued set
bool [:[: the carrier of RealSpace, the carrier of RealSpace:],REAL:] is set
the distance of RealSpace . (b,z2) is complex real ext-real Element of REAL
f0 is complex real ext-real Element of REAL
d is complex real ext-real Element of REAL
f0 - d is complex real ext-real Element of REAL
abs (f0 - d) is complex real ext-real Element of REAL
Re (f0 - d) is complex real ext-real Element of REAL
(Re (f0 - d)) ^2 is complex real ext-real Element of REAL
(Re (f0 - d)) * (Re (f0 - d)) is complex real ext-real set
Im (f0 - d) is complex real ext-real Element of REAL
(Im (f0 - d)) ^2 is complex real ext-real Element of REAL
(Im (f0 - d)) * (Im (f0 - d)) is complex real ext-real set
((Re (f0 - d)) ^2) + ((Im (f0 - d)) ^2) is complex real ext-real Element of REAL
sqrt (((Re (f0 - d)) ^2) + ((Im (f0 - d)) ^2)) is complex real ext-real Element of REAL
f6 is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
f6 - p2 is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
- p2 is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
- p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p2 is Relation-like Function-like set
K214((TOP-REAL p1),f6,(- p2)) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
the U5 of (TOP-REAL p1) is Relation-like [: the carrier of (TOP-REAL p1), the carrier of (TOP-REAL p1):] -defined the carrier of (TOP-REAL p1) -valued Function-like total V30([: the carrier of (TOP-REAL p1), the carrier of (TOP-REAL p1):], the carrier of (TOP-REAL p1)) Element of bool [:[: the carrier of (TOP-REAL p1), the carrier of (TOP-REAL p1):], the carrier of (TOP-REAL p1):]
[: the carrier of (TOP-REAL p1), the carrier of (TOP-REAL p1):] is set
[:[: the carrier of (TOP-REAL p1), the carrier of (TOP-REAL p1):], the carrier of (TOP-REAL p1):] is set
bool [:[: the carrier of (TOP-REAL p1), the carrier of (TOP-REAL p1):], the carrier of (TOP-REAL p1):] is set
K414( the carrier of (TOP-REAL p1), the U5 of (TOP-REAL p1),f6,(- p2)) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
f6 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
f6 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p2) is Relation-like Function-like complex-valued set
K251(f6,K280(p2)) is Relation-like Function-like set
|.(f6 - p2).| is complex real ext-real non negative Element of REAL
sqr (f6 - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((f6 - p2),(f6 - p2)) is Relation-like Function-like set
K339((sqr (f6 - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr (f6 - p2))) is complex real ext-real Element of REAL
f2 is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
f2 - p2 is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
K214((TOP-REAL p1),f2,(- p2)) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
K414( the carrier of (TOP-REAL p1), the U5 of (TOP-REAL p1),f2,(- p2)) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
f2 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
f2 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(f2,K280(p2)) is Relation-like Function-like set
(f6 - p2) - (f2 - p2) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
- (f2 - p2) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
- (f2 - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * (f2 - p2) is Relation-like Function-like set
K214((TOP-REAL p1),(f6 - p2),(- (f2 - p2))) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
K414( the carrier of (TOP-REAL p1), the U5 of (TOP-REAL p1),(f6 - p2),(- (f2 - p2))) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
(f6 - p2) + (- (f2 - p2)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(f6 - p2) - (f2 - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280((f2 - p2)) is Relation-like Function-like complex-valued set
K251((f6 - p2),K280((f2 - p2))) is Relation-like Function-like set
|.((f6 - p2) - (f2 - p2)).| is complex real ext-real non negative Element of REAL
sqr ((f6 - p2) - (f2 - p2)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt (((f6 - p2) - (f2 - p2)),((f6 - p2) - (f2 - p2))) is Relation-like Function-like set
K339((sqr ((f6 - p2) - (f2 - p2)))) is complex real ext-real Element of REAL
sqrt K339((sqr ((f6 - p2) - (f2 - p2)))) is complex real ext-real Element of REAL
(- p2) + f2 is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
K414( the carrier of (TOP-REAL p1), the U5 of (TOP-REAL p1),(- p2),f2) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
(- p2) + f2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(f6 - p2) - ((- p2) + f2) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
- ((- p2) + f2) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
- ((- p2) + f2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * ((- p2) + f2) is Relation-like Function-like set
K214((TOP-REAL p1),(f6 - p2),(- ((- p2) + f2))) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
K414( the carrier of (TOP-REAL p1), the U5 of (TOP-REAL p1),(f6 - p2),(- ((- p2) + f2))) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
(f6 - p2) + (- ((- p2) + f2)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(f6 - p2) - ((- p2) + f2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(((- p2) + f2)) is Relation-like Function-like complex-valued set
K251((f6 - p2),K280(((- p2) + f2))) is Relation-like Function-like set
|.((f6 - p2) - ((- p2) + f2)).| is complex real ext-real non negative Element of REAL
sqr ((f6 - p2) - ((- p2) + f2)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt (((f6 - p2) - ((- p2) + f2)),((f6 - p2) - ((- p2) + f2))) is Relation-like Function-like set
K339((sqr ((f6 - p2) - ((- p2) + f2)))) is complex real ext-real Element of REAL
sqrt K339((sqr ((f6 - p2) - ((- p2) + f2)))) is complex real ext-real Element of REAL
(f6 - p2) - (- p2) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
- (- p2) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
- (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * (- p2) is Relation-like Function-like set
K214((TOP-REAL p1),(f6 - p2),(- (- p2))) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
K414( the carrier of (TOP-REAL p1), the U5 of (TOP-REAL p1),(f6 - p2),(- (- p2))) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
(f6 - p2) + (- (- p2)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(f6 - p2) - (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280((- p2)) is Relation-like Function-like complex-valued set
K251((f6 - p2),K280((- p2))) is Relation-like Function-like set
((f6 - p2) - (- p2)) - f2 is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
- f2 is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
- f2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * f2 is Relation-like Function-like set
K214((TOP-REAL p1),((f6 - p2) - (- p2)),(- f2)) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
K414( the carrier of (TOP-REAL p1), the U5 of (TOP-REAL p1),((f6 - p2) - (- p2)),(- f2)) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
((f6 - p2) - (- p2)) + (- f2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((f6 - p2) - (- p2)) - f2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(f2) is Relation-like Function-like complex-valued set
K251(((f6 - p2) - (- p2)),K280(f2)) is Relation-like Function-like set
|.(((f6 - p2) - (- p2)) - f2).| is complex real ext-real non negative Element of REAL
sqr (((f6 - p2) - (- p2)) - f2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((((f6 - p2) - (- p2)) - f2),(((f6 - p2) - (- p2)) - f2)) is Relation-like Function-like set
K339((sqr (((f6 - p2) - (- p2)) - f2))) is complex real ext-real Element of REAL
sqrt K339((sqr (((f6 - p2) - (- p2)) - f2))) is complex real ext-real Element of REAL
f6 + (- p2) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
(f6 + (- p2)) + p2 is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
K414( the carrier of (TOP-REAL p1), the U5 of (TOP-REAL p1),(f6 + (- p2)),p2) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
(f6 + (- p2)) + p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((f6 + (- p2)) + p2) - f2 is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
K214((TOP-REAL p1),((f6 + (- p2)) + p2),(- f2)) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
K414( the carrier of (TOP-REAL p1), the U5 of (TOP-REAL p1),((f6 + (- p2)) + p2),(- f2)) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
((f6 + (- p2)) + p2) + (- f2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((f6 + (- p2)) + p2) - f2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(((f6 + (- p2)) + p2),K280(f2)) is Relation-like Function-like set
|.(((f6 + (- p2)) + p2) - f2).| is complex real ext-real non negative Element of REAL
sqr (((f6 + (- p2)) + p2) - f2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((((f6 + (- p2)) + p2) - f2),(((f6 + (- p2)) + p2) - f2)) is Relation-like Function-like set
K339((sqr (((f6 + (- p2)) + p2) - f2))) is complex real ext-real Element of REAL
sqrt K339((sqr (((f6 + (- p2)) + p2) - f2))) is complex real ext-real Element of REAL
p2 - p2 is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
K214((TOP-REAL p1),p2,(- p2)) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
K414( the carrier of (TOP-REAL p1), the U5 of (TOP-REAL p1),p2,(- p2)) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
p2 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p2,K280(p2)) is Relation-like Function-like set
f6 + (p2 - p2) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
K414( the carrier of (TOP-REAL p1), the U5 of (TOP-REAL p1),f6,(p2 - p2)) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
f6 + (p2 - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(f6 + (p2 - p2)) - f2 is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
K214((TOP-REAL p1),(f6 + (p2 - p2)),(- f2)) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
K414( the carrier of (TOP-REAL p1), the U5 of (TOP-REAL p1),(f6 + (p2 - p2)),(- f2)) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
(f6 + (p2 - p2)) + (- f2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(f6 + (p2 - p2)) - f2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251((f6 + (p2 - p2)),K280(f2)) is Relation-like Function-like set
|.((f6 + (p2 - p2)) - f2).| is complex real ext-real non negative Element of REAL
sqr ((f6 + (p2 - p2)) - f2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt (((f6 + (p2 - p2)) - f2),((f6 + (p2 - p2)) - f2)) is Relation-like Function-like set
K339((sqr ((f6 + (p2 - p2)) - f2))) is complex real ext-real Element of REAL
sqrt K339((sqr ((f6 + (p2 - p2)) - f2))) is complex real ext-real Element of REAL
0. (TOP-REAL p1) is Relation-like Function-like V42(p1) FinSequence-like zero complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
f6 + (0. (TOP-REAL p1)) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
K414( the carrier of (TOP-REAL p1), the U5 of (TOP-REAL p1),f6,(0. (TOP-REAL p1))) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
f6 + (0. (TOP-REAL p1)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(f6 + (0. (TOP-REAL p1))) - f2 is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
K214((TOP-REAL p1),(f6 + (0. (TOP-REAL p1))),(- f2)) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
K414( the carrier of (TOP-REAL p1), the U5 of (TOP-REAL p1),(f6 + (0. (TOP-REAL p1))),(- f2)) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
(f6 + (0. (TOP-REAL p1))) + (- f2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(f6 + (0. (TOP-REAL p1))) - f2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251((f6 + (0. (TOP-REAL p1))),K280(f2)) is Relation-like Function-like set
|.((f6 + (0. (TOP-REAL p1))) - f2).| is complex real ext-real non negative Element of REAL
sqr ((f6 + (0. (TOP-REAL p1))) - f2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt (((f6 + (0. (TOP-REAL p1))) - f2),((f6 + (0. (TOP-REAL p1))) - f2)) is Relation-like Function-like set
K339((sqr ((f6 + (0. (TOP-REAL p1))) - f2))) is complex real ext-real Element of REAL
sqrt K339((sqr ((f6 + (0. (TOP-REAL p1))) - f2))) is complex real ext-real Element of REAL
f6 - f2 is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
K214((TOP-REAL p1),f6,(- f2)) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
K414( the carrier of (TOP-REAL p1), the U5 of (TOP-REAL p1),f6,(- f2)) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
f6 + (- f2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
f6 - f2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(f6,K280(f2)) is Relation-like Function-like set
|.(f6 - f2).| is complex real ext-real non negative Element of REAL
sqr (f6 - f2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((f6 - f2),(f6 - f2)) is Relation-like Function-like set
K339((sqr (f6 - f2))) is complex real ext-real Element of REAL
sqrt K339((sqr (f6 - f2))) is complex real ext-real Element of REAL
|.(f2 - p2).| is complex real ext-real non negative Element of REAL
sqr (f2 - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((f2 - p2),(f2 - p2)) is Relation-like Function-like set
K339((sqr (f2 - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr (f2 - p2))) is complex real ext-real Element of REAL
p1 is natural complex real ext-real V33() V34() V126() V127() V128() V129() V130() V131() Element of NAT
TOP-REAL p1 is non empty V73() V138() V139() TopSpace-like V186() V187() V188() V189() V190() V191() V192() strict RLTopStruct
the carrier of (TOP-REAL p1) is non empty set
[: the carrier of (TOP-REAL p1), the carrier of R^1:] is complex-valued ext-real-valued real-valued set
bool [: the carrier of (TOP-REAL p1), the carrier of R^1:] is set
p2 is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
p3 is set
p4 is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
p4 - p2 is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
- p2 is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
- p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p2 is Relation-like Function-like set
K214((TOP-REAL p1),p4,(- p2)) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
the U5 of (TOP-REAL p1) is Relation-like [: the carrier of (TOP-REAL p1), the carrier of (TOP-REAL p1):] -defined the carrier of (TOP-REAL p1) -valued Function-like total V30([: the carrier of (TOP-REAL p1), the carrier of (TOP-REAL p1):], the carrier of (TOP-REAL p1)) Element of bool [:[: the carrier of (TOP-REAL p1), the carrier of (TOP-REAL p1):], the carrier of (TOP-REAL p1):]
[: the carrier of (TOP-REAL p1), the carrier of (TOP-REAL p1):] is set
[:[: the carrier of (TOP-REAL p1), the carrier of (TOP-REAL p1):], the carrier of (TOP-REAL p1):] is set
bool [:[: the carrier of (TOP-REAL p1), the carrier of (TOP-REAL p1):], the carrier of (TOP-REAL p1):] is set
K414( the carrier of (TOP-REAL p1), the U5 of (TOP-REAL p1),p4,(- p2)) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
p4 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p4 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p2) is Relation-like Function-like complex-valued set
K251(p4,K280(p2)) is Relation-like Function-like set
|.(p4 - p2).| is complex real ext-real non negative Element of REAL
sqr (p4 - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p4 - p2),(p4 - p2)) is Relation-like Function-like set
K339((sqr (p4 - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr (p4 - p2))) is complex real ext-real Element of REAL
p3 is Relation-like Function-like set
dom p3 is set
rng p3 is set
p4 is set
p is set
p3 . p is set
a is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
a - p2 is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
- p2 is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
- p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p2 is Relation-like Function-like set
K214((TOP-REAL p1),a,(- p2)) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
the U5 of (TOP-REAL p1) is Relation-like [: the carrier of (TOP-REAL p1), the carrier of (TOP-REAL p1):] -defined the carrier of (TOP-REAL p1) -valued Function-like total V30([: the carrier of (TOP-REAL p1), the carrier of (TOP-REAL p1):], the carrier of (TOP-REAL p1)) Element of bool [:[: the carrier of (TOP-REAL p1), the carrier of (TOP-REAL p1):], the carrier of (TOP-REAL p1):]
[: the carrier of (TOP-REAL p1), the carrier of (TOP-REAL p1):] is set
[:[: the carrier of (TOP-REAL p1), the carrier of (TOP-REAL p1):], the carrier of (TOP-REAL p1):] is set
bool [:[: the carrier of (TOP-REAL p1), the carrier of (TOP-REAL p1):], the carrier of (TOP-REAL p1):] is set
K414( the carrier of (TOP-REAL p1), the U5 of (TOP-REAL p1),a,(- p2)) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
a + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
a - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p2) is Relation-like Function-like complex-valued set
K251(a,K280(p2)) is Relation-like Function-like set
|.(a - p2).| is complex real ext-real non negative Element of REAL
sqr (a - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((a - p2),(a - p2)) is Relation-like Function-like set
K339((sqr (a - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr (a - p2))) is complex real ext-real Element of REAL
p is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
p3 . p is set
p - p2 is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
- p2 is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
- p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p2 is Relation-like Function-like set
K214((TOP-REAL p1),p,(- p2)) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
the U5 of (TOP-REAL p1) is Relation-like [: the carrier of (TOP-REAL p1), the carrier of (TOP-REAL p1):] -defined the carrier of (TOP-REAL p1) -valued Function-like total V30([: the carrier of (TOP-REAL p1), the carrier of (TOP-REAL p1):], the carrier of (TOP-REAL p1)) Element of bool [:[: the carrier of (TOP-REAL p1), the carrier of (TOP-REAL p1):], the carrier of (TOP-REAL p1):]
[: the carrier of (TOP-REAL p1), the carrier of (TOP-REAL p1):] is set
[:[: the carrier of (TOP-REAL p1), the carrier of (TOP-REAL p1):], the carrier of (TOP-REAL p1):] is set
bool [:[: the carrier of (TOP-REAL p1), the carrier of (TOP-REAL p1):], the carrier of (TOP-REAL p1):] is set
K414( the carrier of (TOP-REAL p1), the U5 of (TOP-REAL p1),p,(- p2)) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
p + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p2) is Relation-like Function-like complex-valued set
K251(p,K280(p2)) is Relation-like Function-like set
|.(p - p2).| is complex real ext-real non negative Element of REAL
sqr (p - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p - p2),(p - p2)) is Relation-like Function-like set
K339((sqr (p - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr (p - p2))) is complex real ext-real Element of REAL
a is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
a - p2 is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
K214((TOP-REAL p1),a,(- p2)) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
K414( the carrier of (TOP-REAL p1), the U5 of (TOP-REAL p1),a,(- p2)) is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
a + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
a - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(a,K280(p2)) is Relation-like Function-like set
|.(a - p2).| is complex real ext-real non negative Element of REAL
sqr (a - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((a - p2),(a - p2)) is Relation-like Function-like set
K339((sqr (a - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr (a - p2))) is complex real ext-real Element of REAL
p4 is non empty Relation-like the carrier of (TOP-REAL p1) -defined the carrier of R^1 -valued Function-like total V30( the carrier of (TOP-REAL p1), the carrier of R^1) complex-valued ext-real-valued real-valued Element of bool [: the carrier of (TOP-REAL p1), the carrier of R^1:]
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
LSeg (p2,p3) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p2) + (b1 * p3)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p2,p4,p3) is complex real ext-real Element of REAL
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
euc2cpx p4 is complex Element of COMPLEX
p4 `1 is complex real ext-real Element of REAL
K367(p4,1) is complex real ext-real Element of REAL
p4 `2 is complex real ext-real Element of REAL
K367(p4,2) is complex real ext-real Element of REAL
(p4 `2) * <i> is complex set
(p4 `1) + ((p4 `2) * <i>) is complex set
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
angle ((euc2cpx p2),(euc2cpx p4),(euc2cpx p3)) is complex real ext-real set
angle (p1,p4,p3) is complex real ext-real Element of REAL
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx p4),(euc2cpx p3)) is complex real ext-real set
angle (p4,p2,p3) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx p2),(euc2cpx p3)) is complex real ext-real set
LSeg (p3,p4) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p3) + (b1 * p4)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
LSeg (p4,p2) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p4) + (b1 * p2)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
p3 - p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p4 is Relation-like Function-like set
K214((TOP-REAL 2),p3,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (- p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p4) is Relation-like Function-like complex-valued set
K251(p3,K280(p4)) is Relation-like Function-like set
|.(p3 - p4).| is complex real ext-real non negative Element of REAL
sqr (p3 - p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p3 - p4),(p3 - p4)) is Relation-like Function-like set
K339((sqr (p3 - p4))) is complex real ext-real Element of REAL
sqrt K339((sqr (p3 - p4))) is complex real ext-real Element of REAL
angle (p3,p4,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p3),(euc2cpx p4),(euc2cpx p2)) is complex real ext-real set
angle (p2,p3,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p2),(euc2cpx p3),(euc2cpx p4)) is complex real ext-real set
angle (p4,p3,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx p3),(euc2cpx p2)) is complex real ext-real set
angle (p3,p2,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p3),(euc2cpx p2),(euc2cpx p4)) is complex real ext-real set
angle (p4,p3,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx p3),(euc2cpx p2)) is complex real ext-real set
angle (p4,p3,p1) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx p3),(euc2cpx p1)) is complex real ext-real set
angle (p3,p2,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p3),(euc2cpx p2),(euc2cpx p4)) is complex real ext-real set
angle (p3,p1,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p3),(euc2cpx p1),(euc2cpx p4)) is complex real ext-real set
(angle (p2,p4,p3)) + (angle (p4,p3,p2)) is complex real ext-real Element of REAL
((angle (p2,p4,p3)) + (angle (p4,p3,p2))) + (angle (p3,p2,p4)) is complex real ext-real Element of REAL
(angle (p1,p4,p3)) + (angle (p4,p3,p1)) is complex real ext-real Element of REAL
((angle (p1,p4,p3)) + (angle (p4,p3,p1))) + (angle (p3,p1,p4)) is complex real ext-real Element of REAL
(angle (p2,p4,p3)) + (angle (p4,p3,p2)) is complex real ext-real Element of REAL
((angle (p2,p4,p3)) + (angle (p4,p3,p2))) + (angle (p3,p2,p4)) is complex real ext-real Element of REAL
(angle (p1,p4,p3)) + (angle (p4,p3,p1)) is complex real ext-real Element of REAL
((angle (p1,p4,p3)) + (angle (p4,p3,p1))) + (angle (p3,p1,p4)) is complex real ext-real Element of REAL
(angle (p2,p4,p3)) + (angle (p4,p3,p2)) is complex real ext-real Element of REAL
((angle (p2,p4,p3)) + (angle (p4,p3,p2))) + (angle (p3,p2,p4)) is complex real ext-real Element of REAL
(angle (p1,p4,p3)) + (angle (p4,p3,p1)) is complex real ext-real Element of REAL
((angle (p1,p4,p3)) + (angle (p4,p3,p1))) + (angle (p3,p1,p4)) is complex real ext-real Element of REAL
- (angle (p3,p1,p4)) is complex real ext-real Element of REAL
- (2 * PI) is non empty complex real ext-real non positive negative Element of REAL
(angle (p3,p2,p4)) + (- (angle (p3,p1,p4))) is complex real ext-real Element of REAL
0 + (- (2 * PI)) is non empty complex real ext-real non positive negative Element of REAL
(angle (p3,p2,p4)) - (angle (p3,p1,p4)) is complex real ext-real Element of REAL
- (4 * PI) is non empty complex real ext-real non positive negative Element of REAL
(2 * PI) / PI is non empty complex real ext-real positive non negative Element of REAL
(4 * PI) / PI is non empty complex real ext-real positive non negative Element of REAL
(angle (p2,p4,p3)) + (angle (p4,p3,p2)) is complex real ext-real Element of REAL
((angle (p2,p4,p3)) + (angle (p4,p3,p2))) + (angle (p3,p2,p4)) is complex real ext-real Element of REAL
(angle (p1,p4,p3)) + (angle (p4,p3,p1)) is complex real ext-real Element of REAL
((angle (p1,p4,p3)) + (angle (p4,p3,p1))) + (angle (p3,p1,p4)) is complex real ext-real Element of REAL
- 0 is empty complex real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() Element of REAL
(2 * PI) + (- 0) is non empty complex real ext-real positive non negative Element of REAL
- (angle (p3,p1,p4)) is complex real ext-real Element of REAL
(angle (p3,p2,p4)) + (- (angle (p3,p1,p4))) is complex real ext-real Element of REAL
(2 * PI) / PI is non empty complex real ext-real positive non negative Element of REAL
(4 * PI) / PI is non empty complex real ext-real positive non negative Element of REAL
(angle (p2,p4,p3)) + (angle (p4,p3,p2)) is complex real ext-real Element of REAL
((angle (p2,p4,p3)) + (angle (p4,p3,p2))) + (angle (p3,p2,p4)) is complex real ext-real Element of REAL
(angle (p1,p4,p3)) + (angle (p4,p3,p1)) is complex real ext-real Element of REAL
((angle (p1,p4,p3)) + (angle (p4,p3,p1))) + (angle (p3,p1,p4)) is complex real ext-real Element of REAL
p1 - p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p3 is Relation-like Function-like set
K214((TOP-REAL 2),p1,(- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p3) is Relation-like Function-like complex-valued set
K251(p1,K280(p3)) is Relation-like Function-like set
|.(p1 - p3).| is complex real ext-real non negative Element of REAL
sqr (p1 - p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p1 - p3),(p1 - p3)) is Relation-like Function-like set
K339((sqr (p1 - p3))) is complex real ext-real Element of REAL
sqrt K339((sqr (p1 - p3))) is complex real ext-real Element of REAL
|.(p3 - p4).| * |.(p1 - p3).| is complex real ext-real non negative Element of REAL
p2 - p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p2,(- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p2,K280(p3)) is Relation-like Function-like set
|.(p2 - p3).| is complex real ext-real non negative Element of REAL
sqr (p2 - p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p2 - p3),(p2 - p3)) is Relation-like Function-like set
K339((sqr (p2 - p3))) is complex real ext-real Element of REAL
sqrt K339((sqr (p2 - p3))) is complex real ext-real Element of REAL
|.(p2 - p3).| * |.(p3 - p4).| is complex real ext-real non negative Element of REAL
p3 - p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p1 is Relation-like Function-like set
K214((TOP-REAL 2),p3,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p1) is Relation-like Function-like complex-valued set
K251(p3,K280(p1)) is Relation-like Function-like set
|.(p3 - p1).| is complex real ext-real non negative Element of REAL
sqr (p3 - p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p3 - p1),(p3 - p1)) is Relation-like Function-like set
K339((sqr (p3 - p1))) is complex real ext-real Element of REAL
sqrt K339((sqr (p3 - p1))) is complex real ext-real Element of REAL
p3 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p2 is Relation-like Function-like set
K214((TOP-REAL 2),p3,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p2) is Relation-like Function-like complex-valued set
K251(p3,K280(p2)) is Relation-like Function-like set
|.(p3 - p2).| is complex real ext-real non negative Element of REAL
sqr (p3 - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p3 - p2),(p3 - p2)) is Relation-like Function-like set
K339((sqr (p3 - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr (p3 - p2))) is complex real ext-real Element of REAL
|.(p3 - p2).| ^2 is complex real ext-real Element of REAL
|.(p3 - p2).| * |.(p3 - p2).| is complex real ext-real non negative set
p2 - p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p2,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p2,K280(p1)) is Relation-like Function-like set
|.(p2 - p1).| is complex real ext-real non negative Element of REAL
sqr (p2 - p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p2 - p1),(p2 - p1)) is Relation-like Function-like set
K339((sqr (p2 - p1))) is complex real ext-real Element of REAL
sqrt K339((sqr (p2 - p1))) is complex real ext-real Element of REAL
|.(p2 - p1).| ^2 is complex real ext-real Element of REAL
|.(p2 - p1).| * |.(p2 - p1).| is complex real ext-real non negative set
|.(p3 - p1).| ^2 is complex real ext-real Element of REAL
|.(p3 - p1).| * |.(p3 - p1).| is complex real ext-real non negative set
(|.(p2 - p1).| ^2) + (|.(p3 - p1).| ^2) is complex real ext-real Element of REAL
2 * |.(p2 - p1).| is complex real ext-real non negative Element of REAL
(2 * |.(p2 - p1).|) * |.(p3 - p1).| is complex real ext-real non negative Element of REAL
angle (p2,p1,p3) is complex real ext-real Element of REAL
angle ((euc2cpx p2),(euc2cpx p1),(euc2cpx p3)) is complex real ext-real set
cos (angle (p2,p1,p3)) is complex real ext-real Element of REAL
((2 * |.(p2 - p1).|) * |.(p3 - p1).|) * (cos (angle (p2,p1,p3))) is complex real ext-real Element of REAL
((|.(p2 - p1).| ^2) + (|.(p3 - p1).| ^2)) - (((2 * |.(p2 - p1).|) * |.(p3 - p1).|) * (cos (angle (p2,p1,p3)))) is complex real ext-real Element of REAL
((2 * |.(p2 - p1).|) * |.(p3 - p1).|) * (- 1) is complex real ext-real non positive Element of REAL
((|.(p2 - p1).| ^2) + (|.(p3 - p1).| ^2)) - (((2 * |.(p2 - p1).|) * |.(p3 - p1).|) * (- 1)) is complex real ext-real Element of REAL
2 * |.(p3 - p1).| is complex real ext-real non negative Element of REAL
|.(p2 - p1).| + (2 * |.(p3 - p1).|) is complex real ext-real non negative Element of REAL
2 * |.(p3 - p1).| is complex real ext-real non negative Element of REAL
|.(p2 - p1).| + (2 * |.(p3 - p1).|) is complex real ext-real non negative Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
LSeg (p2,p3) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p2) + (b1 * p3)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p2,p4,p3) is complex real ext-real Element of REAL
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
euc2cpx p4 is complex Element of COMPLEX
p4 `1 is complex real ext-real Element of REAL
K367(p4,1) is complex real ext-real Element of REAL
p4 `2 is complex real ext-real Element of REAL
K367(p4,2) is complex real ext-real Element of REAL
(p4 `2) * <i> is complex set
(p4 `1) + ((p4 `2) * <i>) is complex set
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
angle ((euc2cpx p2),(euc2cpx p4),(euc2cpx p3)) is complex real ext-real set
angle (p1,p4,p3) is complex real ext-real Element of REAL
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx p4),(euc2cpx p3)) is complex real ext-real set
{p3} is non empty set
angle (p4,p3,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx p3),(euc2cpx p2)) is complex real ext-real set
angle (p4,p3,p1) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx p3),(euc2cpx p1)) is complex real ext-real set
angle (p3,p2,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p3),(euc2cpx p2),(euc2cpx p4)) is complex real ext-real set
(angle (p2,p4,p3)) + (angle (p3,p2,p4)) is complex real ext-real Element of REAL
angle (p3,p1,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p3),(euc2cpx p1),(euc2cpx p4)) is complex real ext-real set
(angle (p1,p4,p3)) + (angle (p3,p1,p4)) is complex real ext-real Element of REAL
(angle (p2,p4,p3)) + (angle (p4,p3,p2)) is complex real ext-real Element of REAL
((angle (p2,p4,p3)) + (angle (p4,p3,p2))) + (angle (p3,p2,p4)) is complex real ext-real Element of REAL
(angle (p1,p4,p3)) + (angle (p4,p3,p1)) is complex real ext-real Element of REAL
((angle (p1,p4,p3)) + (angle (p4,p3,p1))) + (angle (p3,p1,p4)) is complex real ext-real Element of REAL
(angle (p2,p4,p3)) + (angle (p4,p3,p2)) is complex real ext-real Element of REAL
((angle (p2,p4,p3)) + (angle (p4,p3,p2))) + (angle (p3,p2,p4)) is complex real ext-real Element of REAL
(angle (p1,p4,p3)) + (angle (p4,p3,p1)) is complex real ext-real Element of REAL
((angle (p1,p4,p3)) + (angle (p4,p3,p1))) + (angle (p3,p1,p4)) is complex real ext-real Element of REAL
(angle (p2,p4,p3)) + (angle (p4,p3,p2)) is complex real ext-real Element of REAL
((angle (p2,p4,p3)) + (angle (p4,p3,p2))) + (angle (p3,p2,p4)) is complex real ext-real Element of REAL
(angle (p1,p4,p3)) + (angle (p4,p3,p1)) is complex real ext-real Element of REAL
((angle (p1,p4,p3)) + (angle (p4,p3,p1))) + (angle (p3,p1,p4)) is complex real ext-real Element of REAL
- (angle (p3,p1,p4)) is complex real ext-real Element of REAL
- (2 * PI) is non empty complex real ext-real non positive negative Element of REAL
- (angle (p1,p4,p3)) is complex real ext-real Element of REAL
(- (angle (p1,p4,p3))) + (- (angle (p3,p1,p4))) is complex real ext-real Element of REAL
(- (2 * PI)) + (- (2 * PI)) is non empty complex real ext-real non positive negative Element of REAL
(- (angle (p1,p4,p3))) - (angle (p3,p1,p4)) is complex real ext-real Element of REAL
((angle (p2,p4,p3)) + (angle (p3,p2,p4))) + ((- (angle (p1,p4,p3))) - (angle (p3,p1,p4))) is complex real ext-real Element of REAL
0 + 0 is empty complex real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() Element of REAL
(- (2 * PI)) - (2 * PI) is non empty complex real ext-real non positive negative Element of REAL
(0 + 0) + ((- (2 * PI)) - (2 * PI)) is non empty complex real ext-real non positive negative Element of REAL
(angle (p2,p4,p3)) + (angle (p4,p3,p2)) is complex real ext-real Element of REAL
((angle (p2,p4,p3)) + (angle (p4,p3,p2))) + (angle (p3,p2,p4)) is complex real ext-real Element of REAL
(angle (p1,p4,p3)) + (angle (p4,p3,p1)) is complex real ext-real Element of REAL
((angle (p1,p4,p3)) + (angle (p4,p3,p1))) + (angle (p3,p1,p4)) is complex real ext-real Element of REAL
(2 * PI) + (2 * PI) is non empty complex real ext-real positive non negative Element of REAL
(angle (p3,p2,p4)) + (angle (p2,p4,p3)) is complex real ext-real Element of REAL
0 + 0 is empty complex real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() Element of REAL
((2 * PI) + (2 * PI)) + (0 + 0) is non empty complex real ext-real positive non negative Element of REAL
- (angle (p1,p4,p3)) is complex real ext-real Element of REAL
(- (angle (p1,p4,p3))) - (angle (p3,p1,p4)) is complex real ext-real Element of REAL
((angle (p3,p2,p4)) + (angle (p2,p4,p3))) + ((- (angle (p1,p4,p3))) - (angle (p3,p1,p4))) is complex real ext-real Element of REAL
(angle (p2,p4,p3)) + (angle (p4,p3,p2)) is complex real ext-real Element of REAL
((angle (p2,p4,p3)) + (angle (p4,p3,p2))) + (angle (p3,p2,p4)) is complex real ext-real Element of REAL
(angle (p1,p4,p3)) + (angle (p4,p3,p1)) is complex real ext-real Element of REAL
((angle (p1,p4,p3)) + (angle (p4,p3,p1))) + (angle (p3,p1,p4)) is complex real ext-real Element of REAL
angle (p4,p1,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx p1),(euc2cpx p2)) is complex real ext-real set
(angle (p3,p1,p4)) + (angle (p4,p1,p2)) is complex real ext-real Element of REAL
angle (p1,p2,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p1),(euc2cpx p2),(euc2cpx p4)) is complex real ext-real set
(angle (p4,p1,p2)) + (angle (p1,p2,p4)) is complex real ext-real Element of REAL
angle (p2,p4,p1) is complex real ext-real Element of REAL
angle ((euc2cpx p2),(euc2cpx p4),(euc2cpx p1)) is complex real ext-real set
((angle (p4,p1,p2)) + (angle (p1,p2,p4))) + (angle (p2,p4,p1)) is complex real ext-real Element of REAL
0 + (angle (p1,p2,p4)) is complex real ext-real Element of REAL
(angle (p2,p4,p1)) + (angle (p1,p2,p4)) is complex real ext-real Element of REAL
angle (p4,p1,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx p1),(euc2cpx p2)) is complex real ext-real set
(angle (p3,p1,p4)) + (angle (p4,p1,p2)) is complex real ext-real Element of REAL
angle (p1,p2,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p1),(euc2cpx p2),(euc2cpx p4)) is complex real ext-real set
(angle (p4,p1,p2)) + (angle (p1,p2,p4)) is complex real ext-real Element of REAL
angle (p2,p4,p1) is complex real ext-real Element of REAL
angle ((euc2cpx p2),(euc2cpx p4),(euc2cpx p1)) is complex real ext-real set
((angle (p4,p1,p2)) + (angle (p1,p2,p4))) + (angle (p2,p4,p1)) is complex real ext-real Element of REAL
(angle (p1,p2,p4)) + (angle (p2,p4,p1)) is complex real ext-real Element of REAL
((angle (p1,p2,p4)) + (angle (p2,p4,p1))) + (2 * PI) is complex real ext-real Element of REAL
0 + (2 * PI) is non empty complex real ext-real positive non negative Element of REAL
angle (p4,p1,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx p1),(euc2cpx p2)) is complex real ext-real set
(angle (p3,p1,p4)) + (angle (p4,p1,p2)) is complex real ext-real Element of REAL
angle (p1,p2,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p1),(euc2cpx p2),(euc2cpx p4)) is complex real ext-real set
(angle (p4,p1,p2)) + (angle (p1,p2,p4)) is complex real ext-real Element of REAL
angle (p2,p4,p1) is complex real ext-real Element of REAL
angle ((euc2cpx p2),(euc2cpx p4),(euc2cpx p1)) is complex real ext-real set
((angle (p4,p1,p2)) + (angle (p1,p2,p4))) + (angle (p2,p4,p1)) is complex real ext-real Element of REAL
(2 * PI) + (2 * PI) is non empty complex real ext-real positive non negative Element of REAL
(angle (p1,p2,p4)) + (angle (p2,p4,p1)) is complex real ext-real Element of REAL
0 + (4 * PI) is non empty complex real ext-real positive non negative Element of REAL
(angle (p3,p1,p4)) + (4 * PI) is complex real ext-real Element of REAL
angle (p4,p1,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx p1),(euc2cpx p2)) is complex real ext-real set
(angle (p3,p1,p4)) + (angle (p4,p1,p2)) is complex real ext-real Element of REAL
angle (p1,p2,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p1),(euc2cpx p2),(euc2cpx p4)) is complex real ext-real set
(angle (p4,p1,p2)) + (angle (p1,p2,p4)) is complex real ext-real Element of REAL
angle (p2,p4,p1) is complex real ext-real Element of REAL
angle ((euc2cpx p2),(euc2cpx p4),(euc2cpx p1)) is complex real ext-real set
((angle (p4,p1,p2)) + (angle (p1,p2,p4))) + (angle (p2,p4,p1)) is complex real ext-real Element of REAL
(angle (p4,p1,p2)) + (angle (p2,p4,p1)) is complex real ext-real Element of REAL
PI + PI is non empty complex real ext-real positive non negative Element of REAL
((angle (p4,p1,p2)) + (angle (p2,p4,p1))) + (angle (p1,p2,p4)) is complex real ext-real Element of REAL
(2 * PI) + PI is non empty complex real ext-real positive non negative Element of REAL
angle (p4,p1,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx p1),(euc2cpx p2)) is complex real ext-real set
(angle (p3,p1,p4)) + (angle (p4,p1,p2)) is complex real ext-real Element of REAL
angle (p1,p2,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p1),(euc2cpx p2),(euc2cpx p4)) is complex real ext-real set
(angle (p4,p1,p2)) + (angle (p1,p2,p4)) is complex real ext-real Element of REAL
angle (p2,p4,p1) is complex real ext-real Element of REAL
angle ((euc2cpx p2),(euc2cpx p4),(euc2cpx p1)) is complex real ext-real set
((angle (p4,p1,p2)) + (angle (p1,p2,p4))) + (angle (p2,p4,p1)) is complex real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
LSeg (p2,p3) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p2) + (b1 * p3)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p2,p4,p3) is complex real ext-real Element of REAL
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
euc2cpx p4 is complex Element of COMPLEX
p4 `1 is complex real ext-real Element of REAL
K367(p4,1) is complex real ext-real Element of REAL
p4 `2 is complex real ext-real Element of REAL
K367(p4,2) is complex real ext-real Element of REAL
(p4 `2) * <i> is complex set
(p4 `1) + ((p4 `2) * <i>) is complex set
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
angle ((euc2cpx p2),(euc2cpx p4),(euc2cpx p3)) is complex real ext-real set
angle (p1,p4,p3) is complex real ext-real Element of REAL
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx p4),(euc2cpx p3)) is complex real ext-real set
{p3} is non empty set
angle (p4,p3,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx p3),(euc2cpx p2)) is complex real ext-real set
angle (p4,p3,p1) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx p3),(euc2cpx p1)) is complex real ext-real set
angle (p3,p2,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p3),(euc2cpx p2),(euc2cpx p4)) is complex real ext-real set
(angle (p2,p4,p3)) + (angle (p3,p2,p4)) is complex real ext-real Element of REAL
angle (p3,p1,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p3),(euc2cpx p1),(euc2cpx p4)) is complex real ext-real set
(angle (p1,p4,p3)) + (angle (p3,p1,p4)) is complex real ext-real Element of REAL
(angle (p2,p4,p3)) + (angle (p4,p3,p2)) is complex real ext-real Element of REAL
((angle (p2,p4,p3)) + (angle (p4,p3,p2))) + (angle (p3,p2,p4)) is complex real ext-real Element of REAL
(angle (p1,p4,p3)) + (angle (p4,p3,p1)) is complex real ext-real Element of REAL
((angle (p1,p4,p3)) + (angle (p4,p3,p1))) + (angle (p3,p1,p4)) is complex real ext-real Element of REAL
(angle (p2,p4,p3)) + (angle (p4,p3,p2)) is complex real ext-real Element of REAL
((angle (p2,p4,p3)) + (angle (p4,p3,p2))) + (angle (p3,p2,p4)) is complex real ext-real Element of REAL
(angle (p1,p4,p3)) + (angle (p4,p3,p1)) is complex real ext-real Element of REAL
((angle (p1,p4,p3)) + (angle (p4,p3,p1))) + (angle (p3,p1,p4)) is complex real ext-real Element of REAL
(angle (p2,p4,p3)) + (angle (p4,p3,p2)) is complex real ext-real Element of REAL
((angle (p2,p4,p3)) + (angle (p4,p3,p2))) + (angle (p3,p2,p4)) is complex real ext-real Element of REAL
(angle (p1,p4,p3)) + (angle (p4,p3,p1)) is complex real ext-real Element of REAL
((angle (p1,p4,p3)) + (angle (p4,p3,p1))) + (angle (p3,p1,p4)) is complex real ext-real Element of REAL
- (angle (p3,p1,p4)) is complex real ext-real Element of REAL
- (2 * PI) is non empty complex real ext-real non positive negative Element of REAL
- (angle (p1,p4,p3)) is complex real ext-real Element of REAL
(- (angle (p1,p4,p3))) + (- (angle (p3,p1,p4))) is complex real ext-real Element of REAL
(- (2 * PI)) + (- (2 * PI)) is non empty complex real ext-real non positive negative Element of REAL
(- (angle (p1,p4,p3))) - (angle (p3,p1,p4)) is complex real ext-real Element of REAL
((angle (p2,p4,p3)) + (angle (p3,p2,p4))) + ((- (angle (p1,p4,p3))) - (angle (p3,p1,p4))) is complex real ext-real Element of REAL
0 + 0 is empty complex real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() Element of REAL
(- (2 * PI)) - (2 * PI) is non empty complex real ext-real non positive negative Element of REAL
(0 + 0) + ((- (2 * PI)) - (2 * PI)) is non empty complex real ext-real non positive negative Element of REAL
(angle (p2,p4,p3)) + (angle (p4,p3,p2)) is complex real ext-real Element of REAL
((angle (p2,p4,p3)) + (angle (p4,p3,p2))) + (angle (p3,p2,p4)) is complex real ext-real Element of REAL
(angle (p1,p4,p3)) + (angle (p4,p3,p1)) is complex real ext-real Element of REAL
((angle (p1,p4,p3)) + (angle (p4,p3,p1))) + (angle (p3,p1,p4)) is complex real ext-real Element of REAL
(2 * PI) + (2 * PI) is non empty complex real ext-real positive non negative Element of REAL
(angle (p3,p2,p4)) + (angle (p2,p4,p3)) is complex real ext-real Element of REAL
0 + 0 is empty complex real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() Element of REAL
((2 * PI) + (2 * PI)) + (0 + 0) is non empty complex real ext-real positive non negative Element of REAL
- (angle (p1,p4,p3)) is complex real ext-real Element of REAL
(- (angle (p1,p4,p3))) - (angle (p3,p1,p4)) is complex real ext-real Element of REAL
((angle (p3,p2,p4)) + (angle (p2,p4,p3))) + ((- (angle (p1,p4,p3))) - (angle (p3,p1,p4))) is complex real ext-real Element of REAL
(angle (p2,p4,p3)) + (angle (p4,p3,p2)) is complex real ext-real Element of REAL
((angle (p2,p4,p3)) + (angle (p4,p3,p2))) + (angle (p3,p2,p4)) is complex real ext-real Element of REAL
(angle (p1,p4,p3)) + (angle (p4,p3,p1)) is complex real ext-real Element of REAL
((angle (p1,p4,p3)) + (angle (p4,p3,p1))) + (angle (p3,p1,p4)) is complex real ext-real Element of REAL
angle (p1,p2,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p1),(euc2cpx p2),(euc2cpx p4)) is complex real ext-real set
angle (p4,p1,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx p1),(euc2cpx p2)) is complex real ext-real set
(angle (p3,p1,p4)) + (angle (p4,p1,p2)) is complex real ext-real Element of REAL
(angle (p4,p1,p2)) + (angle (p1,p2,p4)) is complex real ext-real Element of REAL
angle (p2,p4,p1) is complex real ext-real Element of REAL
angle ((euc2cpx p2),(euc2cpx p4),(euc2cpx p1)) is complex real ext-real set
((angle (p4,p1,p2)) + (angle (p1,p2,p4))) + (angle (p2,p4,p1)) is complex real ext-real Element of REAL
(angle (p4,p1,p2)) + (angle (p2,p4,p1)) is complex real ext-real Element of REAL
PI + PI is non empty complex real ext-real positive non negative Element of REAL
((angle (p4,p1,p2)) + (angle (p2,p4,p1))) + (angle (p1,p2,p4)) is complex real ext-real Element of REAL
(2 * PI) + PI is non empty complex real ext-real positive non negative Element of REAL
1 * PI is non empty complex real ext-real positive non negative Element of REAL
angle (p4,p1,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx p1),(euc2cpx p2)) is complex real ext-real set
(angle (p3,p1,p4)) + (angle (p4,p1,p2)) is complex real ext-real Element of REAL
(angle (p4,p1,p2)) + (angle (p1,p2,p4)) is complex real ext-real Element of REAL
angle (p2,p4,p1) is complex real ext-real Element of REAL
angle ((euc2cpx p2),(euc2cpx p4),(euc2cpx p1)) is complex real ext-real set
((angle (p4,p1,p2)) + (angle (p1,p2,p4))) + (angle (p2,p4,p1)) is complex real ext-real Element of REAL
(angle (p1,p2,p4)) + (angle (p2,p4,p1)) is complex real ext-real Element of REAL
((angle (p1,p2,p4)) + (angle (p2,p4,p1))) + (2 * PI) is complex real ext-real Element of REAL
0 + (2 * PI) is non empty complex real ext-real positive non negative Element of REAL
angle (p4,p1,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx p1),(euc2cpx p2)) is complex real ext-real set
(angle (p3,p1,p4)) + (angle (p4,p1,p2)) is complex real ext-real Element of REAL
(angle (p4,p1,p2)) + (angle (p1,p2,p4)) is complex real ext-real Element of REAL
angle (p2,p4,p1) is complex real ext-real Element of REAL
angle ((euc2cpx p2),(euc2cpx p4),(euc2cpx p1)) is complex real ext-real set
((angle (p4,p1,p2)) + (angle (p1,p2,p4))) + (angle (p2,p4,p1)) is complex real ext-real Element of REAL
(2 * PI) + (2 * PI) is non empty complex real ext-real positive non negative Element of REAL
(angle (p1,p2,p4)) + (angle (p2,p4,p1)) is complex real ext-real Element of REAL
0 + (4 * PI) is non empty complex real ext-real positive non negative Element of REAL
(angle (p3,p1,p4)) + (4 * PI) is complex real ext-real Element of REAL
angle (p4,p1,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx p1),(euc2cpx p2)) is complex real ext-real set
(angle (p3,p1,p4)) + (angle (p4,p1,p2)) is complex real ext-real Element of REAL
(angle (p4,p1,p2)) + (angle (p1,p2,p4)) is complex real ext-real Element of REAL
angle (p2,p4,p1) is complex real ext-real Element of REAL
angle ((euc2cpx p2),(euc2cpx p4),(euc2cpx p1)) is complex real ext-real set
((angle (p4,p1,p2)) + (angle (p1,p2,p4))) + (angle (p2,p4,p1)) is complex real ext-real Element of REAL
(angle (p3,p1,p4)) + (2 * PI) is complex real ext-real Element of REAL
(angle (p1,p2,p4)) + (angle (p2,p4,p1)) is complex real ext-real Element of REAL
(angle (p3,p1,p4)) + (angle (p2,p4,p1)) is complex real ext-real Element of REAL
angle (p4,p1,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx p1),(euc2cpx p2)) is complex real ext-real set
(angle (p3,p1,p4)) + (angle (p4,p1,p2)) is complex real ext-real Element of REAL
(angle (p4,p1,p2)) + (angle (p1,p2,p4)) is complex real ext-real Element of REAL
angle (p2,p4,p1) is complex real ext-real Element of REAL
angle ((euc2cpx p2),(euc2cpx p4),(euc2cpx p1)) is complex real ext-real set
((angle (p4,p1,p2)) + (angle (p1,p2,p4))) + (angle (p2,p4,p1)) is complex real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
LSeg (p2,p3) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p2) + (b1 * p3)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p1,p4,p3) is complex real ext-real Element of REAL
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
euc2cpx p4 is complex Element of COMPLEX
p4 `1 is complex real ext-real Element of REAL
K367(p4,1) is complex real ext-real Element of REAL
p4 `2 is complex real ext-real Element of REAL
K367(p4,2) is complex real ext-real Element of REAL
(p4 `2) * <i> is complex set
(p4 `1) + ((p4 `2) * <i>) is complex set
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx p4),(euc2cpx p3)) is complex real ext-real set
angle (p2,p4,p1) is complex real ext-real Element of REAL
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
angle ((euc2cpx p2),(euc2cpx p4),(euc2cpx p1)) is complex real ext-real set
{p2} is non empty set
LSeg (p3,p4) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p3) + (b1 * p4)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
angle (p2,p4,p2) is complex real ext-real Element of REAL
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
angle ((euc2cpx p2),(euc2cpx p4),(euc2cpx p2)) is complex real ext-real set
LSeg (p4,p3) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p4) + (b1 * p3)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
angle (p3,p4,p3) is complex real ext-real Element of REAL
angle ((euc2cpx p3),(euc2cpx p4),(euc2cpx p3)) is complex real ext-real set
LSeg (p2,p4) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p2) + (b1 * p4)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
angle (p2,p4,p3) is complex real ext-real Element of REAL
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
angle ((euc2cpx p2),(euc2cpx p4),(euc2cpx p3)) is complex real ext-real set
LSeg (p3,p4) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p3) + (b1 * p4)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
LSeg (p2,p4) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p2) + (b1 * p4)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
(TOP-REAL 2) | (LSeg (p2,p3)) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (LSeg (p2,p3))) is non empty set
- 2 is non empty complex real ext-real non positive negative Element of REAL
1 * (- 2) is non empty complex real ext-real non positive negative Element of REAL
cos (angle (p1,p4,p3)) is complex real ext-real Element of REAL
(cos (angle (p1,p4,p3))) * (- 2) is complex real ext-real Element of REAL
a is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like total V30( the carrier of (TOP-REAL 2), the carrier of R^1) complex-valued ext-real-valued real-valued Element of bool [: the carrier of (TOP-REAL 2), the carrier of R^1:]
b is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like total V30( the carrier of (TOP-REAL 2), the carrier of R^1) complex-valued ext-real-valued real-valued Element of bool [: the carrier of (TOP-REAL 2), the carrier of R^1:]
r is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like total V30( the carrier of (TOP-REAL 2), the carrier of R^1) complex-valued ext-real-valued real-valued Element of bool [: the carrier of (TOP-REAL 2), the carrier of R^1:]
p5 is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like total V30( the carrier of (TOP-REAL 2), the carrier of R^1) complex-valued ext-real-valued real-valued Element of bool [: the carrier of (TOP-REAL 2), the carrier of R^1:]
p3 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p2 is Relation-like Function-like set
K214((TOP-REAL 2),p3,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p2) is Relation-like Function-like complex-valued set
K251(p3,K280(p2)) is Relation-like Function-like set
|.(p3 - p2).| is complex real ext-real non negative Element of REAL
sqr (p3 - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p3 - p2),(p3 - p2)) is Relation-like Function-like set
K339((sqr (p3 - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr (p3 - p2))) is complex real ext-real Element of REAL
|.(p3 - p2).| ^2 is complex real ext-real Element of REAL
|.(p3 - p2).| * |.(p3 - p2).| is complex real ext-real non negative set
p2 - p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p4 is Relation-like Function-like set
K214((TOP-REAL 2),p2,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p4) is Relation-like Function-like complex-valued set
K251(p2,K280(p4)) is Relation-like Function-like set
|.(p2 - p4).| is complex real ext-real non negative Element of REAL
sqr (p2 - p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p2 - p4),(p2 - p4)) is Relation-like Function-like set
K339((sqr (p2 - p4))) is complex real ext-real Element of REAL
sqrt K339((sqr (p2 - p4))) is complex real ext-real Element of REAL
|.(p2 - p4).| ^2 is complex real ext-real Element of REAL
|.(p2 - p4).| * |.(p2 - p4).| is complex real ext-real non negative set
p3 - p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p3,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (- p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p3,K280(p4)) is Relation-like Function-like set
|.(p3 - p4).| is complex real ext-real non negative Element of REAL
sqr (p3 - p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p3 - p4),(p3 - p4)) is Relation-like Function-like set
K339((sqr (p3 - p4))) is complex real ext-real Element of REAL
sqrt K339((sqr (p3 - p4))) is complex real ext-real Element of REAL
|.(p3 - p4).| ^2 is complex real ext-real Element of REAL
|.(p3 - p4).| * |.(p3 - p4).| is complex real ext-real non negative set
(|.(p2 - p4).| ^2) + (|.(p3 - p4).| ^2) is complex real ext-real Element of REAL
2 * |.(p2 - p4).| is complex real ext-real non negative Element of REAL
(2 * |.(p2 - p4).|) * |.(p3 - p4).| is complex real ext-real non negative Element of REAL
angle (p2,p4,p3) is complex real ext-real Element of REAL
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
angle ((euc2cpx p2),(euc2cpx p4),(euc2cpx p3)) is complex real ext-real set
cos (angle (p2,p4,p3)) is complex real ext-real Element of REAL
((2 * |.(p2 - p4).|) * |.(p3 - p4).|) * (cos (angle (p2,p4,p3))) is complex real ext-real Element of REAL
((|.(p2 - p4).| ^2) + (|.(p3 - p4).| ^2)) - (((2 * |.(p2 - p4).|) * |.(p3 - p4).|) * (cos (angle (p2,p4,p3)))) is complex real ext-real Element of REAL
[: the carrier of ((TOP-REAL 2) | (LSeg (p2,p3))), the carrier of (TOP-REAL 2):] is set
bool [: the carrier of ((TOP-REAL 2) | (LSeg (p2,p3))), the carrier of (TOP-REAL 2):] is set
f0 is non empty Relation-like the carrier of ((TOP-REAL 2) | (LSeg (p2,p3))) -defined the carrier of (TOP-REAL 2) -valued Function-like total V30( the carrier of ((TOP-REAL 2) | (LSeg (p2,p3))), the carrier of (TOP-REAL 2)) Element of bool [: the carrier of ((TOP-REAL 2) | (LSeg (p2,p3))), the carrier of (TOP-REAL 2):]
p3 - p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p1 is Relation-like Function-like set
K214((TOP-REAL 2),p3,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p1) is Relation-like Function-like complex-valued set
K251(p3,K280(p1)) is Relation-like Function-like set
|.(p3 - p1).| is complex real ext-real non negative Element of REAL
sqr (p3 - p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p3 - p1),(p3 - p1)) is Relation-like Function-like set
K339((sqr (p3 - p1))) is complex real ext-real Element of REAL
sqrt K339((sqr (p3 - p1))) is complex real ext-real Element of REAL
|.(p3 - p1).| ^2 is complex real ext-real Element of REAL
|.(p3 - p1).| * |.(p3 - p1).| is complex real ext-real non negative set
p1 - p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p1,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p1,K280(p4)) is Relation-like Function-like set
|.(p1 - p4).| is complex real ext-real non negative Element of REAL
sqr (p1 - p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p1 - p4),(p1 - p4)) is Relation-like Function-like set
K339((sqr (p1 - p4))) is complex real ext-real Element of REAL
sqrt K339((sqr (p1 - p4))) is complex real ext-real Element of REAL
|.(p1 - p4).| ^2 is complex real ext-real Element of REAL
|.(p1 - p4).| * |.(p1 - p4).| is complex real ext-real non negative set
(|.(p3 - p1).| ^2) - (|.(p1 - p4).| ^2) is complex real ext-real Element of REAL
((|.(p3 - p1).| ^2) - (|.(p1 - p4).| ^2)) - (|.(p3 - p4).| ^2) is complex real ext-real Element of REAL
|.(p1 - p4).| * |.(p3 - p4).| is complex real ext-real non negative Element of REAL
(((|.(p3 - p1).| ^2) - (|.(p1 - p4).| ^2)) - (|.(p3 - p4).| ^2)) / (|.(p1 - p4).| * |.(p3 - p4).|) is complex real ext-real Element of REAL
f2 is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like total V30( the carrier of (TOP-REAL 2), the carrier of R^1) complex-valued ext-real-valued real-valued Element of bool [: the carrier of (TOP-REAL 2), the carrier of R^1:]
angle (p4,p3,p1) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx p3),(euc2cpx p1)) is complex real ext-real set
angle (p3,p1,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p3),(euc2cpx p1),(euc2cpx p4)) is complex real ext-real set
angle (p4,p3,p1) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx p3),(euc2cpx p1)) is complex real ext-real set
angle (p3,p1,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p3),(euc2cpx p1),(euc2cpx p4)) is complex real ext-real set
angle (p4,p3,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx p3),(euc2cpx p2)) is complex real ext-real set
angle (p4,p3,p1) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx p3),(euc2cpx p1)) is complex real ext-real set
angle (p3,p1,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p3),(euc2cpx p1),(euc2cpx p4)) is complex real ext-real set
f6 is Element of the carrier of ((TOP-REAL 2) | (LSeg (p2,p3)))
f6 is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like total V30( the carrier of (TOP-REAL 2), the carrier of R^1) complex-valued ext-real-valued real-valued Element of bool [: the carrier of (TOP-REAL 2), the carrier of R^1:]
[: the carrier of ((TOP-REAL 2) | (LSeg (p2,p3))), the carrier of R^1:] is complex-valued ext-real-valued real-valued set
bool [: the carrier of ((TOP-REAL 2) | (LSeg (p2,p3))), the carrier of R^1:] is set
f6 * f0 is non empty Relation-like the carrier of ((TOP-REAL 2) | (LSeg (p2,p3))) -defined the carrier of R^1 -valued Function-like total V30( the carrier of ((TOP-REAL 2) | (LSeg (p2,p3))), the carrier of R^1) complex-valued ext-real-valued real-valued Element of bool [: the carrier of ((TOP-REAL 2) | (LSeg (p2,p3))), the carrier of R^1:]
f22 is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like total V30( the carrier of (TOP-REAL 2), the carrier of R^1) complex-valued ext-real-valued real-valued Element of bool [: the carrier of (TOP-REAL 2), the carrier of R^1:]
f4 is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like total V30( the carrier of (TOP-REAL 2), the carrier of R^1) complex-valued ext-real-valued real-valued Element of bool [: the carrier of (TOP-REAL 2), the carrier of R^1:]
f5 is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like total V30( the carrier of (TOP-REAL 2), the carrier of R^1) complex-valued ext-real-valued real-valued Element of bool [: the carrier of (TOP-REAL 2), the carrier of R^1:]
f5 * f0 is non empty Relation-like the carrier of ((TOP-REAL 2) | (LSeg (p2,p3))) -defined the carrier of R^1 -valued Function-like total V30( the carrier of ((TOP-REAL 2) | (LSeg (p2,p3))), the carrier of R^1) complex-valued ext-real-valued real-valued Element of bool [: the carrier of ((TOP-REAL 2) | (LSeg (p2,p3))), the carrier of R^1:]
f8 is non empty Relation-like the carrier of ((TOP-REAL 2) | (LSeg (p2,p3))) -defined the carrier of R^1 -valued Function-like total V30( the carrier of ((TOP-REAL 2) | (LSeg (p2,p3))), the carrier of R^1) complex-valued ext-real-valued real-valued continuous Element of bool [: the carrier of ((TOP-REAL 2) | (LSeg (p2,p3))), the carrier of R^1:]
f9 is Element of the carrier of ((TOP-REAL 2) | (LSeg (p2,p3)))
f8 . f9 is complex real ext-real set
f is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
f - p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),f,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),f,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
f + (- p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
f - p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(f,K280(p4)) is Relation-like Function-like set
|.(f - p4).| is complex real ext-real non negative Element of REAL
sqr (f - p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((f - p4),(f - p4)) is Relation-like Function-like set
K339((sqr (f - p4))) is complex real ext-real Element of REAL
sqrt K339((sqr (f - p4))) is complex real ext-real Element of REAL
|.(p2 - p4).| * |.(f - p4).| is complex real ext-real non negative Element of REAL
dom f8 is set
f0 . f9 is set
f6 . (f0 . f9) is complex real ext-real set
f6 . f9 is complex real ext-real set
f2 . f9 is complex real ext-real set
r . f9 is complex real ext-real set
(f2 . f9) * (r . f9) is complex real ext-real set
f9 is Element of the carrier of ((TOP-REAL 2) | (LSeg (p2,p3)))
f8 . f9 is complex real ext-real set
f is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
f - p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),f,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),f,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
f + (- p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
f - p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(f,K280(p4)) is Relation-like Function-like set
|.(f - p4).| is complex real ext-real non negative Element of REAL
sqr (f - p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((f - p4),(f - p4)) is Relation-like Function-like set
K339((sqr (f - p4))) is complex real ext-real Element of REAL
sqrt K339((sqr (f - p4))) is complex real ext-real Element of REAL
|.(p2 - p4).| * |.(f - p4).| is complex real ext-real non negative Element of REAL
f7 is non empty Relation-like the carrier of ((TOP-REAL 2) | (LSeg (p2,p3))) -defined the carrier of R^1 -valued Function-like total V30( the carrier of ((TOP-REAL 2) | (LSeg (p2,p3))), the carrier of R^1) complex-valued ext-real-valued real-valued continuous Element of bool [: the carrier of ((TOP-REAL 2) | (LSeg (p2,p3))), the carrier of R^1:]
f9 is non empty Relation-like the carrier of ((TOP-REAL 2) | (LSeg (p2,p3))) -defined the carrier of R^1 -valued Function-like total V30( the carrier of ((TOP-REAL 2) | (LSeg (p2,p3))), the carrier of R^1) complex-valued ext-real-valued real-valued Element of bool [: the carrier of ((TOP-REAL 2) | (LSeg (p2,p3))), the carrier of R^1:]
[: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg (p2,p3))):] is set
bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg (p2,p3))):] is set
f is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | (LSeg (p2,p3))) -valued Function-like total V30( the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg (p2,p3)))) Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg (p2,p3))):]
f . 0 is set
f . 1 is set
the carrier of (Closed-Interval-TSpace (0,1)) is non empty V126() V127() V128() set
[: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of R^1:] is complex-valued ext-real-valued real-valued set
bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of R^1:] is set
f9 * f is non empty Relation-like the carrier of I[01] -defined the carrier of R^1 -valued Function-like total V30( the carrier of I[01], the carrier of R^1) complex-valued ext-real-valued real-valued Element of bool [: the carrier of I[01], the carrier of R^1:]
[: the carrier of I[01], the carrier of R^1:] is complex-valued ext-real-valued real-valued set
bool [: the carrier of I[01], the carrier of R^1:] is set
g is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of R^1 -valued Function-like total V30( the carrier of (Closed-Interval-TSpace (0,1)), the carrier of R^1) complex-valued ext-real-valued real-valued continuous Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of R^1:]
dom g is set
g . 1 is complex real ext-real set
{ b1 where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
f9 . p3 is complex real ext-real set
(|.(p1 - p4).| ^2) + (|.(p3 - p4).| ^2) is complex real ext-real Element of REAL
2 * |.(p1 - p4).| is complex real ext-real non negative Element of REAL
(2 * |.(p1 - p4).|) * |.(p3 - p4).| is complex real ext-real non negative Element of REAL
((2 * |.(p1 - p4).|) * |.(p3 - p4).|) * (cos (angle (p1,p4,p3))) is complex real ext-real Element of REAL
((|.(p1 - p4).| ^2) + (|.(p3 - p4).| ^2)) - (((2 * |.(p1 - p4).|) * |.(p3 - p4).|) * (cos (angle (p1,p4,p3)))) is complex real ext-real Element of REAL
(|.(p1 - p4).| * |.(p3 - p4).|) * (cos (angle (p1,p4,p3))) is complex real ext-real Element of REAL
(- 2) * ((|.(p1 - p4).| * |.(p3 - p4).|) * (cos (angle (p1,p4,p3)))) is complex real ext-real Element of REAL
((- 2) * ((|.(p1 - p4).| * |.(p3 - p4).|) * (cos (angle (p1,p4,p3))))) / (|.(p1 - p4).| * |.(p3 - p4).|) is complex real ext-real Element of REAL
((|.(p1 - p4).| * |.(p3 - p4).|) * (cos (angle (p1,p4,p3)))) / (|.(p1 - p4).| * |.(p3 - p4).|) is complex real ext-real Element of REAL
(- 2) * (((|.(p1 - p4).| * |.(p3 - p4).|) * (cos (angle (p1,p4,p3)))) / (|.(p1 - p4).| * |.(p3 - p4).|)) is complex real ext-real Element of REAL
(- 2) * (cos (angle (p1,p4,p3))) is complex real ext-real Element of REAL
a is Element of the carrier of ((TOP-REAL 2) | (LSeg (p2,p3)))
f9 . a is complex real ext-real set
rc is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
rc - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),rc,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),rc,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
rc + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
rc - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(rc,K280(p2)) is Relation-like Function-like set
|.(rc - p2).| is complex real ext-real non negative Element of REAL
sqr (rc - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((rc - p2),(rc - p2)) is Relation-like Function-like set
K339((sqr (rc - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr (rc - p2))) is complex real ext-real Element of REAL
|.(rc - p2).| ^2 is complex real ext-real Element of REAL
|.(rc - p2).| * |.(rc - p2).| is complex real ext-real non negative set
(|.(rc - p2).| ^2) - (|.(p2 - p4).| ^2) is complex real ext-real Element of REAL
rc - p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),rc,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),rc,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
rc + (- p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
rc - p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(rc,K280(p4)) is Relation-like Function-like set
|.(rc - p4).| is complex real ext-real non negative Element of REAL
sqr (rc - p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((rc - p4),(rc - p4)) is Relation-like Function-like set
K339((sqr (rc - p4))) is complex real ext-real Element of REAL
sqrt K339((sqr (rc - p4))) is complex real ext-real Element of REAL
|.(rc - p4).| ^2 is complex real ext-real Element of REAL
|.(rc - p4).| * |.(rc - p4).| is complex real ext-real non negative set
((|.(rc - p2).| ^2) - (|.(p2 - p4).| ^2)) - (|.(rc - p4).| ^2) is complex real ext-real Element of REAL
|.(p2 - p4).| * |.(rc - p4).| is complex real ext-real non negative Element of REAL
(((|.(rc - p2).| ^2) - (|.(p2 - p4).| ^2)) - (|.(rc - p4).| ^2)) / (|.(p2 - p4).| * |.(rc - p4).|) is complex real ext-real Element of REAL
dom f7 is set
f7 . a is complex real ext-real set
f0 . a is set
f5 . (f0 . a) is complex real ext-real set
f5 . a is complex real ext-real set
f4 . a is complex real ext-real set
p5 . a is complex real ext-real set
(f4 . a) - (p5 . a) is complex real ext-real set
b . a is complex real ext-real set
f22 . a is complex real ext-real set
(b . a) - (f22 . a) is complex real ext-real set
((b . a) - (f22 . a)) - (p5 . a) is complex real ext-real set
r . a is complex real ext-real set
(r . a) * (r . a) is complex real ext-real set
((b . a) - (f22 . a)) - ((r . a) * (r . a)) is complex real ext-real set
a . a is complex real ext-real set
(a . a) * (a . a) is complex real ext-real set
((a . a) * (a . a)) - (f22 . a) is complex real ext-real set
(((a . a) * (a . a)) - (f22 . a)) - ((r . a) * (r . a)) is complex real ext-real set
f2 . a is complex real ext-real set
(f2 . a) * (f2 . a) is complex real ext-real set
((a . a) * (a . a)) - ((f2 . a) * (f2 . a)) is complex real ext-real set
(((a . a) * (a . a)) - ((f2 . a) * (f2 . a))) - ((r . a) * (r . a)) is complex real ext-real set
f8 . a is complex real ext-real set
(f7 . a) / (f8 . a) is complex real ext-real Element of COMPLEX
z2 is Element of the carrier of ((TOP-REAL 2) | (LSeg (p2,p3)))
f9 . z2 is complex real ext-real set
(|.(p3 - p2).| ^2) - (|.(p2 - p4).| ^2) is complex real ext-real Element of REAL
((|.(p3 - p2).| ^2) - (|.(p2 - p4).| ^2)) - (|.(p3 - p4).| ^2) is complex real ext-real Element of REAL
|.(p2 - p4).| * |.(p3 - p4).| is complex real ext-real non negative Element of REAL
(((|.(p3 - p2).| ^2) - (|.(p2 - p4).| ^2)) - (|.(p3 - p4).| ^2)) / (|.(p2 - p4).| * |.(p3 - p4).|) is complex real ext-real Element of REAL
(|.(p2 - p4).| * |.(p3 - p4).|) * (cos (angle (p2,p4,p3))) is complex real ext-real Element of REAL
(- 2) * ((|.(p2 - p4).| * |.(p3 - p4).|) * (cos (angle (p2,p4,p3)))) is complex real ext-real Element of REAL
((- 2) * ((|.(p2 - p4).| * |.(p3 - p4).|) * (cos (angle (p2,p4,p3))))) / (|.(p2 - p4).| * |.(p3 - p4).|) is complex real ext-real Element of REAL
((|.(p2 - p4).| * |.(p3 - p4).|) * (cos (angle (p2,p4,p3)))) / (|.(p2 - p4).| * |.(p3 - p4).|) is complex real ext-real Element of REAL
(- 2) * (((|.(p2 - p4).| * |.(p3 - p4).|) * (cos (angle (p2,p4,p3)))) / (|.(p2 - p4).| * |.(p3 - p4).|)) is complex real ext-real Element of REAL
(- 2) * (cos (angle (p2,p4,p3))) is complex real ext-real Element of REAL
[.0,PI.] is V126() V127() V128() Element of bool REAL
dom cos is set
[.0,PI.] /\ (dom cos) is V126() V127() V128() Element of bool REAL
cos . (angle (p2,p4,p3)) is complex real ext-real set
cos . (angle (p1,p4,p3)) is complex real ext-real set
(2 * PI) * 0 is empty complex real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() Element of REAL
PI + ((2 * PI) * 0) is non empty complex real ext-real positive non negative Element of REAL
[.((2 * PI) * 0),(PI + ((2 * PI) * 0)).] is V126() V127() V128() Element of bool REAL
cos | [.((2 * PI) * 0),(PI + ((2 * PI) * 0)).] is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
[.PI,(2 * PI).] is V126() V127() V128() Element of bool REAL
dom cos is set
[.PI,(2 * PI).] /\ (dom cos) is V126() V127() V128() Element of bool REAL
cos . (angle (p2,p4,p3)) is complex real ext-real set
cos . (angle (p1,p4,p3)) is complex real ext-real set
(2 * PI) * 0 is empty complex real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() Element of REAL
PI + ((2 * PI) * 0) is non empty complex real ext-real positive non negative Element of REAL
(2 * PI) + ((2 * PI) * 0) is non empty complex real ext-real positive non negative Element of REAL
[.(PI + ((2 * PI) * 0)),((2 * PI) + ((2 * PI) * 0)).] is V126() V127() V128() Element of bool REAL
cos | [.(PI + ((2 * PI) * 0)),((2 * PI) + ((2 * PI) * 0)).] is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
g . 0 is complex real ext-real set
f9 . p2 is complex real ext-real set
p is Element of the carrier of ((TOP-REAL 2) | (LSeg (p2,p3)))
f9 . p is complex real ext-real set
p2 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p2,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p2,K280(p2)) is Relation-like Function-like set
|.(p2 - p2).| is complex real ext-real non negative Element of REAL
sqr (p2 - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p2 - p2),(p2 - p2)) is Relation-like Function-like set
K339((sqr (p2 - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr (p2 - p2))) is complex real ext-real Element of REAL
|.(p2 - p2).| ^2 is complex real ext-real Element of REAL
|.(p2 - p2).| * |.(p2 - p2).| is complex real ext-real non negative set
(|.(p2 - p2).| ^2) - (|.(p2 - p4).| ^2) is complex real ext-real Element of REAL
((|.(p2 - p2).| ^2) - (|.(p2 - p4).| ^2)) - (|.(p2 - p4).| ^2) is complex real ext-real Element of REAL
|.(p2 - p4).| * |.(p2 - p4).| is complex real ext-real non negative Element of REAL
(((|.(p2 - p2).| ^2) - (|.(p2 - p4).| ^2)) - (|.(p2 - p4).| ^2)) / (|.(p2 - p4).| * |.(p2 - p4).|) is complex real ext-real Element of REAL
0 ^2 is complex real ext-real Element of REAL
0 * 0 is empty complex real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() set
(0 ^2) - (|.(p2 - p4).| ^2) is complex real ext-real Element of REAL
((0 ^2) - (|.(p2 - p4).| ^2)) - (|.(p2 - p4).| ^2) is complex real ext-real Element of REAL
(((0 ^2) - (|.(p2 - p4).| ^2)) - (|.(p2 - p4).| ^2)) / (|.(p2 - p4).| * |.(p2 - p4).|) is complex real ext-real Element of REAL
(- 2) * (|.(p2 - p4).| ^2) is complex real ext-real Element of REAL
((- 2) * (|.(p2 - p4).| ^2)) / (|.(p2 - p4).| * |.(p2 - p4).|) is complex real ext-real Element of REAL
rc is complex real ext-real Element of REAL
g . rc is complex real ext-real set
f . rc is set
1 - rc is complex real ext-real Element of REAL
(1 - rc) * p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 - rc) * p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
rc * p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
rc * p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((1 - rc) * p2) + (rc * p3) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((1 - rc) * p2),(rc * p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 - rc) * p2) + (rc * p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
angle (p2,p4,(((1 - rc) * p2) + (rc * p3))) is complex real ext-real Element of REAL
euc2cpx (((1 - rc) * p2) + (rc * p3)) is complex Element of COMPLEX
(((1 - rc) * p2) + (rc * p3)) `1 is complex real ext-real Element of REAL
K367((((1 - rc) * p2) + (rc * p3)),1) is complex real ext-real Element of REAL
(((1 - rc) * p2) + (rc * p3)) `2 is complex real ext-real Element of REAL
K367((((1 - rc) * p2) + (rc * p3)),2) is complex real ext-real Element of REAL
((((1 - rc) * p2) + (rc * p3)) `2) * <i> is complex set
((((1 - rc) * p2) + (rc * p3)) `1) + (((((1 - rc) * p2) + (rc * p3)) `2) * <i>) is complex set
angle ((euc2cpx p2),(euc2cpx p4),(euc2cpx (((1 - rc) * p2) + (rc * p3)))) is complex real ext-real set
(((1 - rc) * p2) + (rc * p3)) - p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),(((1 - rc) * p2) + (rc * p3)),(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(((1 - rc) * p2) + (rc * p3)),(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(((1 - rc) * p2) + (rc * p3)) + (- p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(((1 - rc) * p2) + (rc * p3)) - p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251((((1 - rc) * p2) + (rc * p3)),K280(p4)) is Relation-like Function-like set
|.((((1 - rc) * p2) + (rc * p3)) - p4).| is complex real ext-real non negative Element of REAL
sqr ((((1 - rc) * p2) + (rc * p3)) - p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt (((((1 - rc) * p2) + (rc * p3)) - p4),((((1 - rc) * p2) + (rc * p3)) - p4)) is Relation-like Function-like set
K339((sqr ((((1 - rc) * p2) + (rc * p3)) - p4))) is complex real ext-real Element of REAL
sqrt K339((sqr ((((1 - rc) * p2) + (rc * p3)) - p4))) is complex real ext-real Element of REAL
|.(p2 - p4).| * |.((((1 - rc) * p2) + (rc * p3)) - p4).| is complex real ext-real non negative Element of REAL
(((1 - rc) * p2) + (rc * p3)) - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),(((1 - rc) * p2) + (rc * p3)),(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(((1 - rc) * p2) + (rc * p3)),(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(((1 - rc) * p2) + (rc * p3)) + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(((1 - rc) * p2) + (rc * p3)) - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251((((1 - rc) * p2) + (rc * p3)),K280(p2)) is Relation-like Function-like set
|.((((1 - rc) * p2) + (rc * p3)) - p2).| is complex real ext-real non negative Element of REAL
sqr ((((1 - rc) * p2) + (rc * p3)) - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt (((((1 - rc) * p2) + (rc * p3)) - p2),((((1 - rc) * p2) + (rc * p3)) - p2)) is Relation-like Function-like set
K339((sqr ((((1 - rc) * p2) + (rc * p3)) - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr ((((1 - rc) * p2) + (rc * p3)) - p2))) is complex real ext-real Element of REAL
|.((((1 - rc) * p2) + (rc * p3)) - p2).| ^2 is complex real ext-real Element of REAL
|.((((1 - rc) * p2) + (rc * p3)) - p2).| * |.((((1 - rc) * p2) + (rc * p3)) - p2).| is complex real ext-real non negative set
|.((((1 - rc) * p2) + (rc * p3)) - p4).| ^2 is complex real ext-real Element of REAL
|.((((1 - rc) * p2) + (rc * p3)) - p4).| * |.((((1 - rc) * p2) + (rc * p3)) - p4).| is complex real ext-real non negative set
(|.(p2 - p4).| ^2) + (|.((((1 - rc) * p2) + (rc * p3)) - p4).| ^2) is complex real ext-real Element of REAL
(2 * |.(p2 - p4).|) * |.((((1 - rc) * p2) + (rc * p3)) - p4).| is complex real ext-real non negative Element of REAL
cos (angle (p2,p4,(((1 - rc) * p2) + (rc * p3)))) is complex real ext-real Element of REAL
((2 * |.(p2 - p4).|) * |.((((1 - rc) * p2) + (rc * p3)) - p4).|) * (cos (angle (p2,p4,(((1 - rc) * p2) + (rc * p3))))) is complex real ext-real Element of REAL
((|.(p2 - p4).| ^2) + (|.((((1 - rc) * p2) + (rc * p3)) - p4).| ^2)) - (((2 * |.(p2 - p4).|) * |.((((1 - rc) * p2) + (rc * p3)) - p4).|) * (cos (angle (p2,p4,(((1 - rc) * p2) + (rc * p3)))))) is complex real ext-real Element of REAL
q is Element of the carrier of ((TOP-REAL 2) | (LSeg (p2,p3)))
f9 . q is complex real ext-real set
(|.((((1 - rc) * p2) + (rc * p3)) - p2).| ^2) - (|.(p2 - p4).| ^2) is complex real ext-real Element of REAL
((|.((((1 - rc) * p2) + (rc * p3)) - p2).| ^2) - (|.(p2 - p4).| ^2)) - (|.((((1 - rc) * p2) + (rc * p3)) - p4).| ^2) is complex real ext-real Element of REAL
(((|.((((1 - rc) * p2) + (rc * p3)) - p2).| ^2) - (|.(p2 - p4).| ^2)) - (|.((((1 - rc) * p2) + (rc * p3)) - p4).| ^2)) / (|.(p2 - p4).| * |.((((1 - rc) * p2) + (rc * p3)) - p4).|) is complex real ext-real Element of REAL
(|.(p2 - p4).| * |.((((1 - rc) * p2) + (rc * p3)) - p4).|) * (cos (angle (p2,p4,(((1 - rc) * p2) + (rc * p3))))) is complex real ext-real Element of REAL
(- 2) * ((|.(p2 - p4).| * |.((((1 - rc) * p2) + (rc * p3)) - p4).|) * (cos (angle (p2,p4,(((1 - rc) * p2) + (rc * p3)))))) is complex real ext-real Element of REAL
((- 2) * ((|.(p2 - p4).| * |.((((1 - rc) * p2) + (rc * p3)) - p4).|) * (cos (angle (p2,p4,(((1 - rc) * p2) + (rc * p3))))))) / (|.(p2 - p4).| * |.((((1 - rc) * p2) + (rc * p3)) - p4).|) is complex real ext-real Element of REAL
((|.(p2 - p4).| * |.((((1 - rc) * p2) + (rc * p3)) - p4).|) * (cos (angle (p2,p4,(((1 - rc) * p2) + (rc * p3)))))) / (|.(p2 - p4).| * |.((((1 - rc) * p2) + (rc * p3)) - p4).|) is complex real ext-real Element of REAL
(- 2) * (((|.(p2 - p4).| * |.((((1 - rc) * p2) + (rc * p3)) - p4).|) * (cos (angle (p2,p4,(((1 - rc) * p2) + (rc * p3)))))) / (|.(p2 - p4).| * |.((((1 - rc) * p2) + (rc * p3)) - p4).|)) is complex real ext-real Element of REAL
(- 2) * (cos (angle (p2,p4,(((1 - rc) * p2) + (rc * p3))))) is complex real ext-real Element of REAL
0 * |.(p2 - p2).| is empty complex real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() Element of REAL
(2 * |.(p2 - p4).|) * |.(p2 - p4).| is complex real ext-real non negative Element of REAL
((2 * |.(p2 - p4).|) * |.(p2 - p4).|) * (cos (angle (p2,p4,(((1 - rc) * p2) + (rc * p3))))) is complex real ext-real Element of REAL
((2 * |.(p2 - p4).|) * |.(p2 - p4).|) - (((2 * |.(p2 - p4).|) * |.(p2 - p4).|) * (cos (angle (p2,p4,(((1 - rc) * p2) + (rc * p3)))))) is complex real ext-real Element of REAL
angle (p4,p3,p1) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx p3),(euc2cpx p1)) is complex real ext-real set
angle (p4,p3,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx p3),(euc2cpx p2)) is complex real ext-real set
angle (p3,p2,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p3),(euc2cpx p2),(euc2cpx p4)) is complex real ext-real set
angle ((((1 - rc) * p2) + (rc * p3)),p2,p4) is complex real ext-real Element of REAL
angle ((euc2cpx (((1 - rc) * p2) + (rc * p3))),(euc2cpx p2),(euc2cpx p4)) is complex real ext-real set
arccos (cos (angle (p2,p4,(((1 - rc) * p2) + (rc * p3))))) is complex real ext-real Element of REAL
angle (p4,p3,p1) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx p3),(euc2cpx p1)) is complex real ext-real set
angle (p4,p3,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx p3),(euc2cpx p2)) is complex real ext-real set
angle (p3,p2,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p3),(euc2cpx p2),(euc2cpx p4)) is complex real ext-real set
angle ((((1 - rc) * p2) + (rc * p3)),p2,p4) is complex real ext-real Element of REAL
angle ((euc2cpx (((1 - rc) * p2) + (rc * p3))),(euc2cpx p2),(euc2cpx p4)) is complex real ext-real set
- PI is non empty complex real ext-real non positive negative Element of REAL
- (angle (p2,p4,(((1 - rc) * p2) + (rc * p3)))) is complex real ext-real Element of REAL
(- PI) + (2 * PI) is complex real ext-real Element of REAL
(- (angle (p2,p4,(((1 - rc) * p2) + (rc * p3))))) + (2 * PI) is complex real ext-real Element of REAL
(2 * PI) - (angle (p2,p4,(((1 - rc) * p2) + (rc * p3)))) is complex real ext-real Element of REAL
cos ((2 * PI) - (angle (p2,p4,(((1 - rc) * p2) + (rc * p3))))) is complex real ext-real Element of REAL
(2 * PI) * 1 is non empty complex real ext-real positive non negative Element of REAL
(- (angle (p2,p4,(((1 - rc) * p2) + (rc * p3))))) + ((2 * PI) * 1) is complex real ext-real Element of REAL
cos . ((- (angle (p2,p4,(((1 - rc) * p2) + (rc * p3))))) + ((2 * PI) * 1)) is complex real ext-real set
cos . (- (angle (p2,p4,(((1 - rc) * p2) + (rc * p3))))) is complex real ext-real set
cos . (angle (p2,p4,(((1 - rc) * p2) + (rc * p3)))) is complex real ext-real set
cos . (angle (p1,p4,p3)) is complex real ext-real set
- (angle (p1,p4,p3)) is complex real ext-real Element of REAL
cos . (- (angle (p1,p4,p3))) is complex real ext-real set
(- (angle (p1,p4,p3))) + ((2 * PI) * 1) is complex real ext-real Element of REAL
cos . ((- (angle (p1,p4,p3))) + ((2 * PI) * 1)) is complex real ext-real set
(2 * PI) - (angle (p1,p4,p3)) is complex real ext-real Element of REAL
cos ((2 * PI) - (angle (p1,p4,p3))) is complex real ext-real Element of REAL
(- (angle (p1,p4,p3))) + (2 * PI) is complex real ext-real Element of REAL
- (2 * PI) is non empty complex real ext-real non positive negative Element of REAL
(- (2 * PI)) + (2 * PI) is complex real ext-real Element of REAL
arccos (cos ((2 * PI) - (angle (p2,p4,(((1 - rc) * p2) + (rc * p3)))))) is complex real ext-real Element of REAL
LSeg (p3,p4) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p3) + (b1 * p4)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
LSeg (p2,p4) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p2) + (b1 * p4)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 is complex real ext-real set
p4 is complex real ext-real set
p is complex real ext-real set
inside_of_circle (p3,p4,p) is Element of bool the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
outside_of_circle (p3,p4,p) is Element of bool the carrier of (TOP-REAL 2)
LSeg (p1,p2) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p1) + (b1 * p2)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
circle (p3,p4,p) is Element of bool the carrier of (TOP-REAL 2)
(LSeg (p1,p2)) /\ (circle (p3,p4,p)) is Element of bool the carrier of (TOP-REAL 2)
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
LSeg (p1,p2) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p1) + (b1 * p2)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
LSeg (p1,p3) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p1) + (b1 * p3)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p is complex real ext-real set
a is complex real ext-real set
b is complex real ext-real set
circle (p,a,b) is Element of bool the carrier of (TOP-REAL 2)
{p1} is non empty set
{p1} is non empty set
inside_of_circle (p,a,b) is Element of bool the carrier of (TOP-REAL 2)
{p1,p3} is non empty set
(LSeg (p1,p3)) \ {p1,p3} is Element of bool the carrier of (TOP-REAL 2)
(inside_of_circle (p,a,b)) /\ (circle (p,a,b)) is Element of bool the carrier of (TOP-REAL 2)
{p1,p2} is non empty set
(LSeg (p1,p2)) \ {p1,p2} is Element of bool the carrier of (TOP-REAL 2)
(inside_of_circle (p,a,b)) /\ (circle (p,a,b)) is Element of bool the carrier of (TOP-REAL 2)
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
LSeg (p3,p2) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p3) + (b1 * p2)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
angle (p1,p3,p2) is complex real ext-real Element of REAL
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx p3),(euc2cpx p2)) is complex real ext-real set
2 * (angle (p1,p3,p2)) is complex real ext-real Element of REAL
(angle (p1,p3,p2)) - PI is complex real ext-real Element of REAL
2 * ((angle (p1,p3,p2)) - PI) is complex real ext-real Element of REAL
p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p1,p4,p2) is complex real ext-real Element of REAL
euc2cpx p4 is complex Element of COMPLEX
p4 `1 is complex real ext-real Element of REAL
K367(p4,1) is complex real ext-real Element of REAL
p4 `2 is complex real ext-real Element of REAL
K367(p4,2) is complex real ext-real Element of REAL
(p4 `2) * <i> is complex set
(p4 `1) + ((p4 `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx p4),(euc2cpx p2)) is complex real ext-real set
p is complex real ext-real set
a is complex real ext-real set
|[p,a]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
b is complex real ext-real set
circle (p,a,b) is Element of bool the carrier of (TOP-REAL 2)
p1 - p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p4 is Relation-like Function-like set
K214((TOP-REAL 2),p1,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p4) is Relation-like Function-like complex-valued set
K251(p1,K280(p4)) is Relation-like Function-like set
|.(p1 - p4).| is complex real ext-real non negative Element of REAL
sqr (p1 - p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p1 - p4),(p1 - p4)) is Relation-like Function-like set
K339((sqr (p1 - p4))) is complex real ext-real Element of REAL
sqrt K339((sqr (p1 - p4))) is complex real ext-real Element of REAL
p2 - p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p2,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p2,K280(p4)) is Relation-like Function-like set
|.(p2 - p4).| is complex real ext-real non negative Element of REAL
sqr (p2 - p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p2 - p4),(p2 - p4)) is Relation-like Function-like set
K339((sqr (p2 - p4))) is complex real ext-real Element of REAL
sqrt K339((sqr (p2 - p4))) is complex real ext-real Element of REAL
2 * 0 is empty complex real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() Element of REAL
angle (p4,p4,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx p4),(euc2cpx p4)) is complex real ext-real set
p2 - p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p4 is Relation-like Function-like set
K214((TOP-REAL 2),p2,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p4) is Relation-like Function-like complex-valued set
K251(p2,K280(p4)) is Relation-like Function-like set
|.(p2 - p4).| is complex real ext-real non negative Element of REAL
sqr (p2 - p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p2 - p4),(p2 - p4)) is Relation-like Function-like set
K339((sqr (p2 - p4))) is complex real ext-real Element of REAL
sqrt K339((sqr (p2 - p4))) is complex real ext-real Element of REAL
p1 - p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p1,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p1,K280(p4)) is Relation-like Function-like set
|.(p1 - p4).| is complex real ext-real non negative Element of REAL
sqr (p1 - p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p1 - p4),(p1 - p4)) is Relation-like Function-like set
K339((sqr (p1 - p4))) is complex real ext-real Element of REAL
sqrt K339((sqr (p1 - p4))) is complex real ext-real Element of REAL
p3 - p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p3,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (- p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p3,K280(p4)) is Relation-like Function-like set
|.(p3 - p4).| is complex real ext-real non negative Element of REAL
sqr (p3 - p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p3 - p4),(p3 - p4)) is Relation-like Function-like set
K339((sqr (p3 - p4))) is complex real ext-real Element of REAL
sqrt K339((sqr (p3 - p4))) is complex real ext-real Element of REAL
angle (p1,p3,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p1),(euc2cpx p3),(euc2cpx p4)) is complex real ext-real set
p4 - p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p1 is Relation-like Function-like set
K214((TOP-REAL 2),p4,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p4,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p4 + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p4 - p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p1) is Relation-like Function-like complex-valued set
K251(p4,K280(p1)) is Relation-like Function-like set
|.(p4 - p1).| is complex real ext-real non negative Element of REAL
sqr (p4 - p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p4 - p1),(p4 - p1)) is Relation-like Function-like set
K339((sqr (p4 - p1))) is complex real ext-real Element of REAL
sqrt K339((sqr (p4 - p1))) is complex real ext-real Element of REAL
angle (p4,p1,p3) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx p1),(euc2cpx p3)) is complex real ext-real set
(angle (p4,p1,p3)) + (angle (p1,p3,p4)) is complex real ext-real Element of REAL
angle (p3,p4,p1) is complex real ext-real Element of REAL
angle ((euc2cpx p3),(euc2cpx p4),(euc2cpx p1)) is complex real ext-real set
((angle (p4,p1,p3)) + (angle (p1,p3,p4))) + (angle (p3,p4,p1)) is complex real ext-real Element of REAL
(angle (p3,p4,p1)) + (angle (p1,p4,p2)) is complex real ext-real Element of REAL
(2 * (angle (p1,p3,p2))) + (angle (p3,p4,p1)) is complex real ext-real Element of REAL
(angle (p3,p4,p1)) + (angle (p1,p4,p2)) is complex real ext-real Element of REAL
(2 * (angle (p1,p3,p2))) + (angle (p3,p4,p1)) is complex real ext-real Element of REAL
0 + (2 * PI) is non empty complex real ext-real positive non negative Element of REAL
- (2 * (angle (p1,p3,p2))) is complex real ext-real Element of REAL
(- (2 * (angle (p1,p3,p2)))) + (angle (p1,p4,p2)) is complex real ext-real Element of REAL
(angle (p3,p4,p1)) + (angle (p1,p4,p2)) is complex real ext-real Element of REAL
(2 * (angle (p1,p3,p2))) + (angle (p3,p4,p1)) is complex real ext-real Element of REAL
(2 * PI) * 2 is non empty complex real ext-real positive non negative Element of REAL
(angle (p1,p3,p2)) * 2 is complex real ext-real Element of REAL
((2 * PI) * 2) + 0 is non empty complex real ext-real positive non negative Element of REAL
- (angle (p1,p4,p2)) is complex real ext-real Element of REAL
(2 * (angle (p1,p3,p2))) + (- (angle (p1,p4,p2))) is complex real ext-real Element of REAL
(angle (p3,p4,p1)) + (angle (p1,p4,p2)) is complex real ext-real Element of REAL
(2 * (angle (p1,p3,p2))) + (angle (p3,p4,p1)) is complex real ext-real Element of REAL
(angle (p3,p4,p1)) + (angle (p1,p4,p2)) is complex real ext-real Element of REAL
(2 * (angle (p1,p3,p2))) + (angle (p3,p4,p1)) is complex real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is complex real ext-real set
p3 is complex real ext-real set
|[p2,p3]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p4 is complex real ext-real set
circle (p2,p3,p4) is Element of bool the carrier of (TOP-REAL 2)
2 * |[p2,p3]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
2 * |[p2,p3]| is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(2 * |[p2,p3]|) - p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p1 is Relation-like Function-like set
K214((TOP-REAL 2),(2 * |[p2,p3]|),(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(2 * |[p2,p3]|),(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(2 * |[p2,p3]|) + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(2 * |[p2,p3]|) - p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p1) is Relation-like Function-like complex-valued set
K251((2 * |[p2,p3]|),K280(p1)) is Relation-like Function-like set
p1 - |[p2,p3]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- |[p2,p3]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- |[p2,p3]| is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * |[p2,p3]| is Relation-like Function-like set
K214((TOP-REAL 2),p1,(- |[p2,p3]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- |[p2,p3]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- |[p2,p3]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - |[p2,p3]| is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(|[p2,p3]|) is Relation-like Function-like complex-valued set
K251(p1,K280(|[p2,p3]|)) is Relation-like Function-like set
|.(p1 - |[p2,p3]|).| is complex real ext-real non negative Element of REAL
sqr (p1 - |[p2,p3]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p1 - |[p2,p3]|),(p1 - |[p2,p3]|)) is Relation-like Function-like set
K339((sqr (p1 - |[p2,p3]|))) is complex real ext-real Element of REAL
sqrt K339((sqr (p1 - |[p2,p3]|))) is complex real ext-real Element of REAL
LSeg (p1,((2 * |[p2,p3]|) - p1)) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p1) + (b1 * ((2 * |[p2,p3]|) - p1))) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
1 * p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
1 * p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1 * p1) + p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(1 * p1),p1) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 * p1) + p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((2 * |[p2,p3]|) - p1) + p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((2 * |[p2,p3]|) - p1),p1) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((2 * |[p2,p3]|) - p1) + p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1 * p1) + (1 * p1) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(1 * p1),(1 * p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 * p1) + (1 * p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
1 + 1 is non empty complex real ext-real positive non negative Element of REAL
(1 + 1) * p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 + 1) * p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
2 * p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
2 * p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p1,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p1,K280(p1)) is Relation-like Function-like set
(2 * |[p2,p3]|) - (p1 - p1) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- (p1 - p1) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- (p1 - p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * (p1 - p1) is Relation-like Function-like set
K214((TOP-REAL 2),(2 * |[p2,p3]|),(- (p1 - p1))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(2 * |[p2,p3]|),(- (p1 - p1))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(2 * |[p2,p3]|) + (- (p1 - p1)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(2 * |[p2,p3]|) - (p1 - p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280((p1 - p1)) is Relation-like Function-like complex-valued set
K251((2 * |[p2,p3]|),K280((p1 - p1))) is Relation-like Function-like set
(2 * |[p2,p3]|) - (0. (TOP-REAL 2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- (0. (TOP-REAL 2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- (0. (TOP-REAL 2)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * (0. (TOP-REAL 2)) is Relation-like Function-like set
K214((TOP-REAL 2),(2 * |[p2,p3]|),(- (0. (TOP-REAL 2)))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(2 * |[p2,p3]|),(- (0. (TOP-REAL 2)))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(2 * |[p2,p3]|) + (- (0. (TOP-REAL 2))) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(2 * |[p2,p3]|) - (0. (TOP-REAL 2)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280((0. (TOP-REAL 2))) is Relation-like Function-like complex-valued set
K251((2 * |[p2,p3]|),K280((0. (TOP-REAL 2)))) is Relation-like Function-like set
(2 * |[p2,p3]|) + (0. (TOP-REAL 2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(2 * |[p2,p3]|),(0. (TOP-REAL 2))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(2 * |[p2,p3]|) + (0. (TOP-REAL 2)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
|[p2,p3]| - |[p2,p3]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),|[p2,p3]|,(- |[p2,p3]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),|[p2,p3]|,(- |[p2,p3]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
|[p2,p3]| + (- |[p2,p3]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
|[p2,p3]| - |[p2,p3]| is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(|[p2,p3]|,K280(|[p2,p3]|)) is Relation-like Function-like set
|.(|[p2,p3]| - |[p2,p3]|).| is complex real ext-real non negative Element of REAL
sqr (|[p2,p3]| - |[p2,p3]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((|[p2,p3]| - |[p2,p3]|),(|[p2,p3]| - |[p2,p3]|)) is Relation-like Function-like set
K339((sqr (|[p2,p3]| - |[p2,p3]|))) is complex real ext-real Element of REAL
sqrt K339((sqr (|[p2,p3]| - |[p2,p3]|))) is complex real ext-real Element of REAL
((2 * |[p2,p3]|) - p1) - |[p2,p3]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),((2 * |[p2,p3]|) - p1),(- |[p2,p3]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((2 * |[p2,p3]|) - p1),(- |[p2,p3]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((2 * |[p2,p3]|) - p1) + (- |[p2,p3]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((2 * |[p2,p3]|) - p1) - |[p2,p3]| is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(((2 * |[p2,p3]|) - p1),K280(|[p2,p3]|)) is Relation-like Function-like set
|.(((2 * |[p2,p3]|) - p1) - |[p2,p3]|).| is complex real ext-real non negative Element of REAL
sqr (((2 * |[p2,p3]|) - p1) - |[p2,p3]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((((2 * |[p2,p3]|) - p1) - |[p2,p3]|),(((2 * |[p2,p3]|) - p1) - |[p2,p3]|)) is Relation-like Function-like set
K339((sqr (((2 * |[p2,p3]|) - p1) - |[p2,p3]|))) is complex real ext-real Element of REAL
sqrt K339((sqr (((2 * |[p2,p3]|) - p1) - |[p2,p3]|))) is complex real ext-real Element of REAL
(2 * |[p2,p3]|) + (- p1) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((2 * |[p2,p3]|) + (- p1)) - |[p2,p3]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),((2 * |[p2,p3]|) + (- p1)),(- |[p2,p3]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((2 * |[p2,p3]|) + (- p1)),(- |[p2,p3]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((2 * |[p2,p3]|) + (- p1)) + (- |[p2,p3]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((2 * |[p2,p3]|) + (- p1)) - |[p2,p3]| is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(((2 * |[p2,p3]|) + (- p1)),K280(|[p2,p3]|)) is Relation-like Function-like set
|.(((2 * |[p2,p3]|) + (- p1)) - |[p2,p3]|).| is complex real ext-real non negative Element of REAL
sqr (((2 * |[p2,p3]|) + (- p1)) - |[p2,p3]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((((2 * |[p2,p3]|) + (- p1)) - |[p2,p3]|),(((2 * |[p2,p3]|) + (- p1)) - |[p2,p3]|)) is Relation-like Function-like set
K339((sqr (((2 * |[p2,p3]|) + (- p1)) - |[p2,p3]|))) is complex real ext-real Element of REAL
sqrt K339((sqr (((2 * |[p2,p3]|) + (- p1)) - |[p2,p3]|))) is complex real ext-real Element of REAL
(2 * |[p2,p3]|) + (- |[p2,p3]|) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(2 * |[p2,p3]|),(- |[p2,p3]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(2 * |[p2,p3]|) + (- |[p2,p3]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((2 * |[p2,p3]|) + (- |[p2,p3]|)) + (- p1) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((2 * |[p2,p3]|) + (- |[p2,p3]|)),(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((2 * |[p2,p3]|) + (- |[p2,p3]|)) + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
|.(((2 * |[p2,p3]|) + (- |[p2,p3]|)) + (- p1)).| is complex real ext-real non negative Element of REAL
sqr (((2 * |[p2,p3]|) + (- |[p2,p3]|)) + (- p1)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((((2 * |[p2,p3]|) + (- |[p2,p3]|)) + (- p1)),(((2 * |[p2,p3]|) + (- |[p2,p3]|)) + (- p1))) is Relation-like Function-like set
K339((sqr (((2 * |[p2,p3]|) + (- |[p2,p3]|)) + (- p1)))) is complex real ext-real Element of REAL
sqrt K339((sqr (((2 * |[p2,p3]|) + (- |[p2,p3]|)) + (- p1)))) is complex real ext-real Element of REAL
(- 1) * |[p2,p3]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(- 1) * |[p2,p3]| is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(2 * |[p2,p3]|) + ((- 1) * |[p2,p3]|) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(2 * |[p2,p3]|),((- 1) * |[p2,p3]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(2 * |[p2,p3]|) + ((- 1) * |[p2,p3]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((2 * |[p2,p3]|) + ((- 1) * |[p2,p3]|)) + (- p1) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((2 * |[p2,p3]|) + ((- 1) * |[p2,p3]|)),(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((2 * |[p2,p3]|) + ((- 1) * |[p2,p3]|)) + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
|.(((2 * |[p2,p3]|) + ((- 1) * |[p2,p3]|)) + (- p1)).| is complex real ext-real non negative Element of REAL
sqr (((2 * |[p2,p3]|) + ((- 1) * |[p2,p3]|)) + (- p1)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((((2 * |[p2,p3]|) + ((- 1) * |[p2,p3]|)) + (- p1)),(((2 * |[p2,p3]|) + ((- 1) * |[p2,p3]|)) + (- p1))) is Relation-like Function-like set
K339((sqr (((2 * |[p2,p3]|) + ((- 1) * |[p2,p3]|)) + (- p1)))) is complex real ext-real Element of REAL
sqrt K339((sqr (((2 * |[p2,p3]|) + ((- 1) * |[p2,p3]|)) + (- p1)))) is complex real ext-real Element of REAL
2 + (- 1) is complex real ext-real Element of REAL
(2 + (- 1)) * |[p2,p3]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(2 + (- 1)) * |[p2,p3]| is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((2 + (- 1)) * |[p2,p3]|) + (- p1) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((2 + (- 1)) * |[p2,p3]|),(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((2 + (- 1)) * |[p2,p3]|) + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
|.(((2 + (- 1)) * |[p2,p3]|) + (- p1)).| is complex real ext-real non negative Element of REAL
sqr (((2 + (- 1)) * |[p2,p3]|) + (- p1)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((((2 + (- 1)) * |[p2,p3]|) + (- p1)),(((2 + (- 1)) * |[p2,p3]|) + (- p1))) is Relation-like Function-like set
K339((sqr (((2 + (- 1)) * |[p2,p3]|) + (- p1)))) is complex real ext-real Element of REAL
sqrt K339((sqr (((2 + (- 1)) * |[p2,p3]|) + (- p1)))) is complex real ext-real Element of REAL
|[p2,p3]| - p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),|[p2,p3]|,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),|[p2,p3]|,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
|[p2,p3]| + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
|[p2,p3]| - p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(|[p2,p3]|,K280(p1)) is Relation-like Function-like set
|.(|[p2,p3]| - p1).| is complex real ext-real non negative Element of REAL
sqr (|[p2,p3]| - p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((|[p2,p3]| - p1),(|[p2,p3]| - p1)) is Relation-like Function-like set
K339((sqr (|[p2,p3]| - p1))) is complex real ext-real Element of REAL
sqrt K339((sqr (|[p2,p3]| - p1))) is complex real ext-real Element of REAL
1 / 2 is non empty complex real ext-real positive non negative Element of REAL
1 - (1 / 2) is complex real ext-real Element of REAL
(1 - (1 / 2)) * p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 - (1 / 2)) * p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1 / 2) * ((2 * |[p2,p3]|) - p1) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 / 2) * ((2 * |[p2,p3]|) - p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((1 - (1 / 2)) * p1) + ((1 / 2) * ((2 * |[p2,p3]|) - p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),((1 - (1 / 2)) * p1),((1 / 2) * ((2 * |[p2,p3]|) - p1))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 - (1 / 2)) * p1) + ((1 / 2) * ((2 * |[p2,p3]|) - p1)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 + ((2 * |[p2,p3]|) - p1) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,((2 * |[p2,p3]|) - p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + ((2 * |[p2,p3]|) - p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1 / 2) * (p1 + ((2 * |[p2,p3]|) - p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 / 2) * (p1 + ((2 * |[p2,p3]|) - p1)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 + (- p1) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(p1 + (- p1)) + (2 * |[p2,p3]|) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(p1 + (- p1)),(2 * |[p2,p3]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(p1 + (- p1)) + (2 * |[p2,p3]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1 / 2) * ((p1 + (- p1)) + (2 * |[p2,p3]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 / 2) * ((p1 + (- p1)) + (2 * |[p2,p3]|)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(0. (TOP-REAL 2)) + (2 * |[p2,p3]|) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(0. (TOP-REAL 2)),(2 * |[p2,p3]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(0. (TOP-REAL 2)) + (2 * |[p2,p3]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1 / 2) * ((0. (TOP-REAL 2)) + (2 * |[p2,p3]|)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 / 2) * ((0. (TOP-REAL 2)) + (2 * |[p2,p3]|)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1 / 2) * (2 * |[p2,p3]|) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(1 / 2) * (2 * |[p2,p3]|) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1 / 2) * 2 is non empty complex real ext-real positive non negative Element of REAL
((1 / 2) * 2) * |[p2,p3]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
((1 / 2) * 2) * |[p2,p3]| is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p1,p3,p2) is complex real ext-real Element of REAL
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx p3),(euc2cpx p2)) is complex real ext-real set
2 * (angle (p1,p3,p2)) is complex real ext-real Element of REAL
(angle (p1,p3,p2)) - PI is complex real ext-real Element of REAL
2 * ((angle (p1,p3,p2)) - PI) is complex real ext-real Element of REAL
p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p1,p4,p2) is complex real ext-real Element of REAL
euc2cpx p4 is complex Element of COMPLEX
p4 `1 is complex real ext-real Element of REAL
K367(p4,1) is complex real ext-real Element of REAL
p4 `2 is complex real ext-real Element of REAL
K367(p4,2) is complex real ext-real Element of REAL
(p4 `2) * <i> is complex set
(p4 `1) + ((p4 `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx p4),(euc2cpx p2)) is complex real ext-real set
p is complex real ext-real set
a is complex real ext-real set
|[p,a]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
b is complex real ext-real set
circle (p,a,b) is Element of bool the carrier of (TOP-REAL 2)
p1 - p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p4 is Relation-like Function-like set
K214((TOP-REAL 2),p1,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p4) is Relation-like Function-like complex-valued set
K251(p1,K280(p4)) is Relation-like Function-like set
|.(p1 - p4).| is complex real ext-real non negative Element of REAL
sqr (p1 - p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p1 - p4),(p1 - p4)) is Relation-like Function-like set
K339((sqr (p1 - p4))) is complex real ext-real Element of REAL
sqrt K339((sqr (p1 - p4))) is complex real ext-real Element of REAL
p2 - p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p2,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p2,K280(p4)) is Relation-like Function-like set
|.(p2 - p4).| is complex real ext-real non negative Element of REAL
sqr (p2 - p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p2 - p4),(p2 - p4)) is Relation-like Function-like set
K339((sqr (p2 - p4))) is complex real ext-real Element of REAL
sqrt K339((sqr (p2 - p4))) is complex real ext-real Element of REAL
2 * 0 is empty complex real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() Element of REAL
angle (p4,p4,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx p4),(euc2cpx p4)) is complex real ext-real set
p2 - p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p4 is Relation-like Function-like set
K214((TOP-REAL 2),p2,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p4) is Relation-like Function-like complex-valued set
K251(p2,K280(p4)) is Relation-like Function-like set
|.(p2 - p4).| is complex real ext-real non negative Element of REAL
sqr (p2 - p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p2 - p4),(p2 - p4)) is Relation-like Function-like set
K339((sqr (p2 - p4))) is complex real ext-real Element of REAL
sqrt K339((sqr (p2 - p4))) is complex real ext-real Element of REAL
p1 - p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p1,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p1,K280(p4)) is Relation-like Function-like set
|.(p1 - p4).| is complex real ext-real non negative Element of REAL
sqr (p1 - p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p1 - p4),(p1 - p4)) is Relation-like Function-like set
K339((sqr (p1 - p4))) is complex real ext-real Element of REAL
sqrt K339((sqr (p1 - p4))) is complex real ext-real Element of REAL
r is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
LSeg (p3,r) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p3) + (b1 * r)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
angle (p2,p4,r) is complex real ext-real Element of REAL
euc2cpx r is complex Element of COMPLEX
r `1 is complex real ext-real Element of REAL
K367(r,1) is complex real ext-real Element of REAL
r `2 is complex real ext-real Element of REAL
K367(r,2) is complex real ext-real Element of REAL
(r `2) * <i> is complex set
(r `1) + ((r `2) * <i>) is complex set
angle ((euc2cpx p2),(euc2cpx p4),(euc2cpx r)) is complex real ext-real set
r - p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),r,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),r,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
r + (- p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
r - p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(r,K280(p4)) is Relation-like Function-like set
euc2cpx (r - p4) is complex Element of COMPLEX
(r - p4) `1 is complex real ext-real Element of REAL
K367((r - p4),1) is complex real ext-real Element of REAL
(r - p4) `2 is complex real ext-real Element of REAL
K367((r - p4),2) is complex real ext-real Element of REAL
((r - p4) `2) * <i> is complex set
((r - p4) `1) + (((r - p4) `2) * <i>) is complex set
euc2cpx (p2 - p4) is complex Element of COMPLEX
(p2 - p4) `1 is complex real ext-real Element of REAL
K367((p2 - p4),1) is complex real ext-real Element of REAL
(p2 - p4) `2 is complex real ext-real Element of REAL
K367((p2 - p4),2) is complex real ext-real Element of REAL
((p2 - p4) `2) * <i> is complex set
((p2 - p4) `1) + (((p2 - p4) `2) * <i>) is complex set
Arg (p2 - p4) is complex real ext-real Element of REAL
Arg (euc2cpx (p2 - p4)) is complex real ext-real Element of REAL
Arg (r - p4) is complex real ext-real Element of REAL
Arg (euc2cpx (r - p4)) is complex real ext-real Element of REAL
|.(r - p4).| is complex real ext-real non negative Element of REAL
sqr (r - p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((r - p4),(r - p4)) is Relation-like Function-like set
K339((sqr (r - p4))) is complex real ext-real Element of REAL
sqrt K339((sqr (r - p4))) is complex real ext-real Element of REAL
|.(euc2cpx (p2 - p4)).| is complex real ext-real Element of REAL
Re (euc2cpx (p2 - p4)) is complex real ext-real Element of REAL
(Re (euc2cpx (p2 - p4))) ^2 is complex real ext-real Element of REAL
(Re (euc2cpx (p2 - p4))) * (Re (euc2cpx (p2 - p4))) is complex real ext-real set
Im (euc2cpx (p2 - p4)) is complex real ext-real Element of REAL
(Im (euc2cpx (p2 - p4))) ^2 is complex real ext-real Element of REAL
(Im (euc2cpx (p2 - p4))) * (Im (euc2cpx (p2 - p4))) is complex real ext-real set
((Re (euc2cpx (p2 - p4))) ^2) + ((Im (euc2cpx (p2 - p4))) ^2) is complex real ext-real Element of REAL
sqrt (((Re (euc2cpx (p2 - p4))) ^2) + ((Im (euc2cpx (p2 - p4))) ^2)) is complex real ext-real Element of REAL
|.(euc2cpx (r - p4)).| is complex real ext-real Element of REAL
Re (euc2cpx (r - p4)) is complex real ext-real Element of REAL
(Re (euc2cpx (r - p4))) ^2 is complex real ext-real Element of REAL
(Re (euc2cpx (r - p4))) * (Re (euc2cpx (r - p4))) is complex real ext-real set
Im (euc2cpx (r - p4)) is complex real ext-real Element of REAL
(Im (euc2cpx (r - p4))) ^2 is complex real ext-real Element of REAL
(Im (euc2cpx (r - p4))) * (Im (euc2cpx (r - p4))) is complex real ext-real set
((Re (euc2cpx (r - p4))) ^2) + ((Im (euc2cpx (r - p4))) ^2) is complex real ext-real Element of REAL
sqrt (((Re (euc2cpx (r - p4))) ^2) + ((Im (euc2cpx (r - p4))) ^2)) is complex real ext-real Element of REAL
cos (Arg (euc2cpx (p2 - p4))) is complex real ext-real Element of REAL
|.(euc2cpx (p2 - p4)).| * (cos (Arg (euc2cpx (p2 - p4)))) is complex real ext-real Element of REAL
sin (Arg (euc2cpx (p2 - p4))) is complex real ext-real Element of REAL
|.(euc2cpx (p2 - p4)).| * (sin (Arg (euc2cpx (p2 - p4)))) is complex real ext-real Element of REAL
(|.(euc2cpx (p2 - p4)).| * (sin (Arg (euc2cpx (p2 - p4))))) * <i> is complex set
(|.(euc2cpx (p2 - p4)).| * (cos (Arg (euc2cpx (p2 - p4))))) + ((|.(euc2cpx (p2 - p4)).| * (sin (Arg (euc2cpx (p2 - p4))))) * <i>) is complex set
p2 + (0. (TOP-REAL 2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(0. (TOP-REAL 2))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (0. (TOP-REAL 2)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p4 + (- p4) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p4,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p4 + (- p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 + (p4 + (- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(p4 + (- p4))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (p4 + (- p4)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 + (- p4) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(p2 + (- p4)) + p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(p2 + (- p4)),p4) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(p2 + (- p4)) + p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(r - p4) + p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),(r - p4),p4) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
(r - p4) + p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
r + (p4 + (- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),r,(p4 + (- p4))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
r + (p4 + (- p4)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
r + (0. (TOP-REAL 2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),r,(0. (TOP-REAL 2))) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
r + (0. (TOP-REAL 2)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
angle (p2,p3,r) is complex real ext-real Element of REAL
angle ((euc2cpx p2),(euc2cpx p3),(euc2cpx r)) is complex real ext-real set
2 * (angle (p2,p3,r)) is complex real ext-real Element of REAL
(angle (p2,p3,r)) - PI is complex real ext-real Element of REAL
2 * ((angle (p2,p3,r)) - PI) is complex real ext-real Element of REAL
angle (r,p3,p2) is complex real ext-real Element of REAL
angle ((euc2cpx r),(euc2cpx p3),(euc2cpx p2)) is complex real ext-real set
2 * (angle (r,p3,p2)) is complex real ext-real Element of REAL
angle (r,p4,p2) is complex real ext-real Element of REAL
angle ((euc2cpx r),(euc2cpx p4),(euc2cpx p2)) is complex real ext-real set
(2 * PI) - (angle (p2,p3,r)) is complex real ext-real Element of REAL
2 * ((2 * PI) - (angle (p2,p3,r))) is complex real ext-real Element of REAL
(2 * PI) - (2 * ((angle (p2,p3,r)) - PI)) is complex real ext-real Element of REAL
(2 * PI) - (angle (p2,p3,r)) is complex real ext-real Element of REAL
(angle (r,p3,p2)) - PI is complex real ext-real Element of REAL
2 * ((angle (r,p3,p2)) - PI) is complex real ext-real Element of REAL
(2 * PI) - (angle (p2,p4,r)) is complex real ext-real Element of REAL
angle (p1,p3,r) is complex real ext-real Element of REAL
angle ((euc2cpx p1),(euc2cpx p3),(euc2cpx r)) is complex real ext-real set
(angle (p1,p3,r)) + (angle (r,p3,p2)) is complex real ext-real Element of REAL
(angle (p1,p3,p2)) + (2 * PI) is complex real ext-real Element of REAL
angle (p1,p4,r) is complex real ext-real Element of REAL
angle ((euc2cpx p1),(euc2cpx p4),(euc2cpx r)) is complex real ext-real set
(angle (p1,p4,r)) + (angle (r,p4,p2)) is complex real ext-real Element of REAL
2 * (angle (p1,p3,r)) is complex real ext-real Element of REAL
(2 * (angle (p1,p3,p2))) - (2 * PI) is complex real ext-real Element of REAL
(2 * (angle (p1,p3,p2))) + (2 * PI) is complex real ext-real Element of REAL
2 * (angle (p1,p3,r)) is complex real ext-real Element of REAL
(2 * (angle (p1,p3,p2))) + (4 * PI) is complex real ext-real Element of REAL
(angle (p1,p3,r)) - PI is complex real ext-real Element of REAL
2 * ((angle (p1,p3,r)) - PI) is complex real ext-real Element of REAL
2 * ((angle (p1,p3,r)) + (angle (r,p3,p2))) is complex real ext-real Element of REAL
(2 * ((angle (p1,p3,r)) + (angle (r,p3,p2)))) - (4 * PI) is complex real ext-real Element of REAL
(angle (p1,p3,r)) - PI is complex real ext-real Element of REAL
2 * ((angle (p1,p3,r)) - PI) is complex real ext-real Element of REAL
(2 * (angle (p1,p3,p2))) - (2 * PI) is complex real ext-real Element of REAL
(2 * (angle (p1,p3,p2))) + (2 * PI) is complex real ext-real Element of REAL
2 * (angle (p1,p3,r)) is complex real ext-real Element of REAL
(angle (p1,p3,r)) - PI is complex real ext-real Element of REAL
2 * ((angle (p1,p3,r)) - PI) is complex real ext-real Element of REAL
(angle (p1,p4,p2)) + (2 * PI) is complex real ext-real Element of REAL
angle (p1,p4,r) is complex real ext-real Element of REAL
angle ((euc2cpx p1),(euc2cpx p4),(euc2cpx r)) is complex real ext-real set
(angle (p1,p4,r)) + (angle (r,p4,p2)) is complex real ext-real Element of REAL
2 * (angle (p1,p3,r)) is complex real ext-real Element of REAL
2 * ((angle (p1,p3,r)) + (angle (r,p3,p2))) is complex real ext-real Element of REAL
(2 * ((angle (p1,p3,r)) + (angle (r,p3,p2)))) - (4 * PI) is complex real ext-real Element of REAL
2 * (angle (p1,p3,r)) is complex real ext-real Element of REAL
(2 * (angle (p1,p3,p2))) - (2 * PI) is complex real ext-real Element of REAL
(2 * (angle (p1,p3,p2))) + (2 * PI) is complex real ext-real Element of REAL
(angle (p1,p3,r)) - PI is complex real ext-real Element of REAL
2 * ((angle (p1,p3,r)) - PI) is complex real ext-real Element of REAL
2 * ((angle (p1,p3,r)) + (angle (r,p3,p2))) is complex real ext-real Element of REAL
(2 * ((angle (p1,p3,r)) + (angle (r,p3,p2)))) - (6 * PI) is complex real ext-real Element of REAL
(angle (p1,p3,r)) - PI is complex real ext-real Element of REAL
2 * ((angle (p1,p3,r)) - PI) is complex real ext-real Element of REAL
2 * ((angle (p1,p3,r)) + (angle (r,p3,p2))) is complex real ext-real Element of REAL
(2 * ((angle (p1,p3,r)) + (angle (r,p3,p2)))) - (4 * PI) is complex real ext-real Element of REAL
2 * (angle (p1,p3,r)) is complex real ext-real Element of REAL
(angle (p1,p3,r)) - PI is complex real ext-real Element of REAL
2 * ((angle (p1,p3,r)) - PI) is complex real ext-real Element of REAL
angle (p1,p4,r) is complex real ext-real Element of REAL
angle ((euc2cpx p1),(euc2cpx p4),(euc2cpx r)) is complex real ext-real set
(angle (p1,p4,r)) + (angle (r,p4,p2)) is complex real ext-real Element of REAL
(angle (p1,p4,p2)) + (2 * PI) is complex real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p1,p3,p2) is complex real ext-real Element of REAL
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx p3),(euc2cpx p2)) is complex real ext-real set
p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p1,p4,p2) is complex real ext-real Element of REAL
euc2cpx p4 is complex Element of COMPLEX
p4 `1 is complex real ext-real Element of REAL
K367(p4,1) is complex real ext-real Element of REAL
p4 `2 is complex real ext-real Element of REAL
K367(p4,2) is complex real ext-real Element of REAL
(p4 `2) * <i> is complex set
(p4 `1) + ((p4 `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx p4),(euc2cpx p2)) is complex real ext-real set
(angle (p1,p4,p2)) - PI is complex real ext-real Element of REAL
(angle (p1,p4,p2)) + PI is complex real ext-real Element of REAL
p is complex real ext-real set
a is complex real ext-real set
b is complex real ext-real set
circle (p,a,b) is Element of bool the carrier of (TOP-REAL 2)
|[p,a]| is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
2 * (angle (p1,p3,p2)) is complex real ext-real Element of REAL
angle (p1,|[p,a]|,p2) is complex real ext-real Element of REAL
euc2cpx |[p,a]| is complex Element of COMPLEX
|[p,a]| `1 is complex real ext-real Element of REAL
K367(|[p,a]|,1) is complex real ext-real Element of REAL
|[p,a]| `2 is complex real ext-real Element of REAL
K367(|[p,a]|,2) is complex real ext-real Element of REAL
(|[p,a]| `2) * <i> is complex set
(|[p,a]| `1) + ((|[p,a]| `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx |[p,a]|),(euc2cpx p2)) is complex real ext-real set
2 * (angle (p1,p4,p2)) is complex real ext-real Element of REAL
2 * ((angle (p1,p4,p2)) - PI) is complex real ext-real Element of REAL
(angle (p1,p3,p2)) - PI is complex real ext-real Element of REAL
2 * ((angle (p1,p3,p2)) - PI) is complex real ext-real Element of REAL
angle (p1,|[p,a]|,p2) is complex real ext-real Element of REAL
euc2cpx |[p,a]| is complex Element of COMPLEX
|[p,a]| `1 is complex real ext-real Element of REAL
K367(|[p,a]|,1) is complex real ext-real Element of REAL
|[p,a]| `2 is complex real ext-real Element of REAL
K367(|[p,a]|,2) is complex real ext-real Element of REAL
(|[p,a]| `2) * <i> is complex set
(|[p,a]| `1) + ((|[p,a]| `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx |[p,a]|),(euc2cpx p2)) is complex real ext-real set
2 * (angle (p1,p4,p2)) is complex real ext-real Element of REAL
2 * ((angle (p1,p4,p2)) - PI) is complex real ext-real Element of REAL
2 * (angle (p1,p3,p2)) is complex real ext-real Element of REAL
angle (p1,|[p,a]|,p2) is complex real ext-real Element of REAL
euc2cpx |[p,a]| is complex Element of COMPLEX
|[p,a]| `1 is complex real ext-real Element of REAL
K367(|[p,a]|,1) is complex real ext-real Element of REAL
|[p,a]| `2 is complex real ext-real Element of REAL
K367(|[p,a]|,2) is complex real ext-real Element of REAL
(|[p,a]| `2) * <i> is complex set
(|[p,a]| `1) + ((|[p,a]| `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx |[p,a]|),(euc2cpx p2)) is complex real ext-real set
(angle (p1,p3,p2)) - PI is complex real ext-real Element of REAL
2 * ((angle (p1,p3,p2)) - PI) is complex real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p1,p2,p3) is complex real ext-real Element of REAL
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx p2),(euc2cpx p3)) is complex real ext-real set
p4 is complex real ext-real set
p is complex real ext-real set
a is complex real ext-real set
circle (p4,p,a) is Element of bool the carrier of (TOP-REAL 2)
LSeg (p1,p3) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p1) + (b1 * p3)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
{p1,p3} is non empty set
(LSeg (p1,p3)) \ {p1,p3} is Element of bool the carrier of (TOP-REAL 2)
inside_of_circle (p4,p,a) is Element of bool the carrier of (TOP-REAL 2)
(inside_of_circle (p4,p,a)) /\ (circle (p4,p,a)) is Element of bool the carrier of (TOP-REAL 2)
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
LSeg (p1,p2) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p1) + (b1 * p2)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
LSeg (p1,p3) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p1) + (b1 * p3)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 - p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p4 is Relation-like Function-like set
K214((TOP-REAL 2),p1,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p4) is Relation-like Function-like complex-valued set
K251(p1,K280(p4)) is Relation-like Function-like set
|.(p1 - p4).| is complex real ext-real non negative Element of REAL
sqr (p1 - p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p1 - p4),(p1 - p4)) is Relation-like Function-like set
K339((sqr (p1 - p4))) is complex real ext-real Element of REAL
sqrt K339((sqr (p1 - p4))) is complex real ext-real Element of REAL
p4 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p2 is Relation-like Function-like set
K214((TOP-REAL 2),p4,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p4,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p4 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p4 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p2) is Relation-like Function-like complex-valued set
K251(p4,K280(p2)) is Relation-like Function-like set
|.(p4 - p2).| is complex real ext-real non negative Element of REAL
sqr (p4 - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p4 - p2),(p4 - p2)) is Relation-like Function-like set
K339((sqr (p4 - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr (p4 - p2))) is complex real ext-real Element of REAL
|.(p1 - p4).| * |.(p4 - p2).| is complex real ext-real non negative Element of REAL
p4 - p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p3 is Relation-like Function-like set
K214((TOP-REAL 2),p4,(- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p4,(- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p4 + (- p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p4 - p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p3) is Relation-like Function-like complex-valued set
K251(p4,K280(p3)) is Relation-like Function-like set
|.(p4 - p3).| is complex real ext-real non negative Element of REAL
sqr (p4 - p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p4 - p3),(p4 - p3)) is Relation-like Function-like set
K339((sqr (p4 - p3))) is complex real ext-real Element of REAL
sqrt K339((sqr (p4 - p3))) is complex real ext-real Element of REAL
|.(p1 - p4).| * |.(p4 - p3).| is complex real ext-real non negative Element of REAL
p is complex real ext-real set
a is complex real ext-real set
b is complex real ext-real set
circle (p,a,b) is Element of bool the carrier of (TOP-REAL 2)
|.(0. (TOP-REAL 2)).| is complex real ext-real non negative Element of REAL
sqr (0. (TOP-REAL 2)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((0. (TOP-REAL 2)),(0. (TOP-REAL 2))) is Relation-like Function-like set
K339((sqr (0. (TOP-REAL 2)))) is complex real ext-real Element of REAL
sqrt K339((sqr (0. (TOP-REAL 2)))) is complex real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
LSeg (p1,p1) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p1) + (b1 * p1)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
LSeg (p2,p3) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p2) + (b1 * p3)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 - p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p4 is Relation-like Function-like set
K214((TOP-REAL 2),p1,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p4) is Relation-like Function-like complex-valued set
K251(p1,K280(p4)) is Relation-like Function-like set
|.(p1 - p4).| is complex real ext-real non negative Element of REAL
sqr (p1 - p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p1 - p4),(p1 - p4)) is Relation-like Function-like set
K339((sqr (p1 - p4))) is complex real ext-real Element of REAL
sqrt K339((sqr (p1 - p4))) is complex real ext-real Element of REAL
p4 - p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p1 is Relation-like Function-like set
K214((TOP-REAL 2),p4,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p4,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p4 + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p4 - p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p1) is Relation-like Function-like complex-valued set
K251(p4,K280(p1)) is Relation-like Function-like set
|.(p4 - p1).| is complex real ext-real non negative Element of REAL
sqr (p4 - p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p4 - p1),(p4 - p1)) is Relation-like Function-like set
K339((sqr (p4 - p1))) is complex real ext-real Element of REAL
sqrt K339((sqr (p4 - p1))) is complex real ext-real Element of REAL
|.(p1 - p4).| * |.(p4 - p1).| is complex real ext-real non negative Element of REAL
p2 - p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p2,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p2,K280(p4)) is Relation-like Function-like set
|.(p2 - p4).| is complex real ext-real non negative Element of REAL
sqr (p2 - p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p2 - p4),(p2 - p4)) is Relation-like Function-like set
K339((sqr (p2 - p4))) is complex real ext-real Element of REAL
sqrt K339((sqr (p2 - p4))) is complex real ext-real Element of REAL
p4 - p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p3 is Relation-like Function-like set
K214((TOP-REAL 2),p4,(- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p4,(- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p4 + (- p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p4 - p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p3) is Relation-like Function-like complex-valued set
K251(p4,K280(p3)) is Relation-like Function-like set
|.(p4 - p3).| is complex real ext-real non negative Element of REAL
sqr (p4 - p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p4 - p3),(p4 - p3)) is Relation-like Function-like set
K339((sqr (p4 - p3))) is complex real ext-real Element of REAL
sqrt K339((sqr (p4 - p3))) is complex real ext-real Element of REAL
|.(p2 - p4).| * |.(p4 - p3).| is complex real ext-real non negative Element of REAL
p is complex real ext-real set
a is complex real ext-real set
b is complex real ext-real set
circle (p,a,b) is Element of bool the carrier of (TOP-REAL 2)
{p2,p3} is non empty set
(LSeg (p2,p3)) \ {p2,p3} is Element of bool the carrier of (TOP-REAL 2)
inside_of_circle (p,a,b) is Element of bool the carrier of (TOP-REAL 2)
{p1} is non empty set
p4 - p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p4,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p4,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p4 + (- p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p4 - p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p4,K280(p4)) is Relation-like Function-like set
|.(p4 - p4).| is complex real ext-real non negative Element of REAL
sqr (p4 - p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p4 - p4),(p4 - p4)) is Relation-like Function-like set
K339((sqr (p4 - p4))) is complex real ext-real Element of REAL
sqrt K339((sqr (p4 - p4))) is complex real ext-real Element of REAL
|.(0. (TOP-REAL 2)).| is complex real ext-real non negative Element of REAL
sqr (0. (TOP-REAL 2)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((0. (TOP-REAL 2)),(0. (TOP-REAL 2))) is Relation-like Function-like set
K339((sqr (0. (TOP-REAL 2)))) is complex real ext-real Element of REAL
sqrt K339((sqr (0. (TOP-REAL 2)))) is complex real ext-real Element of REAL
0* 2 is Relation-like NAT -defined REAL -valued Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL 2
REAL 2 is non empty FinSequence-membered M10( REAL )
K318(2,REAL) is FinSequence-membered M10( REAL )
K319(REAL,2,0) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued Element of K318(2,REAL)
|.(0* 2).| is complex real ext-real non negative Element of REAL
sqr (0* 2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((0* 2),(0* 2)) is Relation-like Function-like set
K339((sqr (0* 2))) is complex real ext-real Element of REAL
sqrt K339((sqr (0* 2))) is complex real ext-real Element of REAL
(inside_of_circle (p,a,b)) /\ (circle (p,a,b)) is Element of bool the carrier of (TOP-REAL 2)
p1 - p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p1,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p1,K280(p1)) is Relation-like Function-like set
|.(p1 - p1).| is complex real ext-real non negative Element of REAL
sqr (p1 - p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p1 - p1),(p1 - p1)) is Relation-like Function-like set
K339((sqr (p1 - p1))) is complex real ext-real Element of REAL
sqrt K339((sqr (p1 - p1))) is complex real ext-real Element of REAL
p1 - p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p1,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p1,K280(p1)) is Relation-like Function-like set
|.(p1 - p1).| is complex real ext-real non negative Element of REAL
sqr (p1 - p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p1 - p1),(p1 - p1)) is Relation-like Function-like set
K339((sqr (p1 - p1))) is complex real ext-real Element of REAL
sqrt K339((sqr (p1 - p1))) is complex real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
LSeg (p1,p3) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p1) + (b1 * p3)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
angle (p1,p3,p2) is complex real ext-real Element of REAL
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx p3),(euc2cpx p2)) is complex real ext-real set
p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
LSeg (p2,p4) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p2) + (b1 * p4)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
angle (p1,p4,p2) is complex real ext-real Element of REAL
euc2cpx p4 is complex Element of COMPLEX
p4 `1 is complex real ext-real Element of REAL
K367(p4,1) is complex real ext-real Element of REAL
p4 `2 is complex real ext-real Element of REAL
K367(p4,2) is complex real ext-real Element of REAL
(p4 `2) * <i> is complex set
(p4 `1) + ((p4 `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx p4),(euc2cpx p2)) is complex real ext-real set
p is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
a is complex real ext-real set
b is complex real ext-real set
r is complex real ext-real set
circle (a,b,r) is Element of bool the carrier of (TOP-REAL 2)
{p1,p3} is non empty set
(LSeg (p1,p3)) \ {p1,p3} is Element of bool the carrier of (TOP-REAL 2)
inside_of_circle (a,b,r) is Element of bool the carrier of (TOP-REAL 2)
{p2,p4} is non empty set
(LSeg (p2,p4)) \ {p2,p4} is Element of bool the carrier of (TOP-REAL 2)
(inside_of_circle (a,b,r)) /\ (circle (a,b,r)) is Element of bool the carrier of (TOP-REAL 2)
(inside_of_circle (a,b,r)) /\ (circle (a,b,r)) is Element of bool the carrier of (TOP-REAL 2)
angle (p1,p4,p) is complex real ext-real Element of REAL
euc2cpx p is complex Element of COMPLEX
p `1 is complex real ext-real Element of REAL
K367(p,1) is complex real ext-real Element of REAL
p `2 is complex real ext-real Element of REAL
K367(p,2) is complex real ext-real Element of REAL
(p `2) * <i> is complex set
(p `1) + ((p `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx p4),(euc2cpx p)) is complex real ext-real set
(inside_of_circle (a,b,r)) /\ (circle (a,b,r)) is Element of bool the carrier of (TOP-REAL 2)
(inside_of_circle (a,b,r)) /\ (circle (a,b,r)) is Element of bool the carrier of (TOP-REAL 2)
angle (p4,p,p1) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx p),(euc2cpx p1)) is complex real ext-real set
angle (p2,p,p3) is complex real ext-real Element of REAL
angle ((euc2cpx p2),(euc2cpx p),(euc2cpx p3)) is complex real ext-real set
angle (p,p3,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p),(euc2cpx p3),(euc2cpx p2)) is complex real ext-real set
(angle (p1,p3,p2)) - PI is complex real ext-real Element of REAL
(2 * PI) - PI is complex real ext-real Element of REAL
{p1,p2} is non empty set
0 + PI is non empty complex real ext-real positive non negative Element of REAL
((angle (p1,p3,p2)) - PI) + PI is complex real ext-real Element of REAL
LSeg (p1,p2) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p1) + (b1 * p2)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
(LSeg (p1,p2)) \ {p1,p2} is Element of bool the carrier of (TOP-REAL 2)
(inside_of_circle (a,b,r)) /\ (circle (a,b,r)) is Element of bool the carrier of (TOP-REAL 2)
(angle (p1,p3,p2)) + PI is complex real ext-real Element of REAL
(2 * PI) - PI is complex real ext-real Element of REAL
(angle (p1,p4,p2)) - PI is complex real ext-real Element of REAL
{p1,p2} is non empty set
0 + PI is non empty complex real ext-real positive non negative Element of REAL
((angle (p1,p4,p2)) - PI) + PI is complex real ext-real Element of REAL
LSeg (p1,p2) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p1) + (b1 * p2)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
(LSeg (p1,p2)) \ {p1,p2} is Element of bool the carrier of (TOP-REAL 2)
(inside_of_circle (a,b,r)) /\ (circle (a,b,r)) is Element of bool the carrier of (TOP-REAL 2)
(angle (p1,p3,p2)) - PI is complex real ext-real Element of REAL
(angle (p1,p3,p2)) + PI is complex real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p1,p2,p3) is complex real ext-real Element of REAL
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx p2),(euc2cpx p3)) is complex real ext-real set
p4 is complex real ext-real set
p is complex real ext-real set
a is complex real ext-real set
circle (p4,p,a) is Element of bool the carrier of (TOP-REAL 2)
angle (p2,p3,p1) is complex real ext-real Element of REAL
angle ((euc2cpx p2),(euc2cpx p3),(euc2cpx p1)) is complex real ext-real set
angle (p3,p1,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p3),(euc2cpx p1),(euc2cpx p2)) is complex real ext-real set
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
LSeg (p1,p3) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p1) + (b1 * p3)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
LSeg (p2,p4) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p2) + (b1 * p4)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
p is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 - p is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p is Relation-like Function-like set
K214((TOP-REAL 2),p1,(- p)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p) is Relation-like Function-like complex-valued set
K251(p1,K280(p)) is Relation-like Function-like set
|.(p1 - p).| is complex real ext-real non negative Element of REAL
sqr (p1 - p) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p1 - p),(p1 - p)) is Relation-like Function-like set
K339((sqr (p1 - p))) is complex real ext-real Element of REAL
sqrt K339((sqr (p1 - p))) is complex real ext-real Element of REAL
p - p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p3 is Relation-like Function-like set
K214((TOP-REAL 2),p,(- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p,(- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p + (- p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p - p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p3) is Relation-like Function-like complex-valued set
K251(p,K280(p3)) is Relation-like Function-like set
|.(p - p3).| is complex real ext-real non negative Element of REAL
sqr (p - p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p - p3),(p - p3)) is Relation-like Function-like set
K339((sqr (p - p3))) is complex real ext-real Element of REAL
sqrt K339((sqr (p - p3))) is complex real ext-real Element of REAL
|.(p1 - p).| * |.(p - p3).| is complex real ext-real non negative Element of REAL
p2 - p is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p2,(- p)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- p)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- p) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - p is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p2,K280(p)) is Relation-like Function-like set
|.(p2 - p).| is complex real ext-real non negative Element of REAL
sqr (p2 - p) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p2 - p),(p2 - p)) is Relation-like Function-like set
K339((sqr (p2 - p))) is complex real ext-real Element of REAL
sqrt K339((sqr (p2 - p))) is complex real ext-real Element of REAL
p - p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p4 is Relation-like Function-like set
K214((TOP-REAL 2),p,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p + (- p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p - p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p4) is Relation-like Function-like complex-valued set
K251(p,K280(p4)) is Relation-like Function-like set
|.(p - p4).| is complex real ext-real non negative Element of REAL
sqr (p - p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p - p4),(p - p4)) is Relation-like Function-like set
K339((sqr (p - p4))) is complex real ext-real Element of REAL
sqrt K339((sqr (p - p4))) is complex real ext-real Element of REAL
|.(p2 - p).| * |.(p - p4).| is complex real ext-real non negative Element of REAL
a is complex real ext-real set
b is complex real ext-real set
r is complex real ext-real set
circle (a,b,r) is Element of bool the carrier of (TOP-REAL 2)
p - p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p1 is Relation-like Function-like set
K214((TOP-REAL 2),p,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p - p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p1) is Relation-like Function-like complex-valued set
K251(p,K280(p1)) is Relation-like Function-like set
|.(p - p1).| is complex real ext-real non negative Element of REAL
sqr (p - p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p - p1),(p - p1)) is Relation-like Function-like set
K339((sqr (p - p1))) is complex real ext-real Element of REAL
sqrt K339((sqr (p - p1))) is complex real ext-real Element of REAL
p3 - p is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p3,(- p)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(- p)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (- p) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - p is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p3,K280(p)) is Relation-like Function-like set
|.(p3 - p).| is complex real ext-real non negative Element of REAL
sqr (p3 - p) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p3 - p),(p3 - p)) is Relation-like Function-like set
K339((sqr (p3 - p))) is complex real ext-real Element of REAL
sqrt K339((sqr (p3 - p))) is complex real ext-real Element of REAL
p - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p2 is Relation-like Function-like set
K214((TOP-REAL 2),p,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p2) is Relation-like Function-like complex-valued set
K251(p,K280(p2)) is Relation-like Function-like set
|.(p - p2).| is complex real ext-real non negative Element of REAL
sqr (p - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p - p2),(p - p2)) is Relation-like Function-like set
K339((sqr (p - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr (p - p2))) is complex real ext-real Element of REAL
p4 - p is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p4,(- p)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p4,(- p)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p4 + (- p) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p4 - p is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p4,K280(p)) is Relation-like Function-like set
|.(p4 - p).| is complex real ext-real non negative Element of REAL
sqr (p4 - p) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p4 - p),(p4 - p)) is Relation-like Function-like set
K339((sqr (p4 - p))) is complex real ext-real Element of REAL
sqrt K339((sqr (p4 - p))) is complex real ext-real Element of REAL
{p1,p3} is non empty set
(LSeg (p1,p3)) \ {p1,p3} is Element of bool the carrier of (TOP-REAL 2)
inside_of_circle (a,b,r) is Element of bool the carrier of (TOP-REAL 2)
{p2,p4} is non empty set
(LSeg (p2,p4)) \ {p2,p4} is Element of bool the carrier of (TOP-REAL 2)
(inside_of_circle (a,b,r)) /\ (circle (a,b,r)) is Element of bool the carrier of (TOP-REAL 2)
(inside_of_circle (a,b,r)) /\ (circle (a,b,r)) is Element of bool the carrier of (TOP-REAL 2)
(inside_of_circle (a,b,r)) /\ (circle (a,b,r)) is Element of bool the carrier of (TOP-REAL 2)
(inside_of_circle (a,b,r)) /\ (circle (a,b,r)) is Element of bool the carrier of (TOP-REAL 2)
angle (p4,p,p1) is complex real ext-real Element of REAL
euc2cpx p4 is complex Element of COMPLEX
p4 `1 is complex real ext-real Element of REAL
K367(p4,1) is complex real ext-real Element of REAL
p4 `2 is complex real ext-real Element of REAL
K367(p4,2) is complex real ext-real Element of REAL
(p4 `2) * <i> is complex set
(p4 `1) + ((p4 `2) * <i>) is complex set
euc2cpx p is complex Element of COMPLEX
p `1 is complex real ext-real Element of REAL
K367(p,1) is complex real ext-real Element of REAL
p `2 is complex real ext-real Element of REAL
K367(p,2) is complex real ext-real Element of REAL
(p `2) * <i> is complex set
(p `1) + ((p `2) * <i>) is complex set
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
angle ((euc2cpx p4),(euc2cpx p),(euc2cpx p1)) is complex real ext-real set
angle (p2,p,p3) is complex real ext-real Element of REAL
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
angle ((euc2cpx p2),(euc2cpx p),(euc2cpx p3)) is complex real ext-real set
angle (p3,p2,p) is complex real ext-real Element of REAL
angle ((euc2cpx p3),(euc2cpx p2),(euc2cpx p)) is complex real ext-real set
angle (p3,p2,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p3),(euc2cpx p2),(euc2cpx p4)) is complex real ext-real set
angle (p,p3,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p),(euc2cpx p3),(euc2cpx p2)) is complex real ext-real set
angle (p1,p3,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p1),(euc2cpx p3),(euc2cpx p2)) is complex real ext-real set
angle (p,p1,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p),(euc2cpx p1),(euc2cpx p4)) is complex real ext-real set
angle (p3,p1,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p3),(euc2cpx p1),(euc2cpx p4)) is complex real ext-real set
angle (p1,p3,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p1),(euc2cpx p3),(euc2cpx p2)) is complex real ext-real set
angle (p1,p4,p) is complex real ext-real Element of REAL
angle ((euc2cpx p1),(euc2cpx p4),(euc2cpx p)) is complex real ext-real set
angle (p1,p4,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p1),(euc2cpx p4),(euc2cpx p2)) is complex real ext-real set
LSeg (p1,p4) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p1) + (b1 * p4)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p2 is Relation-like Function-like set
K214((TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p2) is Relation-like Function-like complex-valued set
K251(p1,K280(p2)) is Relation-like Function-like set
|.(p1 - p2).| is complex real ext-real non negative Element of REAL
sqr (p1 - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p1 - p2),(p1 - p2)) is Relation-like Function-like set
K339((sqr (p1 - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr (p1 - p2))) is complex real ext-real Element of REAL
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 - p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p1 is Relation-like Function-like set
K214((TOP-REAL 2),p3,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p1) is Relation-like Function-like complex-valued set
K251(p3,K280(p1)) is Relation-like Function-like set
|.(p3 - p1).| is complex real ext-real non negative Element of REAL
sqr (p3 - p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p3 - p1),(p3 - p1)) is Relation-like Function-like set
K339((sqr (p3 - p1))) is complex real ext-real Element of REAL
sqrt K339((sqr (p3 - p1))) is complex real ext-real Element of REAL
p2 - p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p3 is Relation-like Function-like set
K214((TOP-REAL 2),p2,(- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p3) is Relation-like Function-like complex-valued set
K251(p2,K280(p3)) is Relation-like Function-like set
|.(p2 - p3).| is complex real ext-real non negative Element of REAL
sqr (p2 - p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p2 - p3),(p2 - p3)) is Relation-like Function-like set
K339((sqr (p2 - p3))) is complex real ext-real Element of REAL
sqrt K339((sqr (p2 - p3))) is complex real ext-real Element of REAL
(p2,p1,p3) is complex real ext-real set
|.(p1 - p2).| + |.(p3 - p1).| is complex real ext-real non negative Element of REAL
(|.(p1 - p2).| + |.(p3 - p1).|) + |.(p2 - p3).| is complex real ext-real non negative Element of REAL
(p2,p1,p3) / 2 is complex real ext-real Element of REAL
(p2,p1,p3) is complex real ext-real set
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p2 `1) * (p1 `2) is complex real ext-real Element of REAL
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p1 `1) * (p2 `2) is complex real ext-real Element of REAL
((p2 `1) * (p1 `2)) - ((p1 `1) * (p2 `2)) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p1 `1) * (p3 `2) is complex real ext-real Element of REAL
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
(p3 `1) * (p1 `2) is complex real ext-real Element of REAL
((p1 `1) * (p3 `2)) - ((p3 `1) * (p1 `2)) is complex real ext-real Element of REAL
(((p2 `1) * (p1 `2)) - ((p1 `1) * (p2 `2))) + (((p1 `1) * (p3 `2)) - ((p3 `1) * (p1 `2))) is complex real ext-real Element of REAL
(p3 `1) * (p2 `2) is complex real ext-real Element of REAL
(p2 `1) * (p3 `2) is complex real ext-real Element of REAL
((p3 `1) * (p2 `2)) - ((p2 `1) * (p3 `2)) is complex real ext-real Element of REAL
((((p2 `1) * (p1 `2)) - ((p1 `1) * (p2 `2))) + (((p1 `1) * (p3 `2)) - ((p3 `1) * (p1 `2)))) + (((p3 `1) * (p2 `2)) - ((p2 `1) * (p3 `2))) is complex real ext-real Element of REAL
(((((p2 `1) * (p1 `2)) - ((p1 `1) * (p2 `2))) + (((p1 `1) * (p3 `2)) - ((p3 `1) * (p1 `2)))) + (((p3 `1) * (p2 `2)) - ((p2 `1) * (p3 `2)))) / 2 is complex real ext-real Element of REAL
abs (p2,p1,p3) is complex real ext-real Element of REAL
Re (p2,p1,p3) is complex real ext-real Element of REAL
(Re (p2,p1,p3)) ^2 is complex real ext-real Element of REAL
(Re (p2,p1,p3)) * (Re (p2,p1,p3)) is complex real ext-real set
Im (p2,p1,p3) is complex real ext-real Element of REAL
(Im (p2,p1,p3)) ^2 is complex real ext-real Element of REAL
(Im (p2,p1,p3)) * (Im (p2,p1,p3)) is complex real ext-real set
((Re (p2,p1,p3)) ^2) + ((Im (p2,p1,p3)) ^2) is complex real ext-real Element of REAL
sqrt (((Re (p2,p1,p3)) ^2) + ((Im (p2,p1,p3)) ^2)) is complex real ext-real Element of REAL
p4 is complex real ext-real set
p is complex real ext-real set
a is complex real ext-real set
b is complex real ext-real set
b - p4 is complex real ext-real set
b * (b - p4) is complex real ext-real set
b - p is complex real ext-real set
(b * (b - p4)) * (b - p) is complex real ext-real set
b - a is complex real ext-real set
((b * (b - p4)) * (b - p)) * (b - a) is complex real ext-real set
sqrt (((b * (b - p4)) * (b - p)) * (b - a)) is complex real ext-real set
p2 - p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p2,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p2,K280(p1)) is Relation-like Function-like set
|.(p2 - p1).| is complex real ext-real non negative Element of REAL
sqr (p2 - p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p2 - p1),(p2 - p1)) is Relation-like Function-like set
K339((sqr (p2 - p1))) is complex real ext-real Element of REAL
sqrt K339((sqr (p2 - p1))) is complex real ext-real Element of REAL
p3 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p3,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p3,K280(p2)) is Relation-like Function-like set
|.(p3 - p2).| is complex real ext-real non negative Element of REAL
sqr (p3 - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p3 - p2),(p3 - p2)) is Relation-like Function-like set
K339((sqr (p3 - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr (p3 - p2))) is complex real ext-real Element of REAL
a ^2 is complex real ext-real set
a * a is complex real ext-real set
p4 ^2 is complex real ext-real set
p4 * p4 is complex real ext-real set
p ^2 is complex real ext-real set
p * p is complex real ext-real set
(p4 ^2) + (p ^2) is complex real ext-real set
2 * p4 is complex real ext-real Element of REAL
(2 * p4) * p is complex real ext-real Element of REAL
angle (p2,p1,p3) is complex real ext-real Element of REAL
euc2cpx p2 is complex Element of COMPLEX
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
euc2cpx p1 is complex Element of COMPLEX
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
euc2cpx p3 is complex Element of COMPLEX
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
angle ((euc2cpx p2),(euc2cpx p1),(euc2cpx p3)) is complex real ext-real set
cos (angle (p2,p1,p3)) is complex real ext-real Element of REAL
((2 * p4) * p) * (cos (angle (p2,p1,p3))) is complex real ext-real Element of REAL
((p4 ^2) + (p ^2)) - (((2 * p4) * p) * (cos (angle (p2,p1,p3)))) is complex real ext-real Element of REAL
angle (p3,p1,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p3),(euc2cpx p1),(euc2cpx p2)) is complex real ext-real set
sin (angle (p3,p1,p2)) is complex real ext-real Element of REAL
(sin (angle (p3,p1,p2))) ^2 is complex real ext-real Element of REAL
(sin (angle (p3,p1,p2))) * (sin (angle (p3,p1,p2))) is complex real ext-real set
cos (angle (p3,p1,p2)) is complex real ext-real Element of REAL
(cos (angle (p3,p1,p2))) ^2 is complex real ext-real Element of REAL
(cos (angle (p3,p1,p2))) * (cos (angle (p3,p1,p2))) is complex real ext-real set
((sin (angle (p3,p1,p2))) ^2) + ((cos (angle (p3,p1,p2))) ^2) is complex real ext-real Element of REAL
(p2,p1,p3) ^2 is complex real ext-real set
(p2,p1,p3) * (p2,p1,p3) is complex real ext-real set
p4 * p is complex real ext-real set
(p4 * p) * (sin (angle (p3,p1,p2))) is complex real ext-real Element of REAL
((p4 * p) * (sin (angle (p3,p1,p2)))) / 2 is complex real ext-real Element of REAL
(((p4 * p) * (sin (angle (p3,p1,p2)))) / 2) ^2 is complex real ext-real Element of REAL
(((p4 * p) * (sin (angle (p3,p1,p2)))) / 2) * (((p4 * p) * (sin (angle (p3,p1,p2)))) / 2) is complex real ext-real set
((p4 * p) * (sin (angle (p3,p1,p2)))) ^2 is complex real ext-real Element of REAL
((p4 * p) * (sin (angle (p3,p1,p2)))) * ((p4 * p) * (sin (angle (p3,p1,p2)))) is complex real ext-real set
1 / 2 is non empty complex real ext-real positive non negative Element of REAL
(1 / 2) ^2 is complex real ext-real Element of REAL
(1 / 2) * (1 / 2) is non empty complex real ext-real positive non negative set
(((p4 * p) * (sin (angle (p3,p1,p2)))) ^2) * ((1 / 2) ^2) is complex real ext-real Element of REAL
(p4 * p) ^2 is complex real ext-real set
(p4 * p) * (p4 * p) is complex real ext-real set
1 - ((cos (angle (p3,p1,p2))) ^2) is complex real ext-real Element of REAL
((p4 * p) ^2) * (1 - ((cos (angle (p3,p1,p2))) ^2)) is complex real ext-real Element of REAL
(((p4 * p) ^2) * (1 - ((cos (angle (p3,p1,p2))) ^2))) * ((1 / 2) ^2) is complex real ext-real Element of REAL
((p4 * p) ^2) * ((cos (angle (p3,p1,p2))) ^2) is complex real ext-real Element of REAL
((p4 * p) ^2) - (((p4 * p) ^2) * ((cos (angle (p3,p1,p2))) ^2)) is complex real ext-real Element of REAL
2 ^2 is complex real ext-real Element of REAL
2 * 2 is non empty complex real ext-real positive non negative set
(((p4 * p) ^2) - (((p4 * p) ^2) * ((cos (angle (p3,p1,p2))) ^2))) * (2 ^2) is complex real ext-real Element of REAL
((((p4 * p) ^2) - (((p4 * p) ^2) * ((cos (angle (p3,p1,p2))) ^2))) * (2 ^2)) / (2 ^2) is complex real ext-real Element of REAL
(((((p4 * p) ^2) - (((p4 * p) ^2) * ((cos (angle (p3,p1,p2))) ^2))) * (2 ^2)) / (2 ^2)) * ((1 / 2) ^2) is complex real ext-real Element of REAL
(2 ^2) * ((p4 * p) ^2) is complex real ext-real Element of REAL
((2 * p4) * p) * (cos (angle (p3,p1,p2))) is complex real ext-real Element of REAL
(((2 * p4) * p) * (cos (angle (p3,p1,p2)))) ^2 is complex real ext-real Element of REAL
(((2 * p4) * p) * (cos (angle (p3,p1,p2)))) * (((2 * p4) * p) * (cos (angle (p3,p1,p2)))) is complex real ext-real set
((2 ^2) * ((p4 * p) ^2)) - ((((2 * p4) * p) * (cos (angle (p3,p1,p2)))) ^2) is complex real ext-real Element of REAL
(((2 ^2) * ((p4 * p) ^2)) - ((((2 * p4) * p) * (cos (angle (p3,p1,p2)))) ^2)) / (2 ^2) is complex real ext-real Element of REAL
((((2 ^2) * ((p4 * p) ^2)) - ((((2 * p4) * p) * (cos (angle (p3,p1,p2)))) ^2)) / (2 ^2)) * ((1 / 2) ^2) is complex real ext-real Element of REAL
- (a ^2) is complex real ext-real set
(- (a ^2)) + (p4 ^2) is complex real ext-real set
((- (a ^2)) + (p4 ^2)) + (p ^2) is complex real ext-real set
(((- (a ^2)) + (p4 ^2)) + (p ^2)) ^2 is complex real ext-real set
(((- (a ^2)) + (p4 ^2)) + (p ^2)) * (((- (a ^2)) + (p4 ^2)) + (p ^2)) is complex real ext-real set
((2 ^2) * ((p4 * p) ^2)) - ((((- (a ^2)) + (p4 ^2)) + (p ^2)) ^2) is complex real ext-real Element of REAL
(((2 ^2) * ((p4 * p) ^2)) - ((((- (a ^2)) + (p4 ^2)) + (p ^2)) ^2)) / (2 ^2) is complex real ext-real Element of REAL
((((2 ^2) * ((p4 * p) ^2)) - ((((- (a ^2)) + (p4 ^2)) + (p ^2)) ^2)) / (2 ^2)) * ((1 / 2) ^2) is complex real ext-real Element of REAL
16 is non empty natural complex real ext-real positive non negative V33() V34() V126() V127() V128() V129() V130() V131() Element of NAT
16 * (b - p4) is complex real ext-real Element of REAL
(16 * (b - p4)) * (b - p) is complex real ext-real Element of REAL
(b - a) * b is complex real ext-real set
((16 * (b - p4)) * (b - p)) * ((b - a) * b) is complex real ext-real Element of REAL
2 * 2 is non empty complex real ext-real positive non negative Element of REAL
(((16 * (b - p4)) * (b - p)) * ((b - a) * b)) / (2 * 2) is complex real ext-real Element of REAL
((((16 * (b - p4)) * (b - p)) * ((b - a) * b)) / (2 * 2)) * ((1 / 2) ^2) is complex real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 - p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p1 is Relation-like Function-like set
K214((TOP-REAL 2),p2,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p1) is Relation-like Function-like complex-valued set
K251(p2,K280(p1)) is Relation-like Function-like set
|.(p2 - p1).| is complex real ext-real non negative Element of REAL
sqr (p2 - p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p2 - p1),(p2 - p1)) is Relation-like Function-like set
K339((sqr (p2 - p1))) is complex real ext-real Element of REAL
sqrt K339((sqr (p2 - p1))) is complex real ext-real Element of REAL
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
LSeg (p1,p3) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p1) + (b1 * p3)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
p3 - p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p3,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p3,K280(p1)) is Relation-like Function-like set
|.(p3 - p1).| is complex real ext-real non negative Element of REAL
sqr (p3 - p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p3 - p1),(p3 - p1)) is Relation-like Function-like set
K339((sqr (p3 - p1))) is complex real ext-real Element of REAL
sqrt K339((sqr (p3 - p1))) is complex real ext-real Element of REAL
p3 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p2 is Relation-like Function-like set
K214((TOP-REAL 2),p3,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p2) is Relation-like Function-like complex-valued set
K251(p3,K280(p2)) is Relation-like Function-like set
|.(p3 - p2).| is complex real ext-real non negative Element of REAL
sqr (p3 - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p3 - p2),(p3 - p2)) is Relation-like Function-like set
K339((sqr (p3 - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr (p3 - p2))) is complex real ext-real Element of REAL
p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
LSeg (p2,p4) is non empty V244( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * p2) + (b1 * p4)) where b1 is complex real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
p4 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p4,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p4,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p4 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p4 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p4,K280(p2)) is Relation-like Function-like set
|.(p4 - p2).| is complex real ext-real non negative Element of REAL
sqr (p4 - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p4 - p2),(p4 - p2)) is Relation-like Function-like set
K339((sqr (p4 - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr (p4 - p2))) is complex real ext-real Element of REAL
|.(p3 - p1).| * |.(p4 - p2).| is complex real ext-real non negative Element of REAL
p4 - p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p3 is Relation-like Function-like set
K214((TOP-REAL 2),p4,(- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p4,(- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p4 + (- p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p4 - p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p3) is Relation-like Function-like complex-valued set
K251(p4,K280(p3)) is Relation-like Function-like set
|.(p4 - p3).| is complex real ext-real non negative Element of REAL
sqr (p4 - p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p4 - p3),(p4 - p3)) is Relation-like Function-like set
K339((sqr (p4 - p3))) is complex real ext-real Element of REAL
sqrt K339((sqr (p4 - p3))) is complex real ext-real Element of REAL
|.(p2 - p1).| * |.(p4 - p3).| is complex real ext-real non negative Element of REAL
p4 - p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p4,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p4,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p4 + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p4 - p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p4,K280(p1)) is Relation-like Function-like set
|.(p4 - p1).| is complex real ext-real non negative Element of REAL
sqr (p4 - p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p4 - p1),(p4 - p1)) is Relation-like Function-like set
K339((sqr (p4 - p1))) is complex real ext-real Element of REAL
sqrt K339((sqr (p4 - p1))) is complex real ext-real Element of REAL
|.(p3 - p2).| * |.(p4 - p1).| is complex real ext-real non negative Element of REAL
(|.(p2 - p1).| * |.(p4 - p3).|) + (|.(p3 - p2).| * |.(p4 - p1).|) is complex real ext-real non negative Element of REAL
p is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
a is complex real ext-real set
b is complex real ext-real set
r is complex real ext-real set
circle (a,b,r) is Element of bool the carrier of (TOP-REAL 2)
p1 - p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p1,(- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p1,K280(p3)) is Relation-like Function-like set
|.(p1 - p3).| is complex real ext-real non negative Element of REAL
sqr (p1 - p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p1 - p3),(p1 - p3)) is Relation-like Function-like set
K339((sqr (p1 - p3))) is complex real ext-real Element of REAL
sqrt K339((sqr (p1 - p3))) is complex real ext-real Element of REAL
{p1} is non empty set
(LSeg (p2,p4)) /\ (circle (a,b,r)) is Element of bool the carrier of (TOP-REAL 2)
{p2,p4} is non empty set
{p2} is non empty set
(LSeg (p1,p3)) /\ (circle (a,b,r)) is Element of bool the carrier of (TOP-REAL 2)
{p1,p3} is non empty set
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
euc2cpx p4 is complex Element of COMPLEX
p4 `1 is complex real ext-real Element of REAL
K367(p4,1) is complex real ext-real Element of REAL
p4 `2 is complex real ext-real Element of REAL
K367(p4,2) is complex real ext-real Element of REAL
(p4 `2) * <i> is complex set
(p4 `1) + ((p4 `2) * <i>) is complex set
angle (p3,p4,p2) is complex real ext-real Element of REAL
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
angle ((euc2cpx p3),(euc2cpx p4),(euc2cpx p2)) is complex real ext-real set
angle (p1,p2,p4) is complex real ext-real Element of REAL
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx p2),(euc2cpx p4)) is complex real ext-real set
angle (p4,p1,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx p1),(euc2cpx p2)) is complex real ext-real set
angle (p2,p4,p1) is complex real ext-real Element of REAL
angle ((euc2cpx p2),(euc2cpx p4),(euc2cpx p1)) is complex real ext-real set
angle (p2,p3,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p2),(euc2cpx p3),(euc2cpx p4)) is complex real ext-real set
{p1,p3} is non empty set
(LSeg (p1,p3)) \ {p1,p3} is Element of bool the carrier of (TOP-REAL 2)
inside_of_circle (a,b,r) is Element of bool the carrier of (TOP-REAL 2)
(inside_of_circle (a,b,r)) /\ (circle (a,b,r)) is Element of bool the carrier of (TOP-REAL 2)
angle (p,p2,p3) is complex real ext-real Element of REAL
euc2cpx p is complex Element of COMPLEX
p `1 is complex real ext-real Element of REAL
K367(p,1) is complex real ext-real Element of REAL
p `2 is complex real ext-real Element of REAL
K367(p,2) is complex real ext-real Element of REAL
(p `2) * <i> is complex set
(p `1) + ((p `2) * <i>) is complex set
angle ((euc2cpx p),(euc2cpx p2),(euc2cpx p3)) is complex real ext-real set
p5 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p1,p2,p5) is complex real ext-real Element of REAL
euc2cpx p5 is complex Element of COMPLEX
p5 `1 is complex real ext-real Element of REAL
K367(p5,1) is complex real ext-real Element of REAL
p5 `2 is complex real ext-real Element of REAL
K367(p5,2) is complex real ext-real Element of REAL
(p5 `2) * <i> is complex set
(p5 `1) + ((p5 `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx p2),(euc2cpx p5)) is complex real ext-real set
angle (p4,p2,p3) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx p2),(euc2cpx p3)) is complex real ext-real set
angle (p1,p2,p1) is complex real ext-real Element of REAL
angle ((euc2cpx p1),(euc2cpx p2),(euc2cpx p1)) is complex real ext-real set
angle (p3,p2,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p3),(euc2cpx p2),(euc2cpx p4)) is complex real ext-real set
(angle (p4,p2,p3)) + (angle (p3,p2,p4)) is complex real ext-real Element of REAL
angle (p4,p2,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p4),(euc2cpx p2),(euc2cpx p4)) is complex real ext-real set
(angle (p4,p2,p4)) + (2 * PI) is complex real ext-real Element of REAL
0 + (2 * PI) is non empty complex real ext-real positive non negative Element of REAL
angle (p1,p2,p3) is complex real ext-real Element of REAL
angle ((euc2cpx p1),(euc2cpx p2),(euc2cpx p3)) is complex real ext-real set
(angle (p1,p2,p3)) + (angle (p3,p2,p4)) is complex real ext-real Element of REAL
(angle (p1,p2,p4)) + (2 * PI) is complex real ext-real Element of REAL
(angle (p1,p2,p3)) + (angle (p3,p2,p4)) is complex real ext-real Element of REAL
(angle (p1,p2,p3)) + (angle (p3,p2,p4)) is complex real ext-real Element of REAL
(angle (p1,p2,p4)) + (2 * PI) is complex real ext-real Element of REAL
- (2 * PI) is non empty complex real ext-real non positive negative Element of REAL
(angle (p1,p2,p3)) + (angle (p3,p2,p4)) is complex real ext-real Element of REAL
(angle (p1,p2,p4)) + (2 * PI) is complex real ext-real Element of REAL
angle (p5,p2,p3) is complex real ext-real Element of REAL
angle ((euc2cpx p5),(euc2cpx p2),(euc2cpx p3)) is complex real ext-real set
angle (p5,p2,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p5),(euc2cpx p2),(euc2cpx p4)) is complex real ext-real set
(angle (p5,p2,p4)) + (angle (p4,p2,p3)) is complex real ext-real Element of REAL
(angle (p4,p2,p3)) + (angle (p5,p2,p4)) is complex real ext-real Element of REAL
(angle (p5,p2,p3)) + (2 * PI) is complex real ext-real Element of REAL
(angle (p1,p2,p4)) + (2 * PI) is complex real ext-real Element of REAL
(angle (p5,p2,p3)) + (2 * PI) is complex real ext-real Element of REAL
angle (p5,p2,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p5),(euc2cpx p2),(euc2cpx p4)) is complex real ext-real set
(angle (p5,p2,p4)) + (angle (p4,p2,p3)) is complex real ext-real Element of REAL
(angle (p4,p2,p3)) + (angle (p5,p2,p4)) is complex real ext-real Element of REAL
0 + (2 * PI) is non empty complex real ext-real positive non negative Element of REAL
angle (p5,p2,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p5),(euc2cpx p2),(euc2cpx p4)) is complex real ext-real set
(angle (p5,p2,p4)) + (angle (p4,p2,p3)) is complex real ext-real Element of REAL
(angle (p1,p2,p4)) + (2 * PI) is complex real ext-real Element of REAL
(angle (p4,p2,p3)) + (angle (p5,p2,p4)) is complex real ext-real Element of REAL
0 + (2 * PI) is non empty complex real ext-real positive non negative Element of REAL
angle (p5,p2,p4) is complex real ext-real Element of REAL
angle ((euc2cpx p5),(euc2cpx p2),(euc2cpx p4)) is complex real ext-real set
(angle (p5,p2,p4)) + (angle (p4,p2,p3)) is complex real ext-real Element of REAL
(angle (p4,p2,p3)) + (angle (p5,p2,p4)) is complex real ext-real Element of REAL
(angle (p5,p2,p3)) + (2 * PI) is complex real ext-real Element of REAL
(angle (p1,p2,p4)) + (2 * PI) is complex real ext-real Element of REAL
{p1,p3} is non empty set
(LSeg (p1,p3)) \ {p1,p3} is Element of bool the carrier of (TOP-REAL 2)
inside_of_circle (a,b,r) is Element of bool the carrier of (TOP-REAL 2)
(inside_of_circle (a,b,r)) /\ (circle (a,b,r)) is Element of bool the carrier of (TOP-REAL 2)
angle (p2,p1,p3) is complex real ext-real Element of REAL
angle ((euc2cpx p2),(euc2cpx p1),(euc2cpx p3)) is complex real ext-real set
angle (p2,p4,p3) is complex real ext-real Element of REAL
angle ((euc2cpx p2),(euc2cpx p4),(euc2cpx p3)) is complex real ext-real set
angle (p3,p1,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p3),(euc2cpx p1),(euc2cpx p2)) is complex real ext-real set
(2 * PI) - (angle (p2,p1,p3)) is complex real ext-real Element of REAL
angle (p5,p1,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p5),(euc2cpx p1),(euc2cpx p2)) is complex real ext-real set
angle (p2,p5,p1) is complex real ext-real Element of REAL
angle ((euc2cpx p2),(euc2cpx p5),(euc2cpx p1)) is complex real ext-real set
(angle (p2,p3,p4)) + (angle (p3,p4,p2)) is complex real ext-real Element of REAL
((angle (p2,p3,p4)) + (angle (p3,p4,p2))) + (angle (p4,p2,p3)) is complex real ext-real Element of REAL
(angle (p2,p5,p1)) + (angle (p5,p1,p2)) is complex real ext-real Element of REAL
((angle (p2,p5,p1)) + (angle (p5,p1,p2))) + (angle (p1,p2,p5)) is complex real ext-real Element of REAL
(angle (p2,p3,p4)) + (angle (p3,p4,p2)) is complex real ext-real Element of REAL
((angle (p2,p3,p4)) + (angle (p3,p4,p2))) + (angle (p4,p2,p3)) is complex real ext-real Element of REAL
(angle (p2,p5,p1)) + (angle (p5,p1,p2)) is complex real ext-real Element of REAL
((angle (p2,p5,p1)) + (angle (p5,p1,p2))) + (angle (p1,p2,p5)) is complex real ext-real Element of REAL
(2 * PI) - 0 is non empty complex real ext-real positive non negative Element of REAL
(angle (p2,p3,p4)) - (angle (p2,p5,p1)) is complex real ext-real Element of REAL
(angle (p2,p3,p4)) + (angle (p3,p4,p2)) is complex real ext-real Element of REAL
((angle (p2,p3,p4)) + (angle (p3,p4,p2))) + (angle (p4,p2,p3)) is complex real ext-real Element of REAL
(angle (p2,p5,p1)) + (angle (p5,p1,p2)) is complex real ext-real Element of REAL
((angle (p2,p5,p1)) + (angle (p5,p1,p2))) + (angle (p1,p2,p5)) is complex real ext-real Element of REAL
(2 * PI) - 0 is non empty complex real ext-real positive non negative Element of REAL
(angle (p2,p5,p1)) - (angle (p2,p3,p4)) is complex real ext-real Element of REAL
(angle (p2,p3,p4)) + (angle (p3,p4,p2)) is complex real ext-real Element of REAL
((angle (p2,p3,p4)) + (angle (p3,p4,p2))) + (angle (p4,p2,p3)) is complex real ext-real Element of REAL
(angle (p2,p5,p1)) + (angle (p5,p1,p2)) is complex real ext-real Element of REAL
((angle (p2,p5,p1)) + (angle (p5,p1,p2))) + (angle (p1,p2,p5)) is complex real ext-real Element of REAL
angle (p1,p4,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p1),(euc2cpx p4),(euc2cpx p2)) is complex real ext-real set
angle (p1,p3,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p1),(euc2cpx p3),(euc2cpx p2)) is complex real ext-real set
angle (p2,p3,p1) is complex real ext-real Element of REAL
angle ((euc2cpx p2),(euc2cpx p3),(euc2cpx p1)) is complex real ext-real set
(2 * PI) - (angle (p1,p4,p2)) is complex real ext-real Element of REAL
angle (p2,p3,p5) is complex real ext-real Element of REAL
angle ((euc2cpx p2),(euc2cpx p3),(euc2cpx p5)) is complex real ext-real set
angle (p3,p5,p2) is complex real ext-real Element of REAL
angle ((euc2cpx p3),(euc2cpx p5),(euc2cpx p2)) is complex real ext-real set
(angle (p2,p4,p1)) + (angle (p4,p1,p2)) is complex real ext-real Element of REAL
((angle (p2,p4,p1)) + (angle (p4,p1,p2))) + (angle (p1,p2,p4)) is complex real ext-real Element of REAL
(angle (p2,p3,p5)) + (angle (p3,p5,p2)) is complex real ext-real Element of REAL
((angle (p2,p3,p5)) + (angle (p3,p5,p2))) + (angle (p5,p2,p3)) is complex real ext-real Element of REAL
(angle (p2,p4,p1)) + (angle (p4,p1,p2)) is complex real ext-real Element of REAL
((angle (p2,p4,p1)) + (angle (p4,p1,p2))) + (angle (p1,p2,p4)) is complex real ext-real Element of REAL
(angle (p2,p3,p5)) + (angle (p3,p5,p2)) is complex real ext-real Element of REAL
((angle (p2,p3,p5)) + (angle (p3,p5,p2))) + (angle (p5,p2,p3)) is complex real ext-real Element of REAL
(2 * PI) - 0 is non empty complex real ext-real positive non negative Element of REAL
(angle (p4,p1,p2)) - (angle (p3,p5,p2)) is complex real ext-real Element of REAL
(angle (p2,p4,p1)) + (angle (p4,p1,p2)) is complex real ext-real Element of REAL
((angle (p2,p4,p1)) + (angle (p4,p1,p2))) + (angle (p1,p2,p4)) is complex real ext-real Element of REAL
(angle (p2,p3,p5)) + (angle (p3,p5,p2)) is complex real ext-real Element of REAL
((angle (p2,p3,p5)) + (angle (p3,p5,p2))) + (angle (p5,p2,p3)) is complex real ext-real Element of REAL
(2 * PI) - 0 is non empty complex real ext-real positive non negative Element of REAL
(angle (p3,p5,p2)) - (angle (p4,p1,p2)) is complex real ext-real Element of REAL
(angle (p2,p4,p1)) + (angle (p4,p1,p2)) is complex real ext-real Element of REAL
((angle (p2,p4,p1)) + (angle (p4,p1,p2))) + (angle (p1,p2,p4)) is complex real ext-real Element of REAL
(angle (p2,p3,p5)) + (angle (p3,p5,p2)) is complex real ext-real Element of REAL
((angle (p2,p3,p5)) + (angle (p3,p5,p2))) + (angle (p5,p2,p3)) is complex real ext-real Element of REAL
p5 - p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p5,(- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p5,(- p3)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p5 + (- p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p5 - p3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p5,K280(p3)) is Relation-like Function-like set
|.(p5 - p3).| is complex real ext-real non negative Element of REAL
sqr (p5 - p3) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p5 - p3),(p5 - p3)) is Relation-like Function-like set
K339((sqr (p5 - p3))) is complex real ext-real Element of REAL
sqrt K339((sqr (p5 - p3))) is complex real ext-real Element of REAL
|.(p5 - p3).| * |.(p4 - p2).| is complex real ext-real non negative Element of REAL
p1 - p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p4 is Relation-like Function-like set
K214((TOP-REAL 2),p1,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p4) is Relation-like Function-like complex-valued set
K251(p1,K280(p4)) is Relation-like Function-like set
|.(p1 - p4).| is complex real ext-real non negative Element of REAL
sqr (p1 - p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p1 - p4),(p1 - p4)) is Relation-like Function-like set
K339((sqr (p1 - p4))) is complex real ext-real Element of REAL
sqrt K339((sqr (p1 - p4))) is complex real ext-real Element of REAL
|.(p3 - p2).| * |.(p1 - p4).| is complex real ext-real non negative Element of REAL
p3 - p5 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p5 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p5 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p5 is Relation-like Function-like set
K214((TOP-REAL 2),p3,(- p5)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(- p5)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (- p5) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - p5 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p5) is Relation-like Function-like complex-valued set
K251(p3,K280(p5)) is Relation-like Function-like set
|.(p3 - p5).| is complex real ext-real non negative Element of REAL
sqr (p3 - p5) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p3 - p5),(p3 - p5)) is Relation-like Function-like set
K339((sqr (p3 - p5))) is complex real ext-real Element of REAL
sqrt K339((sqr (p3 - p5))) is complex real ext-real Element of REAL
|.(p3 - p5).| * |.(p4 - p2).| is complex real ext-real non negative Element of REAL
|.(p3 - p1).| ^2 is complex real ext-real Element of REAL
|.(p3 - p1).| * |.(p3 - p1).| is complex real ext-real non negative set
sqrt (|.(p3 - p1).| ^2) is complex real ext-real Element of REAL
p1 - p5 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p1,(- p5)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p5)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p5) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p5 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p1,K280(p5)) is Relation-like Function-like set
|.(p1 - p5).| is complex real ext-real non negative Element of REAL
sqr (p1 - p5) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p1 - p5),(p1 - p5)) is Relation-like Function-like set
K339((sqr (p1 - p5))) is complex real ext-real Element of REAL
sqrt K339((sqr (p1 - p5))) is complex real ext-real Element of REAL
|.(p1 - p5).| ^2 is complex real ext-real Element of REAL
|.(p1 - p5).| * |.(p1 - p5).| is complex real ext-real non negative set
|.(p3 - p5).| ^2 is complex real ext-real Element of REAL
|.(p3 - p5).| * |.(p3 - p5).| is complex real ext-real non negative set
(|.(p1 - p5).| ^2) + (|.(p3 - p5).| ^2) is complex real ext-real Element of REAL
2 * |.(p1 - p5).| is complex real ext-real non negative Element of REAL
(2 * |.(p1 - p5).|) * |.(p3 - p5).| is complex real ext-real non negative Element of REAL
angle (p1,p5,p3) is complex real ext-real Element of REAL
angle ((euc2cpx p1),(euc2cpx p5),(euc2cpx p3)) is complex real ext-real set
cos (angle (p1,p5,p3)) is complex real ext-real Element of REAL
((2 * |.(p1 - p5).|) * |.(p3 - p5).|) * (cos (angle (p1,p5,p3))) is complex real ext-real Element of REAL
((|.(p1 - p5).| ^2) + (|.(p3 - p5).| ^2)) - (((2 * |.(p1 - p5).|) * |.(p3 - p5).|) * (cos (angle (p1,p5,p3)))) is complex real ext-real Element of REAL
sqrt (((|.(p1 - p5).| ^2) + (|.(p3 - p5).| ^2)) - (((2 * |.(p1 - p5).|) * |.(p3 - p5).|) * (cos (angle (p1,p5,p3))))) is complex real ext-real Element of REAL
((2 * |.(p1 - p5).|) * |.(p3 - p5).|) * (cos PI) is complex real ext-real Element of REAL
((|.(p1 - p5).| ^2) + (|.(p3 - p5).| ^2)) - (((2 * |.(p1 - p5).|) * |.(p3 - p5).|) * (cos PI)) is complex real ext-real Element of REAL
sqrt (((|.(p1 - p5).| ^2) + (|.(p3 - p5).| ^2)) - (((2 * |.(p1 - p5).|) * |.(p3 - p5).|) * (cos PI))) is complex real ext-real Element of REAL
|.(p1 - p5).| + |.(p3 - p5).| is complex real ext-real non negative Element of REAL
(|.(p1 - p5).| + |.(p3 - p5).|) ^2 is complex real ext-real Element of REAL
(|.(p1 - p5).| + |.(p3 - p5).|) * (|.(p1 - p5).| + |.(p3 - p5).|) is complex real ext-real non negative set
sqrt ((|.(p1 - p5).| + |.(p3 - p5).|) ^2) is complex real ext-real Element of REAL
p2 - p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p2,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p2,K280(p4)) is Relation-like Function-like set
|.(p2 - p4).| is complex real ext-real non negative Element of REAL
sqr (p2 - p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p2 - p4),(p2 - p4)) is Relation-like Function-like set
K339((sqr (p2 - p4))) is complex real ext-real Element of REAL
sqrt K339((sqr (p2 - p4))) is complex real ext-real Element of REAL
|.(p1 - p5).| * |.(p2 - p4).| is complex real ext-real non negative Element of REAL
|.(p1 - p5).| * |.(p4 - p2).| is complex real ext-real non negative Element of REAL
p5 - p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p5,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p5,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p5 + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p5 - p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p5,K280(p1)) is Relation-like Function-like set
|.(p5 - p1).| is complex real ext-real non negative Element of REAL
sqr (p5 - p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p5 - p1),(p5 - p1)) is Relation-like Function-like set
K339((sqr (p5 - p1))) is complex real ext-real Element of REAL
sqrt K339((sqr (p5 - p1))) is complex real ext-real Element of REAL
|.(p5 - p1).| * |.(p4 - p2).| is complex real ext-real non negative Element of REAL
(|.(p5 - p1).| * |.(p4 - p2).|) + (|.(p3 - p5).| * |.(p4 - p2).|) is complex real ext-real non negative Element of REAL
|.(p5 - p1).| + |.(p3 - p5).| is complex real ext-real non negative Element of REAL
(|.(p5 - p1).| + |.(p3 - p5).|) * |.(p4 - p2).| is complex real ext-real non negative Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p2 is Relation-like Function-like set
K214((TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p2) is Relation-like Function-like complex-valued set
K251(p1,K280(p2)) is Relation-like Function-like set
(p1 - p2) `1 is complex real ext-real Element of REAL
K367((p1 - p2),1) is complex real ext-real Element of REAL
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
(p1 `1) - (p2 `1) is complex real ext-real Element of REAL
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 - p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p4 is Relation-like Function-like set
K214((TOP-REAL 2),p3,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (- p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p4) is Relation-like Function-like complex-valued set
K251(p3,K280(p4)) is Relation-like Function-like set
(p3 - p4) `2 is complex real ext-real Element of REAL
K367((p3 - p4),2) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
p4 `2 is complex real ext-real Element of REAL
K367(p4,2) is complex real ext-real Element of REAL
(p3 `2) - (p4 `2) is complex real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p2 is Relation-like Function-like set
K214((TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p2) is Relation-like Function-like complex-valued set
K251(p1,K280(p2)) is Relation-like Function-like set
|.(p1 - p2).| is complex real ext-real non negative Element of REAL
sqr (p1 - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p1 - p2),(p1 - p2)) is Relation-like Function-like set
K339((sqr (p1 - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr (p1 - p2))) is complex real ext-real Element of REAL
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 - p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p4 is Relation-like Function-like set
K214((TOP-REAL 2),p3,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(- p4)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (- p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - p4 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p4) is Relation-like Function-like complex-valued set
K251(p3,K280(p4)) is Relation-like Function-like set
|.(p3 - p4).| is complex real ext-real non negative Element of REAL
sqr (p3 - p4) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p3 - p4),(p3 - p4)) is Relation-like Function-like set
K339((sqr (p3 - p4))) is complex real ext-real Element of REAL
sqrt K339((sqr (p3 - p4))) is complex real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p2 is Relation-like Function-like set
K214((TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p2) is Relation-like Function-like complex-valued set
K251(p1,K280(p2)) is Relation-like Function-like set
|.(p1 - p2).| is complex real ext-real non negative Element of REAL
sqr (p1 - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p1 - p2),(p1 - p2)) is Relation-like Function-like set
K339((sqr (p1 - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr (p1 - p2))) is complex real ext-real Element of REAL
p2 - p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p1 is Relation-like Function-like set
K214((TOP-REAL 2),p2,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p2,(- p1)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 + (- p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p2 - p1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p1) is Relation-like Function-like complex-valued set
K251(p2,K280(p1)) is Relation-like Function-like set
|.(p2 - p1).| is complex real ext-real non negative Element of REAL
sqr (p2 - p1) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p2 - p1),(p2 - p1)) is Relation-like Function-like set
K339((sqr (p2 - p1))) is complex real ext-real Element of REAL
sqrt K339((sqr (p2 - p1))) is complex real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p1,p2,p3) is complex real ext-real Element of REAL
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx p2),(euc2cpx p3)) is complex real ext-real set
p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
a is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p4,p,a) is complex real ext-real Element of REAL
euc2cpx p4 is complex Element of COMPLEX
p4 `1 is complex real ext-real Element of REAL
K367(p4,1) is complex real ext-real Element of REAL
p4 `2 is complex real ext-real Element of REAL
K367(p4,2) is complex real ext-real Element of REAL
(p4 `2) * <i> is complex set
(p4 `1) + ((p4 `2) * <i>) is complex set
euc2cpx p is complex Element of COMPLEX
p `1 is complex real ext-real Element of REAL
K367(p,1) is complex real ext-real Element of REAL
p `2 is complex real ext-real Element of REAL
K367(p,2) is complex real ext-real Element of REAL
(p `2) * <i> is complex set
(p `1) + ((p `2) * <i>) is complex set
euc2cpx a is complex Element of COMPLEX
a `1 is complex real ext-real Element of REAL
K367(a,1) is complex real ext-real Element of REAL
a `2 is complex real ext-real Element of REAL
K367(a,2) is complex real ext-real Element of REAL
(a `2) * <i> is complex set
(a `1) + ((a `2) * <i>) is complex set
angle ((euc2cpx p4),(euc2cpx p),(euc2cpx a)) is complex real ext-real set
2 * (angle (p4,p,a)) is complex real ext-real Element of REAL
(2 * (angle (p4,p,a))) + (2 * PI) is complex real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p1,p2,p3) is complex real ext-real Element of REAL
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx p2),(euc2cpx p3)) is complex real ext-real set
p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
a is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p4,p,a) is complex real ext-real Element of REAL
euc2cpx p4 is complex Element of COMPLEX
p4 `1 is complex real ext-real Element of REAL
K367(p4,1) is complex real ext-real Element of REAL
p4 `2 is complex real ext-real Element of REAL
K367(p4,2) is complex real ext-real Element of REAL
(p4 `2) * <i> is complex set
(p4 `1) + ((p4 `2) * <i>) is complex set
euc2cpx p is complex Element of COMPLEX
p `1 is complex real ext-real Element of REAL
K367(p,1) is complex real ext-real Element of REAL
p `2 is complex real ext-real Element of REAL
K367(p,2) is complex real ext-real Element of REAL
(p `2) * <i> is complex set
(p `1) + ((p `2) * <i>) is complex set
euc2cpx a is complex Element of COMPLEX
a `1 is complex real ext-real Element of REAL
K367(a,1) is complex real ext-real Element of REAL
a `2 is complex real ext-real Element of REAL
K367(a,2) is complex real ext-real Element of REAL
(a `2) * <i> is complex set
(a `1) + ((a `2) * <i>) is complex set
angle ((euc2cpx p4),(euc2cpx p),(euc2cpx a)) is complex real ext-real set
2 * (angle (p4,p,a)) is complex real ext-real Element of REAL
(2 * (angle (p4,p,a))) + (4 * PI) is complex real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p1,p2,p3) is complex real ext-real Element of REAL
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx p2),(euc2cpx p3)) is complex real ext-real set
p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
a is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p4,p,a) is complex real ext-real Element of REAL
euc2cpx p4 is complex Element of COMPLEX
p4 `1 is complex real ext-real Element of REAL
K367(p4,1) is complex real ext-real Element of REAL
p4 `2 is complex real ext-real Element of REAL
K367(p4,2) is complex real ext-real Element of REAL
(p4 `2) * <i> is complex set
(p4 `1) + ((p4 `2) * <i>) is complex set
euc2cpx p is complex Element of COMPLEX
p `1 is complex real ext-real Element of REAL
K367(p,1) is complex real ext-real Element of REAL
p `2 is complex real ext-real Element of REAL
K367(p,2) is complex real ext-real Element of REAL
(p `2) * <i> is complex set
(p `1) + ((p `2) * <i>) is complex set
euc2cpx a is complex Element of COMPLEX
a `1 is complex real ext-real Element of REAL
K367(a,1) is complex real ext-real Element of REAL
a `2 is complex real ext-real Element of REAL
K367(a,2) is complex real ext-real Element of REAL
(a `2) * <i> is complex set
(a `1) + ((a `2) * <i>) is complex set
angle ((euc2cpx p4),(euc2cpx p),(euc2cpx a)) is complex real ext-real set
2 * (angle (p4,p,a)) is complex real ext-real Element of REAL
(2 * (angle (p4,p,a))) - (4 * PI) is complex real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p1,p2,p3) is complex real ext-real Element of REAL
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx p2),(euc2cpx p3)) is complex real ext-real set
p4 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
a is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
angle (p4,p,a) is complex real ext-real Element of REAL
euc2cpx p4 is complex Element of COMPLEX
p4 `1 is complex real ext-real Element of REAL
K367(p4,1) is complex real ext-real Element of REAL
p4 `2 is complex real ext-real Element of REAL
K367(p4,2) is complex real ext-real Element of REAL
(p4 `2) * <i> is complex set
(p4 `1) + ((p4 `2) * <i>) is complex set
euc2cpx p is complex Element of COMPLEX
p `1 is complex real ext-real Element of REAL
K367(p,1) is complex real ext-real Element of REAL
p `2 is complex real ext-real Element of REAL
K367(p,2) is complex real ext-real Element of REAL
(p `2) * <i> is complex set
(p `1) + ((p `2) * <i>) is complex set
euc2cpx a is complex Element of COMPLEX
a `1 is complex real ext-real Element of REAL
K367(a,1) is complex real ext-real Element of REAL
a `2 is complex real ext-real Element of REAL
K367(a,2) is complex real ext-real Element of REAL
(a `2) * <i> is complex set
(a `1) + ((a `2) * <i>) is complex set
angle ((euc2cpx p4),(euc2cpx p),(euc2cpx a)) is complex real ext-real set
2 * (angle (p4,p,a)) is complex real ext-real Element of REAL
(2 * (angle (p4,p,a))) - (6 * PI) is complex real ext-real Element of REAL
p4 is complex Element of COMPLEX
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p2 is Relation-like Function-like set
K214((TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p2) is Relation-like Function-like complex-valued set
K251(p1,K280(p2)) is Relation-like Function-like set
euc2cpx (p1 - p2) is complex Element of COMPLEX
(p1 - p2) `1 is complex real ext-real Element of REAL
K367((p1 - p2),1) is complex real ext-real Element of REAL
(p1 - p2) `2 is complex real ext-real Element of REAL
K367((p1 - p2),2) is complex real ext-real Element of REAL
((p1 - p2) `2) * <i> is complex set
((p1 - p2) `1) + (((p1 - p2) `2) * <i>) is complex set
p is complex Element of COMPLEX
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p3,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p3,K280(p2)) is Relation-like Function-like set
euc2cpx (p3 - p2) is complex Element of COMPLEX
(p3 - p2) `1 is complex real ext-real Element of REAL
K367((p3 - p2),1) is complex real ext-real Element of REAL
(p3 - p2) `2 is complex real ext-real Element of REAL
K367((p3 - p2),2) is complex real ext-real Element of REAL
((p3 - p2) `2) * <i> is complex set
((p3 - p2) `1) + (((p3 - p2) `2) * <i>) is complex set
angle (p1,p2,p3) is complex real ext-real Element of REAL
euc2cpx p1 is complex Element of COMPLEX
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
(p1 `2) * <i> is complex set
(p1 `1) + ((p1 `2) * <i>) is complex set
euc2cpx p2 is complex Element of COMPLEX
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p2 `2) * <i> is complex set
(p2 `1) + ((p2 `2) * <i>) is complex set
euc2cpx p3 is complex Element of COMPLEX
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) * <i> is complex set
(p3 `1) + ((p3 `2) * <i>) is complex set
angle ((euc2cpx p1),(euc2cpx p2),(euc2cpx p3)) is complex real ext-real set
angle (p4,p) is complex real ext-real Element of REAL
p1 is complex Element of COMPLEX
p2 is complex Element of COMPLEX
angle (p1,p2) is complex real ext-real Element of REAL
p3 is complex Element of COMPLEX
angle (p2,p3) is complex real ext-real Element of REAL
(angle (p1,p2)) + (angle (p2,p3)) is complex real ext-real Element of REAL
angle (p1,p3) is complex real ext-real Element of REAL
(angle (p1,p3)) + (2 * PI) is complex real ext-real Element of REAL
p4 is complex Element of COMPLEX
p1 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
- p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * p2 is Relation-like Function-like set
K214((TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p1,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p1 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p1 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K280(p2) is Relation-like Function-like complex-valued set
K251(p1,K280(p2)) is Relation-like Function-like set
euc2cpx (p1 - p2) is complex Element of COMPLEX
(p1 - p2) `1 is complex real ext-real Element of REAL
K367((p1 - p2),1) is complex real ext-real Element of REAL
(p1 - p2) `2 is complex real ext-real Element of REAL
K367((p1 - p2),2) is complex real ext-real Element of REAL
((p1 - p2) `2) * <i> is complex set
((p1 - p2) `1) + (((p1 - p2) `2) * <i>) is complex set
p is complex Element of COMPLEX
p3 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 - p2 is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K214((TOP-REAL 2),p3,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
K414( the carrier of (TOP-REAL 2), the U5 of (TOP-REAL 2),p3,(- p2)) is Relation-like Function-like V42(2) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL 2)
p3 + (- p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
p3 - p2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K251(p3,K280(p2)) is Relation-like Function-like set
euc2cpx (p3 - p2) is complex Element of COMPLEX
(p3 - p2) `1 is complex real ext-real Element of REAL
K367((p3 - p2),1) is complex real ext-real Element of REAL
(p3 - p2) `2 is complex real ext-real Element of REAL
K367((p3 - p2),2) is complex real ext-real Element of REAL
((p3 - p2) `2) * <i> is complex set
((p3 - p2) `1) + (((p3 - p2) `2) * <i>) is complex set
p4 .|. p is complex Element of COMPLEX
Re (p4 .|. p) is complex real ext-real Element of REAL
p1 `1 is complex real ext-real Element of REAL
K367(p1,1) is complex real ext-real Element of REAL
p2 `1 is complex real ext-real Element of REAL
K367(p2,1) is complex real ext-real Element of REAL
(p1 `1) - (p2 `1) is complex real ext-real Element of REAL
p3 `1 is complex real ext-real Element of REAL
K367(p3,1) is complex real ext-real Element of REAL
(p3 `1) - (p2 `1) is complex real ext-real Element of REAL
((p1 `1) - (p2 `1)) * ((p3 `1) - (p2 `1)) is complex real ext-real Element of REAL
p1 `2 is complex real ext-real Element of REAL
K367(p1,2) is complex real ext-real Element of REAL
p2 `2 is complex real ext-real Element of REAL
K367(p2,2) is complex real ext-real Element of REAL
(p1 `2) - (p2 `2) is complex real ext-real Element of REAL
p3 `2 is complex real ext-real Element of REAL
K367(p3,2) is complex real ext-real Element of REAL
(p3 `2) - (p2 `2) is complex real ext-real Element of REAL
((p1 `2) - (p2 `2)) * ((p3 `2) - (p2 `2)) is complex real ext-real Element of REAL
(((p1 `1) - (p2 `1)) * ((p3 `1) - (p2 `1))) + (((p1 `2) - (p2 `2)) * ((p3 `2) - (p2 `2))) is complex real ext-real Element of REAL
Im (p4 .|. p) is complex real ext-real Element of REAL
((p1 `1) - (p2 `1)) * ((p3 `2) - (p2 `2)) is complex real ext-real Element of REAL
- (((p1 `1) - (p2 `1)) * ((p3 `2) - (p2 `2))) is complex real ext-real Element of REAL
((p1 `2) - (p2 `2)) * ((p3 `1) - (p2 `1)) is complex real ext-real Element of REAL
(- (((p1 `1) - (p2 `1)) * ((p3 `2) - (p2 `2)))) + (((p1 `2) - (p2 `2)) * ((p3 `1) - (p2 `1))) is complex real ext-real Element of REAL
|.p4.| is complex real ext-real Element of REAL
Re p4 is complex real ext-real Element of REAL
(Re p4) ^2 is complex real ext-real Element of REAL
(Re p4) * (Re p4) is complex real ext-real set
Im p4 is complex real ext-real Element of REAL
(Im p4) ^2 is complex real ext-real Element of REAL
(Im p4) * (Im p4) is complex real ext-real set
((Re p4) ^2) + ((Im p4) ^2) is complex real ext-real Element of REAL
sqrt (((Re p4) ^2) + ((Im p4) ^2)) is complex real ext-real Element of REAL
((p1 `1) - (p2 `1)) ^2 is complex real ext-real Element of REAL
((p1 `1) - (p2 `1)) * ((p1 `1) - (p2 `1)) is complex real ext-real set
((p1 `2) - (p2 `2)) ^2 is complex real ext-real Element of REAL
((p1 `2) - (p2 `2)) * ((p1 `2) - (p2 `2)) is complex real ext-real set
(((p1 `1) - (p2 `1)) ^2) + (((p1 `2) - (p2 `2)) ^2) is complex real ext-real Element of REAL
sqrt ((((p1 `1) - (p2 `1)) ^2) + (((p1 `2) - (p2 `2)) ^2)) is complex real ext-real Element of REAL
|.(p1 - p2).| is complex real ext-real non negative Element of REAL
sqr (p1 - p2) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
mlt ((p1 - p2),(p1 - p2)) is Relation-like Function-like set
K339((sqr (p1 - p2))) is complex real ext-real Element of REAL
sqrt K339((sqr (p1 - p2))) is complex real ext-real Element of REAL
p1 is natural complex real ext-real V33() V34() V126() V127() V128() V129() V130() V131() Element of NAT
TOP-REAL p1 is non empty V73() V138() V139() TopSpace-like V186() V187() V188() V189() V190() V191() V192() strict RLTopStruct
the carrier of (TOP-REAL p1) is non empty set
[: the carrier of (TOP-REAL p1), the carrier of R^1:] is complex-valued ext-real-valued real-valued set
bool [: the carrier of (TOP-REAL p1), the carrier of R^1:] is set
p3 is non empty Relation-like the carrier of (TOP-REAL p1) -defined the carrier of R^1 -valued Function-like total V30( the carrier of (TOP-REAL p1), the carrier of R^1) complex-valued ext-real-valued real-valued Element of bool [: the carrier of (TOP-REAL p1), the carrier of R^1:]
p2 is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)
p1 is natural complex real ext-real V33() V34() V126() V127() V128() V129() V130() V131() Element of NAT
TOP-REAL p1 is non empty V73() V138() V139() TopSpace-like V186() V187() V188() V189() V190() V191() V192() strict RLTopStruct
the carrier of (TOP-REAL p1) is non empty set
[: the carrier of (TOP-REAL p1), the carrier of R^1:] is complex-valued ext-real-valued real-valued set
bool [: the carrier of (TOP-REAL p1), the carrier of R^1:] is set
p2 is Relation-like Function-like V42(p1) FinSequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL p1)