REAL is V142() V143() V144() V148() V201() V202() V204() set
NAT is V142() V143() V144() V145() V146() V147() V148() V201() Element of K6(REAL)
K6(REAL) is set
COMPLEX is V142() V148() set
omega is V142() V143() V144() V145() V146() V147() V148() V201() set
K6(omega) is set
K6(NAT) is set
1 is non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() Element of NAT
K7(1,1) is set
K6(K7(1,1)) is set
K7(K7(1,1),1) is set
K6(K7(K7(1,1),1)) is set
K7(K7(1,1),REAL) is set
K6(K7(K7(1,1),REAL)) is set
K7(REAL,REAL) is set
K7(K7(REAL,REAL),REAL) is set
K6(K7(K7(REAL,REAL),REAL)) is set
2 is non empty natural V11() real ext-real positive non negative V79() V80() V142() V143() V144() V145() V146() V147() V199() V201() Element of NAT
K7(2,2) is set
K7(K7(2,2),REAL) is set
K6(K7(K7(2,2),REAL)) is set
RAT is V142() V143() V144() V145() V148() set
INT is V142() V143() V144() V145() V146() V148() set
K6(K7(REAL,REAL)) is set
TOP-REAL 2 is non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict RLTopStruct
the carrier of (TOP-REAL 2) is non empty functional set
K6( the carrier of (TOP-REAL 2)) is set
K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)) is set
K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2))) is set
K448() is non empty strict TopSpace-like V196() TopStruct
the carrier of K448() is non empty V142() V143() V144() set
RealSpace is non empty strict Reflexive discerning V91() triangle Discerning V196() MetrStruct
R^1 is non empty strict TopSpace-like V196() TopStruct
the carrier of R^1 is non empty V142() V143() V144() set
K7( the carrier of (TOP-REAL 2),REAL) is set
K6(K7( the carrier of (TOP-REAL 2),REAL)) is set
K7(COMPLEX,COMPLEX) is set
K6(K7(COMPLEX,COMPLEX)) is set
K7(COMPLEX,REAL) is set
K6(K7(COMPLEX,REAL)) is set
K7(K7(COMPLEX,COMPLEX),COMPLEX) is set
K6(K7(K7(COMPLEX,COMPLEX),COMPLEX)) is set
K7(RAT,RAT) is set
K6(K7(RAT,RAT)) is set
K7(K7(RAT,RAT),RAT) is set
K6(K7(K7(RAT,RAT),RAT)) is set
K7(INT,INT) is set
K6(K7(INT,INT)) is set
K7(K7(INT,INT),INT) is set
K6(K7(K7(INT,INT),INT)) is set
K7(NAT,NAT) is set
K7(K7(NAT,NAT),NAT) is set
K6(K7(K7(NAT,NAT),NAT)) is set
0 is empty Function-like functional V142() V143() V144() V145() V146() V147() V148() V201() V204() set
K6( the carrier of R^1) is set
0 is empty natural V11() real ext-real non positive non negative Function-like functional V79() V80() V142() V143() V144() V145() V146() V147() V148() V201() V204() Element of NAT
Closed-Interval-TSpace (0,1) is non empty strict TopSpace-like V196() SubSpace of R^1
K7( the carrier of R^1, the carrier of R^1) is set
K6(K7( the carrier of R^1, the carrier of R^1)) is set
0. (TOP-REAL 2) is Relation-like Function-like V43(2) V52( TOP-REAL 2) V76() V134() Element of the carrier of (TOP-REAL 2)
the ZeroF of (TOP-REAL 2) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|[0,0]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
sqrt 1 is V11() real ext-real Element of REAL
K38(1) is V11() real ext-real non positive set
proj1 is Relation-like the carrier of (TOP-REAL 2) -defined REAL -valued Function-like quasi_total Element of K6(K7( the carrier of (TOP-REAL 2),REAL))
proj2 is Relation-like the carrier of (TOP-REAL 2) -defined REAL -valued Function-like quasi_total Element of K6(K7( the carrier of (TOP-REAL 2),REAL))
real_dist is Relation-like K7(REAL,REAL) -defined REAL -valued Function-like quasi_total Element of K6(K7(K7(REAL,REAL),REAL))
MetrStruct(# REAL,real_dist #) is strict MetrStruct
(0. (TOP-REAL 2)) `1 is V11() real ext-real Element of REAL
(0. (TOP-REAL 2)) `2 is V11() real ext-real Element of REAL
I[01] is non empty strict TopSpace-like V196() SubSpace of R^1
the carrier of I[01] is non empty V142() V143() V144() set
K7( the carrier of I[01], the carrier of (TOP-REAL 2)) is set
K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2))) is set
[.0,1.] is V142() V143() V144() V204() Element of K6(REAL)
Sq_Circ is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : |.b1.| = 1 } is set
Sq_Circ " is Relation-like Function-like set
rng Sq_Circ is functional Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : |.b1.| <= 1 } is set
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : ( |.b1.| = 1 & b1 `2 <= b1 `1 & - (b1 `1) <= b1 `2 ) } is set
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : ( |.b1.| = 1 & b1 `1 <= b1 `2 & b1 `2 <= - (b1 `1) ) } is set
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : ( |.b1.| = 1 & b1 `1 <= b1 `2 & - (b1 `1) <= b1 `2 ) } is set
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : ( |.b1.| = 1 & b1 `2 <= b1 `1 & b1 `2 <= - (b1 `1) ) } is set
- 1 is V11() real ext-real non positive Element of REAL
p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.p1.| is V11() real ext-real non negative Element of REAL
p1 `1 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
|.p1.| ^2 is V11() real ext-real Element of REAL
K37(|.p1.|,|.p1.|) is V11() real ext-real non negative set
(p1 `1) ^2 is V11() real ext-real Element of REAL
K37((p1 `1),(p1 `1)) is V11() real ext-real set
(p1 `2) ^2 is V11() real ext-real Element of REAL
K37((p1 `2),(p1 `2)) is V11() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V11() real ext-real Element of REAL
(|.p1.| ^2) - ((p1 `1) ^2) is V11() real ext-real Element of REAL
0 + ((p1 `1) ^2) is V11() real ext-real Element of REAL
((|.p1.| ^2) - ((p1 `1) ^2)) + ((p1 `1) ^2) is V11() real ext-real Element of REAL
- |.p1.| is V11() real ext-real non positive Element of REAL
(|.p1.| ^2) - ((p1 `2) ^2) is V11() real ext-real Element of REAL
0 + ((p1 `2) ^2) is V11() real ext-real Element of REAL
((|.p1.| ^2) - ((p1 `2) ^2)) + ((p1 `2) ^2) is V11() real ext-real Element of REAL
p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.p1.| is V11() real ext-real non negative Element of REAL
p1 `1 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
|.p1.| ^2 is V11() real ext-real Element of REAL
K37(|.p1.|,|.p1.|) is V11() real ext-real non negative set
(p1 `1) ^2 is V11() real ext-real Element of REAL
K37((p1 `1),(p1 `1)) is V11() real ext-real set
(p1 `2) ^2 is V11() real ext-real Element of REAL
K37((p1 `2),(p1 `2)) is V11() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V11() real ext-real Element of REAL
(|.p1.| ^2) - ((p1 `1) ^2) is V11() real ext-real Element of REAL
((|.p1.| ^2) - ((p1 `1) ^2)) + ((p1 `1) ^2) is V11() real ext-real Element of REAL
0 + ((p1 `1) ^2) is V11() real ext-real Element of REAL
- |.p1.| is V11() real ext-real non positive Element of REAL
(|.p1.| ^2) - ((p1 `2) ^2) is V11() real ext-real Element of REAL
((|.p1.| ^2) - ((p1 `2) ^2)) + ((p1 `2) ^2) is V11() real ext-real Element of REAL
0 + ((p1 `2) ^2) is V11() real ext-real Element of REAL
p3 is V11() real ext-real Element of REAL
p1 is V11() real ext-real Element of REAL
p2 is V11() real ext-real Element of REAL
p4 is V11() real ext-real Element of REAL
Closed-Interval-MSpace (p1,p2) is non empty strict Reflexive discerning V91() triangle Discerning SubSpace of RealSpace
Closed-Interval-MSpace (p3,p4) is non empty strict Reflexive discerning V91() triangle Discerning SubSpace of RealSpace
P is V11() real ext-real Element of REAL
C0 is non empty MetrStruct
the carrier of C0 is non empty set
f is non empty MetrStruct
the carrier of f is non empty set
g is Element of the carrier of C0
Ball (g,P) is Element of K6( the carrier of C0)
K6( the carrier of C0) is set
h is Element of the carrier of f
Ball (h,P) is Element of K6( the carrier of f)
K6( the carrier of f) is set
[.p3,p4.] is V142() V143() V144() V204() Element of K6(REAL)
f2 is set
{ b1 where b1 is Element of the carrier of C0 : not P <= dist (g,b1) } is set
g2 is Element of the carrier of C0
dist (g,g2) is V11() real ext-real Element of REAL
[.p1,p2.] is V142() V143() V144() V204() Element of K6(REAL)
the distance of C0 is Relation-like K7( the carrier of C0, the carrier of C0) -defined REAL -valued Function-like quasi_total Element of K6(K7(K7( the carrier of C0, the carrier of C0),REAL))
K7( the carrier of C0, the carrier of C0) is set
K7(K7( the carrier of C0, the carrier of C0),REAL) is set
K6(K7(K7( the carrier of C0, the carrier of C0),REAL)) is set
the distance of C0 . (g,g2) is V11() real ext-real Element of REAL
real_dist . (g,g2) is set
the distance of f is Relation-like K7( the carrier of f, the carrier of f) -defined REAL -valued Function-like quasi_total Element of K6(K7(K7( the carrier of f, the carrier of f),REAL))
K7( the carrier of f, the carrier of f) is set
K7(K7( the carrier of f, the carrier of f),REAL) is set
K6(K7(K7( the carrier of f, the carrier of f),REAL)) is set
h1 is Element of the carrier of f
the distance of f . (h,h1) is V11() real ext-real Element of REAL
dist (h,h1) is V11() real ext-real Element of REAL
{ b1 where b1 is Element of the carrier of f : not P <= dist (h,b1) } is set
K6( the carrier of I[01]) is set
p1 is V11() real ext-real set
p2 is V11() real ext-real set
p3 is V142() V143() V144() Element of K6( the carrier of I[01])
[.p1,p2.] is V142() V143() V144() V204() Element of K6(REAL)
Closed-Interval-TSpace (p1,p2) is non empty strict TopSpace-like V196() SubSpace of R^1
I[01] | p3 is strict TopSpace-like V196() SubSpace of I[01]
p1 is TopStruct
the carrier of p1 is set
p2 is non empty TopStruct
the carrier of p2 is non empty set
K7( the carrier of p1, the carrier of p2) is set
K6(K7( the carrier of p1, the carrier of p2)) is set
p3 is non empty TopStruct
the carrier of p3 is non empty set
K7( the carrier of p2, the carrier of p3) is set
K6(K7( the carrier of p2, the carrier of p3)) is set
p4 is Relation-like the carrier of p1 -defined the carrier of p2 -valued Function-like V29( the carrier of p1) quasi_total Element of K6(K7( the carrier of p1, the carrier of p2))
P is non empty Relation-like the carrier of p2 -defined the carrier of p3 -valued Function-like V29( the carrier of p2) quasi_total Element of K6(K7( the carrier of p2, the carrier of p3))
P * p4 is Relation-like the carrier of p1 -defined the carrier of p3 -valued Function-like V29( the carrier of p1) quasi_total Element of K6(K7( the carrier of p1, the carrier of p3))
K7( the carrier of p1, the carrier of p3) is set
K6(K7( the carrier of p1, the carrier of p3)) is set
p1 is TopStruct
the carrier of p1 is set
p2 is TopStruct
the carrier of p2 is set
K7( the carrier of p1, the carrier of p2) is set
K6(K7( the carrier of p1, the carrier of p2)) is set
p3 is TopStruct
the carrier of p3 is set
K7( the carrier of p2, the carrier of p3) is set
K6(K7( the carrier of p2, the carrier of p3)) is set
p4 is Relation-like the carrier of p1 -defined the carrier of p2 -valued Function-like quasi_total Element of K6(K7( the carrier of p1, the carrier of p2))
P is Relation-like the carrier of p2 -defined the carrier of p3 -valued Function-like quasi_total Element of K6(K7( the carrier of p2, the carrier of p3))
P * p4 is Relation-like the carrier of p1 -defined the carrier of p3 -valued Function-like Element of K6(K7( the carrier of p1, the carrier of p3))
K7( the carrier of p1, the carrier of p3) is set
K6(K7( the carrier of p1, the carrier of p3)) is set
p1 is TopStruct
the carrier of p1 is set
p2 is non empty TopStruct
the carrier of p2 is non empty set
K6( the carrier of p2) is set
p3 is non empty TopStruct
the carrier of p3 is non empty set
K7( the carrier of p2, the carrier of p3) is set
K6(K7( the carrier of p2, the carrier of p3)) is set
K7( the carrier of p1, the carrier of p3) is set
K6(K7( the carrier of p1, the carrier of p3)) is set
p4 is non empty Element of K6( the carrier of p2)
p2 | p4 is non empty strict SubSpace of p2
the carrier of (p2 | p4) is non empty set
K7( the carrier of p1, the carrier of (p2 | p4)) is set
K6(K7( the carrier of p1, the carrier of (p2 | p4))) is set
P is Relation-like the carrier of p1 -defined the carrier of (p2 | p4) -valued Function-like V29( the carrier of p1) quasi_total Element of K6(K7( the carrier of p1, the carrier of (p2 | p4)))
C0 is non empty Relation-like the carrier of p2 -defined the carrier of p3 -valued Function-like V29( the carrier of p2) quasi_total Element of K6(K7( the carrier of p2, the carrier of p3))
C0 * P is Relation-like the carrier of p1 -defined the carrier of p3 -valued Function-like Element of K6(K7( the carrier of p1, the carrier of p3))
f is Relation-like the carrier of p1 -defined the carrier of p3 -valued Function-like V29( the carrier of p1) quasi_total Element of K6(K7( the carrier of p1, the carrier of p3))
K6( the carrier of p3) is set
g is Element of K6( the carrier of p3)
(C0 * P) " g is Element of K6( the carrier of p1)
K6( the carrier of p1) is set
C0 " g is Element of K6( the carrier of p2)
P " (C0 " g) is Element of K6( the carrier of p1)
K6( the carrier of (p2 | p4)) is set
p4 /\ (C0 " g) is Element of K6( the carrier of p2)
rng P is Element of K6( the carrier of (p2 | p4))
(rng P) /\ the carrier of (p2 | p4) is Element of K6( the carrier of (p2 | p4))
[#] (p2 | p4) is non empty non proper Element of K6( the carrier of (p2 | p4))
h is Element of K6( the carrier of (p2 | p4))
f " g is Element of K6( the carrier of p1)
(rng P) /\ (C0 " g) is Element of K6( the carrier of p2)
P " ((rng P) /\ (C0 " g)) is Element of K6( the carrier of p1)
the carrier of (p2 | p4) /\ (C0 " g) is Element of K6( the carrier of p2)
(rng P) /\ ( the carrier of (p2 | p4) /\ (C0 " g)) is Element of K6( the carrier of p2)
P " ((rng P) /\ ( the carrier of (p2 | p4) /\ (C0 " g))) is Element of K6( the carrier of p1)
P " h is Element of K6( the carrier of p1)
p1 is V11() real ext-real Element of REAL
p2 is V11() real ext-real Element of REAL
Closed-Interval-TSpace (p1,p2) is non empty strict TopSpace-like V196() SubSpace of R^1
the carrier of (Closed-Interval-TSpace (p1,p2)) is non empty V142() V143() V144() set
p3 is V11() real ext-real Element of REAL
p4 is V11() real ext-real Element of REAL
Closed-Interval-TSpace (p3,p4) is non empty strict TopSpace-like V196() SubSpace of R^1
the carrier of (Closed-Interval-TSpace (p3,p4)) is non empty V142() V143() V144() set
K7( the carrier of (Closed-Interval-TSpace (p1,p2)), the carrier of (Closed-Interval-TSpace (p3,p4))) is set
K6(K7( the carrier of (Closed-Interval-TSpace (p1,p2)), the carrier of (Closed-Interval-TSpace (p3,p4)))) is set
P is V11() real ext-real Element of REAL
f is V11() real ext-real Element of REAL
C0 is V11() real ext-real Element of REAL
g is V11() real ext-real Element of REAL
[.p1,p2.] is V142() V143() V144() V204() Element of K6(REAL)
h is non empty Relation-like the carrier of (Closed-Interval-TSpace (p1,p2)) -defined the carrier of (Closed-Interval-TSpace (p3,p4)) -valued Function-like V29( the carrier of (Closed-Interval-TSpace (p1,p2))) quasi_total Element of K6(K7( the carrier of (Closed-Interval-TSpace (p1,p2)), the carrier of (Closed-Interval-TSpace (p3,p4))))
h . P is set
h . C0 is set
h . p2 is set
[.p3,p4.] is V142() V143() V144() V204() Element of K6(REAL)
f2 is non empty V142() V143() V144() Element of K6( the carrier of R^1)
R^1 | f2 is non empty strict TopSpace-like V196() SubSpace of R^1
K6( the carrier of (Closed-Interval-TSpace (p1,p2))) is set
[.P,p2.] is V142() V143() V144() V204() Element of K6(REAL)
dom h is V142() V143() V144() Element of K6( the carrier of (Closed-Interval-TSpace (p1,p2)))
[#] (Closed-Interval-TSpace (p1,p2)) is non empty non proper closed V142() V143() V144() Element of K6( the carrier of (Closed-Interval-TSpace (p1,p2)))
[.C0,P.] is V142() V143() V144() V204() Element of K6(REAL)
h1 is V142() V143() V144() Element of K6( the carrier of (Closed-Interval-TSpace (p1,p2)))
(Closed-Interval-TSpace (p1,p2)) | h1 is strict TopSpace-like V196() SubSpace of Closed-Interval-TSpace (p1,p2)
the carrier of ((Closed-Interval-TSpace (p1,p2)) | h1) is V142() V143() V144() set
K7( the carrier of ((Closed-Interval-TSpace (p1,p2)) | h1), the carrier of (Closed-Interval-TSpace (p3,p4))) is set
K6(K7( the carrier of ((Closed-Interval-TSpace (p1,p2)) | h1), the carrier of (Closed-Interval-TSpace (p3,p4)))) is set
O is V142() V143() V144() Element of K6( the carrier of (Closed-Interval-TSpace (p1,p2)))
h | O is Relation-like the carrier of (Closed-Interval-TSpace (p1,p2)) -defined the carrier of (Closed-Interval-TSpace (p3,p4)) -valued Function-like Element of K6(K7( the carrier of (Closed-Interval-TSpace (p1,p2)), the carrier of (Closed-Interval-TSpace (p3,p4))))
Closed-Interval-TSpace (C0,P) is non empty strict TopSpace-like V196() SubSpace of R^1
I is Relation-like the carrier of ((Closed-Interval-TSpace (p1,p2)) | h1) -defined the carrier of (Closed-Interval-TSpace (p3,p4)) -valued Function-like V29( the carrier of ((Closed-Interval-TSpace (p1,p2)) | h1)) quasi_total Element of K6(K7( the carrier of ((Closed-Interval-TSpace (p1,p2)) | h1), the carrier of (Closed-Interval-TSpace (p3,p4))))
the carrier of (Closed-Interval-TSpace (C0,P)) is non empty V142() V143() V144() set
K7( the carrier of (Closed-Interval-TSpace (C0,P)), the carrier of R^1) is set
K6(K7( the carrier of (Closed-Interval-TSpace (C0,P)), the carrier of R^1)) is set
h | h1 is Relation-like the carrier of (Closed-Interval-TSpace (p1,p2)) -defined the carrier of (Closed-Interval-TSpace (p3,p4)) -valued Function-like Element of K6(K7( the carrier of (Closed-Interval-TSpace (p1,p2)), the carrier of (Closed-Interval-TSpace (p3,p4))))
KXP is non empty Relation-like the carrier of (Closed-Interval-TSpace (C0,P)) -defined the carrier of R^1 -valued Function-like V29( the carrier of (Closed-Interval-TSpace (C0,P))) quasi_total Element of K6(K7( the carrier of (Closed-Interval-TSpace (C0,P)), the carrier of R^1))
KXP . C0 is set
f + g is V11() real ext-real Element of REAL
(f + g) / 2 is V11() real ext-real Element of REAL
f + f is V11() real ext-real Element of REAL
2 * f is V11() real ext-real Element of REAL
(2 * f) / 2 is V11() real ext-real Element of REAL
dom KXP is V142() V143() V144() Element of K6( the carrier of (Closed-Interval-TSpace (C0,P)))
K6( the carrier of (Closed-Interval-TSpace (C0,P))) is set
rng I is V142() V143() V144() Element of K6( the carrier of (Closed-Interval-TSpace (p3,p4)))
K6( the carrier of (Closed-Interval-TSpace (p3,p4))) is set
g + g is V11() real ext-real Element of REAL
2 * g is V11() real ext-real Element of REAL
(2 * g) / 2 is V11() real ext-real Element of REAL
g2 is V142() V143() V144() Element of K6( the carrier of (Closed-Interval-TSpace (p1,p2)))
(Closed-Interval-TSpace (p1,p2)) | g2 is strict TopSpace-like V196() SubSpace of Closed-Interval-TSpace (p1,p2)
the carrier of ((Closed-Interval-TSpace (p1,p2)) | g2) is V142() V143() V144() set
K7( the carrier of ((Closed-Interval-TSpace (p1,p2)) | g2), the carrier of (Closed-Interval-TSpace (p3,p4))) is set
K6(K7( the carrier of ((Closed-Interval-TSpace (p1,p2)) | g2), the carrier of (Closed-Interval-TSpace (p3,p4)))) is set
KYP is V142() V143() V144() Element of K6( the carrier of (Closed-Interval-TSpace (p1,p2)))
h | KYP is Relation-like the carrier of (Closed-Interval-TSpace (p1,p2)) -defined the carrier of (Closed-Interval-TSpace (p3,p4)) -valued Function-like Element of K6(K7( the carrier of (Closed-Interval-TSpace (p1,p2)), the carrier of (Closed-Interval-TSpace (p3,p4))))
Closed-Interval-TSpace (P,p2) is non empty strict TopSpace-like V196() SubSpace of R^1
KYN is Relation-like the carrier of ((Closed-Interval-TSpace (p1,p2)) | g2) -defined the carrier of (Closed-Interval-TSpace (p3,p4)) -valued Function-like V29( the carrier of ((Closed-Interval-TSpace (p1,p2)) | g2)) quasi_total Element of K6(K7( the carrier of ((Closed-Interval-TSpace (p1,p2)) | g2), the carrier of (Closed-Interval-TSpace (p3,p4))))
the carrier of (Closed-Interval-TSpace (P,p2)) is non empty V142() V143() V144() set
K7( the carrier of (Closed-Interval-TSpace (P,p2)), the carrier of R^1) is set
K6(K7( the carrier of (Closed-Interval-TSpace (P,p2)), the carrier of R^1)) is set
h | g2 is Relation-like the carrier of (Closed-Interval-TSpace (p1,p2)) -defined the carrier of (Closed-Interval-TSpace (p3,p4)) -valued Function-like Element of K6(K7( the carrier of (Closed-Interval-TSpace (p1,p2)), the carrier of (Closed-Interval-TSpace (p3,p4))))
x2 is non empty Relation-like the carrier of (Closed-Interval-TSpace (P,p2)) -defined the carrier of R^1 -valued Function-like V29( the carrier of (Closed-Interval-TSpace (P,p2))) quasi_total Element of K6(K7( the carrier of (Closed-Interval-TSpace (P,p2)), the carrier of R^1))
x2 . p2 is set
x2 . P is set
z3 is V11() real ext-real Element of REAL
x2 . z3 is set
KXP . P is set
z2 is V11() real ext-real Element of REAL
KXP . z2 is set
h . z2 is set
h . z3 is set
p1 is V11() real ext-real Element of REAL
p2 is V11() real ext-real Element of REAL
Closed-Interval-TSpace (p1,p2) is non empty strict TopSpace-like V196() SubSpace of R^1
the carrier of (Closed-Interval-TSpace (p1,p2)) is non empty V142() V143() V144() set
p3 is V11() real ext-real Element of REAL
p4 is V11() real ext-real Element of REAL
Closed-Interval-TSpace (p3,p4) is non empty strict TopSpace-like V196() SubSpace of R^1
the carrier of (Closed-Interval-TSpace (p3,p4)) is non empty V142() V143() V144() set
K7( the carrier of (Closed-Interval-TSpace (p1,p2)), the carrier of (Closed-Interval-TSpace (p3,p4))) is set
K6(K7( the carrier of (Closed-Interval-TSpace (p1,p2)), the carrier of (Closed-Interval-TSpace (p3,p4)))) is set
P is V11() real ext-real Element of REAL
f is V11() real ext-real Element of REAL
C0 is V11() real ext-real Element of REAL
g is V11() real ext-real Element of REAL
[.p1,p2.] is V142() V143() V144() V204() Element of K6(REAL)
h is non empty Relation-like the carrier of (Closed-Interval-TSpace (p1,p2)) -defined the carrier of (Closed-Interval-TSpace (p3,p4)) -valued Function-like V29( the carrier of (Closed-Interval-TSpace (p1,p2))) quasi_total Element of K6(K7( the carrier of (Closed-Interval-TSpace (p1,p2)), the carrier of (Closed-Interval-TSpace (p3,p4))))
h . P is set
h . C0 is set
h . p2 is set
[.p3,p4.] is V142() V143() V144() V204() Element of K6(REAL)
f2 is non empty V142() V143() V144() Element of K6( the carrier of R^1)
R^1 | f2 is non empty strict TopSpace-like V196() SubSpace of R^1
K6( the carrier of (Closed-Interval-TSpace (p1,p2))) is set
[.P,p2.] is V142() V143() V144() V204() Element of K6(REAL)
dom h is V142() V143() V144() Element of K6( the carrier of (Closed-Interval-TSpace (p1,p2)))
[#] (Closed-Interval-TSpace (p1,p2)) is non empty non proper closed V142() V143() V144() Element of K6( the carrier of (Closed-Interval-TSpace (p1,p2)))
[.C0,P.] is V142() V143() V144() V204() Element of K6(REAL)
h1 is V142() V143() V144() Element of K6( the carrier of (Closed-Interval-TSpace (p1,p2)))
(Closed-Interval-TSpace (p1,p2)) | h1 is strict TopSpace-like V196() SubSpace of Closed-Interval-TSpace (p1,p2)
the carrier of ((Closed-Interval-TSpace (p1,p2)) | h1) is V142() V143() V144() set
K7( the carrier of ((Closed-Interval-TSpace (p1,p2)) | h1), the carrier of (Closed-Interval-TSpace (p3,p4))) is set
K6(K7( the carrier of ((Closed-Interval-TSpace (p1,p2)) | h1), the carrier of (Closed-Interval-TSpace (p3,p4)))) is set
O is V142() V143() V144() Element of K6( the carrier of (Closed-Interval-TSpace (p1,p2)))
h | O is Relation-like the carrier of (Closed-Interval-TSpace (p1,p2)) -defined the carrier of (Closed-Interval-TSpace (p3,p4)) -valued Function-like Element of K6(K7( the carrier of (Closed-Interval-TSpace (p1,p2)), the carrier of (Closed-Interval-TSpace (p3,p4))))
Closed-Interval-TSpace (C0,P) is non empty strict TopSpace-like V196() SubSpace of R^1
I is Relation-like the carrier of ((Closed-Interval-TSpace (p1,p2)) | h1) -defined the carrier of (Closed-Interval-TSpace (p3,p4)) -valued Function-like V29( the carrier of ((Closed-Interval-TSpace (p1,p2)) | h1)) quasi_total Element of K6(K7( the carrier of ((Closed-Interval-TSpace (p1,p2)) | h1), the carrier of (Closed-Interval-TSpace (p3,p4))))
the carrier of (Closed-Interval-TSpace (C0,P)) is non empty V142() V143() V144() set
K7( the carrier of (Closed-Interval-TSpace (C0,P)), the carrier of R^1) is set
K6(K7( the carrier of (Closed-Interval-TSpace (C0,P)), the carrier of R^1)) is set
h | h1 is Relation-like the carrier of (Closed-Interval-TSpace (p1,p2)) -defined the carrier of (Closed-Interval-TSpace (p3,p4)) -valued Function-like Element of K6(K7( the carrier of (Closed-Interval-TSpace (p1,p2)), the carrier of (Closed-Interval-TSpace (p3,p4))))
KXP is non empty Relation-like the carrier of (Closed-Interval-TSpace (C0,P)) -defined the carrier of R^1 -valued Function-like V29( the carrier of (Closed-Interval-TSpace (C0,P))) quasi_total Element of K6(K7( the carrier of (Closed-Interval-TSpace (C0,P)), the carrier of R^1))
KXP . C0 is set
f + g is V11() real ext-real Element of REAL
(f + g) / 2 is V11() real ext-real Element of REAL
f + f is V11() real ext-real Element of REAL
2 * f is V11() real ext-real Element of REAL
(2 * f) / 2 is V11() real ext-real Element of REAL
dom KXP is V142() V143() V144() Element of K6( the carrier of (Closed-Interval-TSpace (C0,P)))
K6( the carrier of (Closed-Interval-TSpace (C0,P))) is set
rng I is V142() V143() V144() Element of K6( the carrier of (Closed-Interval-TSpace (p3,p4)))
K6( the carrier of (Closed-Interval-TSpace (p3,p4))) is set
g + g is V11() real ext-real Element of REAL
2 * g is V11() real ext-real Element of REAL
(2 * g) / 2 is V11() real ext-real Element of REAL
g2 is V142() V143() V144() Element of K6( the carrier of (Closed-Interval-TSpace (p1,p2)))
(Closed-Interval-TSpace (p1,p2)) | g2 is strict TopSpace-like V196() SubSpace of Closed-Interval-TSpace (p1,p2)
the carrier of ((Closed-Interval-TSpace (p1,p2)) | g2) is V142() V143() V144() set
K7( the carrier of ((Closed-Interval-TSpace (p1,p2)) | g2), the carrier of (Closed-Interval-TSpace (p3,p4))) is set
K6(K7( the carrier of ((Closed-Interval-TSpace (p1,p2)) | g2), the carrier of (Closed-Interval-TSpace (p3,p4)))) is set
KYP is V142() V143() V144() Element of K6( the carrier of (Closed-Interval-TSpace (p1,p2)))
h | KYP is Relation-like the carrier of (Closed-Interval-TSpace (p1,p2)) -defined the carrier of (Closed-Interval-TSpace (p3,p4)) -valued Function-like Element of K6(K7( the carrier of (Closed-Interval-TSpace (p1,p2)), the carrier of (Closed-Interval-TSpace (p3,p4))))
Closed-Interval-TSpace (P,p2) is non empty strict TopSpace-like V196() SubSpace of R^1
KYN is Relation-like the carrier of ((Closed-Interval-TSpace (p1,p2)) | g2) -defined the carrier of (Closed-Interval-TSpace (p3,p4)) -valued Function-like V29( the carrier of ((Closed-Interval-TSpace (p1,p2)) | g2)) quasi_total Element of K6(K7( the carrier of ((Closed-Interval-TSpace (p1,p2)) | g2), the carrier of (Closed-Interval-TSpace (p3,p4))))
the carrier of (Closed-Interval-TSpace (P,p2)) is non empty V142() V143() V144() set
K7( the carrier of (Closed-Interval-TSpace (P,p2)), the carrier of R^1) is set
K6(K7( the carrier of (Closed-Interval-TSpace (P,p2)), the carrier of R^1)) is set
h | g2 is Relation-like the carrier of (Closed-Interval-TSpace (p1,p2)) -defined the carrier of (Closed-Interval-TSpace (p3,p4)) -valued Function-like Element of K6(K7( the carrier of (Closed-Interval-TSpace (p1,p2)), the carrier of (Closed-Interval-TSpace (p3,p4))))
x2 is non empty Relation-like the carrier of (Closed-Interval-TSpace (P,p2)) -defined the carrier of R^1 -valued Function-like V29( the carrier of (Closed-Interval-TSpace (P,p2))) quasi_total Element of K6(K7( the carrier of (Closed-Interval-TSpace (P,p2)), the carrier of R^1))
x2 . p2 is set
x2 . P is set
z3 is V11() real ext-real Element of REAL
x2 . z3 is set
KXP . P is set
z2 is V11() real ext-real Element of REAL
KXP . z2 is set
h . z2 is set
h . z3 is set
p1 is natural V11() real ext-real V79() V80() V142() V143() V144() V145() V146() V147() V201() Element of NAT
TOP-REAL p1 is non empty TopSpace-like T_0 T_1 T_2 V108() V154() V155() V156() V157() V158() V159() V160() strict RLTopStruct
0. (TOP-REAL p1) is Relation-like Function-like V43(p1) V52( TOP-REAL p1) V76() V134() Element of the carrier of (TOP-REAL p1)
the carrier of (TOP-REAL p1) is non empty functional set
the ZeroF of (TOP-REAL p1) is Relation-like Function-like V43(p1) V76() V134() Element of the carrier of (TOP-REAL p1)
- (0. (TOP-REAL p1)) is Relation-like Function-like V43(p1) V76() V134() Element of the carrier of (TOP-REAL p1)
(0. (TOP-REAL p1)) + (0. (TOP-REAL p1)) is Relation-like Function-like V43(p1) V76() V134() Element of the carrier of (TOP-REAL p1)
p1 is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p2 is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng p1 is functional Element of K6( the carrier of (TOP-REAL 2))
rng p2 is functional Element of K6( the carrier of (TOP-REAL 2))
p3 is V11() real ext-real Element of REAL
p4 is V11() real ext-real Element of REAL
P is V11() real ext-real Element of REAL
C0 is V11() real ext-real Element of REAL
f is V11() real ext-real Element of the carrier of I[01]
g is V11() real ext-real Element of the carrier of I[01]
p1 . f is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(p1 . f) `1 is V11() real ext-real Element of REAL
(p1 . f) `2 is V11() real ext-real Element of REAL
p1 . g is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(p1 . g) `1 is V11() real ext-real Element of REAL
(p1 . g) `2 is V11() real ext-real Element of REAL
p2 . f is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(p2 . f) `2 is V11() real ext-real Element of REAL
(p2 . f) `1 is V11() real ext-real Element of REAL
p2 . g is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(p2 . g) `2 is V11() real ext-real Element of REAL
(p2 . g) `1 is V11() real ext-real Element of REAL
p1 is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p1 . 1 is Relation-like Function-like set
p1 . 0 is Relation-like Function-like set
rng p1 is functional Element of K6( the carrier of (TOP-REAL 2))
dom p1 is V142() V143() V144() Element of K6( the carrier of I[01])
p2 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | p2 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | p2) is non empty set
K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | p2)) is set
K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | p2))) is set
p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | p2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | p2)))
P is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | p2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | p2)))
P . 0 is set
P . 1 is set
rng P is Element of K6( the carrier of ((TOP-REAL 2) | p2))
K6( the carrier of ((TOP-REAL 2) | p2)) is set
[#] ((TOP-REAL 2) | p2) is non empty non proper closed Element of K6( the carrier of ((TOP-REAL 2) | p2))
C0 is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p1 is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p2 is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng p1 is functional Element of K6( the carrier of (TOP-REAL 2))
rng p2 is functional Element of K6( the carrier of (TOP-REAL 2))
p3 is functional Element of K6( the carrier of (TOP-REAL 2))
p4 is functional Element of K6( the carrier of (TOP-REAL 2))
P is functional Element of K6( the carrier of (TOP-REAL 2))
C0 is functional Element of K6( the carrier of (TOP-REAL 2))
f is functional Element of K6( the carrier of (TOP-REAL 2))
g is V11() real ext-real Element of the carrier of I[01]
h is V11() real ext-real Element of the carrier of I[01]
p1 . g is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p1 . h is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 . g is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 . h is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 . 1 is Relation-like Function-like set
p2 . 0 is Relation-like Function-like set
f2 is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 . 0 is Relation-like Function-like set
f2 . 1 is Relation-like Function-like set
rng f2 is functional Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : 1 <= |.b1.| } is set
p1 is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p2 is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng p1 is functional Element of K6( the carrier of (TOP-REAL 2))
rng p2 is functional Element of K6( the carrier of (TOP-REAL 2))
p3 is functional Element of K6( the carrier of (TOP-REAL 2))
p4 is functional Element of K6( the carrier of (TOP-REAL 2))
P is functional Element of K6( the carrier of (TOP-REAL 2))
C0 is functional Element of K6( the carrier of (TOP-REAL 2))
f is functional Element of K6( the carrier of (TOP-REAL 2))
g is V11() real ext-real Element of the carrier of I[01]
h is V11() real ext-real Element of the carrier of I[01]
p1 . g is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p1 . h is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 . g is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 . h is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
dom p2 is V142() V143() V144() Element of K6( the carrier of I[01])
p2 (#) (Sq_Circ ") is Relation-like Function-like set
p1 (#) (Sq_Circ ") is Relation-like Function-like set
f2 is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
dom f2 is V142() V143() V144() Element of K6( the carrier of I[01])
g2 is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
dom g2 is V142() V143() V144() Element of K6( the carrier of I[01])
g2 . g is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(g2 . g) `1 is V11() real ext-real Element of REAL
g2 . h is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(g2 . h) `1 is V11() real ext-real Element of REAL
f2 . g is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(f2 . g) `2 is V11() real ext-real Element of REAL
f2 . h is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(f2 . h) `2 is V11() real ext-real Element of REAL
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
I `1 is V11() real ext-real Element of REAL
I `2 is V11() real ext-real Element of REAL
(I `2) / (I `1) is V11() real ext-real Element of REAL
((I `2) / (I `1)) ^2 is V11() real ext-real Element of REAL
K37(((I `2) / (I `1)),((I `2) / (I `1))) is V11() real ext-real set
1 + (((I `2) / (I `1)) ^2) is V11() real ext-real Element of REAL
sqrt (1 + (((I `2) / (I `1)) ^2)) is V11() real ext-real Element of REAL
(I `1) / (sqrt (1 + (((I `2) / (I `1)) ^2))) is V11() real ext-real Element of REAL
(I `2) / (sqrt (1 + (((I `2) / (I `1)) ^2))) is V11() real ext-real Element of REAL
|[((I `1) / (sqrt (1 + (((I `2) / (I `1)) ^2)))),((I `2) / (sqrt (1 + (((I `2) / (I `1)) ^2))))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|[((I `1) / (sqrt (1 + (((I `2) / (I `1)) ^2)))),((I `2) / (sqrt (1 + (((I `2) / (I `1)) ^2))))]| `1 is V11() real ext-real Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
O `1 is V11() real ext-real Element of REAL
O `2 is V11() real ext-real Element of REAL
(O `2) / (O `1) is V11() real ext-real Element of REAL
((O `2) / (O `1)) ^2 is V11() real ext-real Element of REAL
K37(((O `2) / (O `1)),((O `2) / (O `1))) is V11() real ext-real set
1 + (((O `2) / (O `1)) ^2) is V11() real ext-real Element of REAL
sqrt (1 + (((O `2) / (O `1)) ^2)) is V11() real ext-real Element of REAL
(O `1) / (sqrt (1 + (((O `2) / (O `1)) ^2))) is V11() real ext-real Element of REAL
(O `2) / (sqrt (1 + (((O `2) / (O `1)) ^2))) is V11() real ext-real Element of REAL
|[((O `1) / (sqrt (1 + (((O `2) / (O `1)) ^2)))),((O `2) / (sqrt (1 + (((O `2) / (O `1)) ^2))))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|[((O `1) / (sqrt (1 + (((O `2) / (O `1)) ^2)))),((O `2) / (sqrt (1 + (((O `2) / (O `1)) ^2))))]| `1 is V11() real ext-real Element of REAL
KYP is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.KYP.| is V11() real ext-real non negative Element of REAL
KYP `2 is V11() real ext-real Element of REAL
KYP `1 is V11() real ext-real Element of REAL
- (KYP `1) is V11() real ext-real Element of REAL
(Sq_Circ ") . (p1 . h) is set
Sq_Circ . O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(Sq_Circ ") . KYP is set
(KYP `2) / (KYP `1) is V11() real ext-real Element of REAL
((KYP `2) / (KYP `1)) ^2 is V11() real ext-real Element of REAL
K37(((KYP `2) / (KYP `1)),((KYP `2) / (KYP `1))) is V11() real ext-real set
1 + (((KYP `2) / (KYP `1)) ^2) is V11() real ext-real Element of REAL
sqrt (1 + (((KYP `2) / (KYP `1)) ^2)) is V11() real ext-real Element of REAL
(KYP `1) * (sqrt (1 + (((KYP `2) / (KYP `1)) ^2))) is V11() real ext-real Element of REAL
(KYP `2) * (sqrt (1 + (((KYP `2) / (KYP `1)) ^2))) is V11() real ext-real Element of REAL
|[((KYP `1) * (sqrt (1 + (((KYP `2) / (KYP `1)) ^2)))),((KYP `2) * (sqrt (1 + (((KYP `2) / (KYP `1)) ^2))))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(- (KYP `1)) * (sqrt (1 + (((KYP `2) / (KYP `1)) ^2))) is V11() real ext-real Element of REAL
- (O `1) is V11() real ext-real Element of REAL
- (KYP `2) is V11() real ext-real Element of REAL
- (- (KYP `1)) is V11() real ext-real Element of REAL
- (- (KYP `2)) is V11() real ext-real Element of REAL
- 0 is empty V11() real ext-real non positive non negative Function-like functional V142() V143() V144() V145() V146() V147() V148() V201() V204() Element of REAL
|[((O `1) / (sqrt (1 + (((O `2) / (O `1)) ^2)))),((O `2) / (sqrt (1 + (((O `2) / (O `1)) ^2))))]| `2 is V11() real ext-real Element of REAL
|.KYP.| ^2 is V11() real ext-real Element of REAL
K37(|.KYP.|,|.KYP.|) is V11() real ext-real non negative set
((O `1) / (sqrt (1 + (((O `2) / (O `1)) ^2)))) ^2 is V11() real ext-real Element of REAL
K37(((O `1) / (sqrt (1 + (((O `2) / (O `1)) ^2)))),((O `1) / (sqrt (1 + (((O `2) / (O `1)) ^2))))) is V11() real ext-real set
((O `2) / (sqrt (1 + (((O `2) / (O `1)) ^2)))) ^2 is V11() real ext-real Element of REAL
K37(((O `2) / (sqrt (1 + (((O `2) / (O `1)) ^2)))),((O `2) / (sqrt (1 + (((O `2) / (O `1)) ^2))))) is V11() real ext-real set
(((O `1) / (sqrt (1 + (((O `2) / (O `1)) ^2)))) ^2) + (((O `2) / (sqrt (1 + (((O `2) / (O `1)) ^2)))) ^2) is V11() real ext-real Element of REAL
(O `1) ^2 is V11() real ext-real Element of REAL
K37((O `1),(O `1)) is V11() real ext-real set
(sqrt (1 + (((O `2) / (O `1)) ^2))) ^2 is V11() real ext-real Element of REAL
K37((sqrt (1 + (((O `2) / (O `1)) ^2))),(sqrt (1 + (((O `2) / (O `1)) ^2)))) is V11() real ext-real set
((O `1) ^2) / ((sqrt (1 + (((O `2) / (O `1)) ^2))) ^2) is V11() real ext-real Element of REAL
(((O `1) ^2) / ((sqrt (1 + (((O `2) / (O `1)) ^2))) ^2)) + (((O `2) / (sqrt (1 + (((O `2) / (O `1)) ^2)))) ^2) is V11() real ext-real Element of REAL
(O `2) ^2 is V11() real ext-real Element of REAL
K37((O `2),(O `2)) is V11() real ext-real set
((O `2) ^2) / ((sqrt (1 + (((O `2) / (O `1)) ^2))) ^2) is V11() real ext-real Element of REAL
(((O `1) ^2) / ((sqrt (1 + (((O `2) / (O `1)) ^2))) ^2)) + (((O `2) ^2) / ((sqrt (1 + (((O `2) / (O `1)) ^2))) ^2)) is V11() real ext-real Element of REAL
((O `1) ^2) / (1 + (((O `2) / (O `1)) ^2)) is V11() real ext-real Element of REAL
(((O `1) ^2) / (1 + (((O `2) / (O `1)) ^2))) + (((O `2) ^2) / ((sqrt (1 + (((O `2) / (O `1)) ^2))) ^2)) is V11() real ext-real Element of REAL
((O `2) ^2) / (1 + (((O `2) / (O `1)) ^2)) is V11() real ext-real Element of REAL
(((O `1) ^2) / (1 + (((O `2) / (O `1)) ^2))) + (((O `2) ^2) / (1 + (((O `2) / (O `1)) ^2))) is V11() real ext-real Element of REAL
((O `1) ^2) + ((O `2) ^2) is V11() real ext-real Element of REAL
(((O `1) ^2) + ((O `2) ^2)) / (1 + (((O `2) / (O `1)) ^2)) is V11() real ext-real Element of REAL
((((O `1) ^2) + ((O `2) ^2)) / (1 + (((O `2) / (O `1)) ^2))) * (1 + (((O `2) / (O `1)) ^2)) is V11() real ext-real Element of REAL
1 * (1 + (((O `2) / (O `1)) ^2)) is V11() real ext-real Element of REAL
(((O `1) ^2) + ((O `2) ^2)) - 1 is V11() real ext-real Element of REAL
((O `2) ^2) / ((O `1) ^2) is V11() real ext-real Element of REAL
((((O `1) ^2) + ((O `2) ^2)) - 1) * ((O `1) ^2) is V11() real ext-real Element of REAL
((O `1) ^2) - 1 is V11() real ext-real Element of REAL
(((O `1) ^2) - 1) * (((O `1) ^2) + ((O `2) ^2)) is V11() real ext-real Element of REAL
(O `1) - 1 is V11() real ext-real Element of REAL
(O `1) + 1 is V11() real ext-real Element of REAL
((O `1) - 1) * ((O `1) + 1) is V11() real ext-real Element of REAL
h1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
h1 `1 is V11() real ext-real Element of REAL
h1 `2 is V11() real ext-real Element of REAL
(h1 `1) / (h1 `2) is V11() real ext-real Element of REAL
((h1 `1) / (h1 `2)) ^2 is V11() real ext-real Element of REAL
K37(((h1 `1) / (h1 `2)),((h1 `1) / (h1 `2))) is V11() real ext-real set
1 + (((h1 `1) / (h1 `2)) ^2) is V11() real ext-real Element of REAL
sqrt (1 + (((h1 `1) / (h1 `2)) ^2)) is V11() real ext-real Element of REAL
(h1 `1) / (sqrt (1 + (((h1 `1) / (h1 `2)) ^2))) is V11() real ext-real Element of REAL
(h1 `2) / (sqrt (1 + (((h1 `1) / (h1 `2)) ^2))) is V11() real ext-real Element of REAL
|[((h1 `1) / (sqrt (1 + (((h1 `1) / (h1 `2)) ^2)))),((h1 `2) / (sqrt (1 + (((h1 `1) / (h1 `2)) ^2))))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|[((h1 `1) / (sqrt (1 + (((h1 `1) / (h1 `2)) ^2)))),((h1 `2) / (sqrt (1 + (((h1 `1) / (h1 `2)) ^2))))]| `2 is V11() real ext-real Element of REAL
KYN is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.KYN.| is V11() real ext-real non negative Element of REAL
KYN `1 is V11() real ext-real Element of REAL
KYN `2 is V11() real ext-real Element of REAL
- (KYN `1) is V11() real ext-real Element of REAL
(KYN `2) / (KYN `1) is V11() real ext-real Element of REAL
((KYN `2) / (KYN `1)) ^2 is V11() real ext-real Element of REAL
K37(((KYN `2) / (KYN `1)),((KYN `2) / (KYN `1))) is V11() real ext-real set
1 + (((KYN `2) / (KYN `1)) ^2) is V11() real ext-real Element of REAL
sqrt (1 + (((KYN `2) / (KYN `1)) ^2)) is V11() real ext-real Element of REAL
(Sq_Circ ") . (p1 . g) is set
Sq_Circ . I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(Sq_Circ ") . KYN is set
(KYN `1) * (sqrt (1 + (((KYN `2) / (KYN `1)) ^2))) is V11() real ext-real Element of REAL
(KYN `2) * (sqrt (1 + (((KYN `2) / (KYN `1)) ^2))) is V11() real ext-real Element of REAL
|[((KYN `1) * (sqrt (1 + (((KYN `2) / (KYN `1)) ^2)))),((KYN `2) * (sqrt (1 + (((KYN `2) / (KYN `1)) ^2))))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(- (KYN `1)) * (sqrt (1 + (((KYN `2) / (KYN `1)) ^2))) is V11() real ext-real Element of REAL
- (I `1) is V11() real ext-real Element of REAL
- (- (KYN `1)) is V11() real ext-real Element of REAL
- (KYN `2) is V11() real ext-real Element of REAL
- (- (KYN `2)) is V11() real ext-real Element of REAL
|[((I `1) / (sqrt (1 + (((I `2) / (I `1)) ^2)))),((I `2) / (sqrt (1 + (((I `2) / (I `1)) ^2))))]| `2 is V11() real ext-real Element of REAL
|.KYN.| ^2 is V11() real ext-real Element of REAL
K37(|.KYN.|,|.KYN.|) is V11() real ext-real non negative set
((I `1) / (sqrt (1 + (((I `2) / (I `1)) ^2)))) ^2 is V11() real ext-real Element of REAL
K37(((I `1) / (sqrt (1 + (((I `2) / (I `1)) ^2)))),((I `1) / (sqrt (1 + (((I `2) / (I `1)) ^2))))) is V11() real ext-real set
((I `2) / (sqrt (1 + (((I `2) / (I `1)) ^2)))) ^2 is V11() real ext-real Element of REAL
K37(((I `2) / (sqrt (1 + (((I `2) / (I `1)) ^2)))),((I `2) / (sqrt (1 + (((I `2) / (I `1)) ^2))))) is V11() real ext-real set
(((I `1) / (sqrt (1 + (((I `2) / (I `1)) ^2)))) ^2) + (((I `2) / (sqrt (1 + (((I `2) / (I `1)) ^2)))) ^2) is V11() real ext-real Element of REAL
(I `1) ^2 is V11() real ext-real Element of REAL
K37((I `1),(I `1)) is V11() real ext-real set
(sqrt (1 + (((I `2) / (I `1)) ^2))) ^2 is V11() real ext-real Element of REAL
K37((sqrt (1 + (((I `2) / (I `1)) ^2))),(sqrt (1 + (((I `2) / (I `1)) ^2)))) is V11() real ext-real set
((I `1) ^2) / ((sqrt (1 + (((I `2) / (I `1)) ^2))) ^2) is V11() real ext-real Element of REAL
(((I `1) ^2) / ((sqrt (1 + (((I `2) / (I `1)) ^2))) ^2)) + (((I `2) / (sqrt (1 + (((I `2) / (I `1)) ^2)))) ^2) is V11() real ext-real Element of REAL
(I `2) ^2 is V11() real ext-real Element of REAL
K37((I `2),(I `2)) is V11() real ext-real set
((I `2) ^2) / ((sqrt (1 + (((I `2) / (I `1)) ^2))) ^2) is V11() real ext-real Element of REAL
(((I `1) ^2) / ((sqrt (1 + (((I `2) / (I `1)) ^2))) ^2)) + (((I `2) ^2) / ((sqrt (1 + (((I `2) / (I `1)) ^2))) ^2)) is V11() real ext-real Element of REAL
((I `1) ^2) / (1 + (((I `2) / (I `1)) ^2)) is V11() real ext-real Element of REAL
(((I `1) ^2) / (1 + (((I `2) / (I `1)) ^2))) + (((I `2) ^2) / ((sqrt (1 + (((I `2) / (I `1)) ^2))) ^2)) is V11() real ext-real Element of REAL
((I `2) ^2) / (1 + (((I `2) / (I `1)) ^2)) is V11() real ext-real Element of REAL
(((I `1) ^2) / (1 + (((I `2) / (I `1)) ^2))) + (((I `2) ^2) / (1 + (((I `2) / (I `1)) ^2))) is V11() real ext-real Element of REAL
((I `1) ^2) + ((I `2) ^2) is V11() real ext-real Element of REAL
(((I `1) ^2) + ((I `2) ^2)) / (1 + (((I `2) / (I `1)) ^2)) is V11() real ext-real Element of REAL
((((I `1) ^2) + ((I `2) ^2)) / (1 + (((I `2) / (I `1)) ^2))) * (1 + (((I `2) / (I `1)) ^2)) is V11() real ext-real Element of REAL
1 * (1 + (((I `2) / (I `1)) ^2)) is V11() real ext-real Element of REAL
(((I `1) ^2) + ((I `2) ^2)) - 1 is V11() real ext-real Element of REAL
((I `2) ^2) / ((I `1) ^2) is V11() real ext-real Element of REAL
((((I `1) ^2) + ((I `2) ^2)) - 1) * ((I `1) ^2) is V11() real ext-real Element of REAL
((I `1) ^2) - 1 is V11() real ext-real Element of REAL
(((I `1) ^2) - 1) * (((I `1) ^2) + ((I `2) ^2)) is V11() real ext-real Element of REAL
KXN is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KXN `1 is V11() real ext-real Element of REAL
KXN `2 is V11() real ext-real Element of REAL
(KXN `1) / (KXN `2) is V11() real ext-real Element of REAL
((KXN `1) / (KXN `2)) ^2 is V11() real ext-real Element of REAL
K37(((KXN `1) / (KXN `2)),((KXN `1) / (KXN `2))) is V11() real ext-real set
1 + (((KXN `1) / (KXN `2)) ^2) is V11() real ext-real Element of REAL
sqrt (1 + (((KXN `1) / (KXN `2)) ^2)) is V11() real ext-real Element of REAL
(KXN `1) / (sqrt (1 + (((KXN `1) / (KXN `2)) ^2))) is V11() real ext-real Element of REAL
(KXN `2) / (sqrt (1 + (((KXN `1) / (KXN `2)) ^2))) is V11() real ext-real Element of REAL
|[((KXN `1) / (sqrt (1 + (((KXN `1) / (KXN `2)) ^2)))),((KXN `2) / (sqrt (1 + (((KXN `1) / (KXN `2)) ^2))))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|[((KXN `1) / (sqrt (1 + (((KXN `1) / (KXN `2)) ^2)))),((KXN `2) / (sqrt (1 + (((KXN `1) / (KXN `2)) ^2))))]| `2 is V11() real ext-real Element of REAL
x2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.x2.| is V11() real ext-real non negative Element of REAL
x2 `1 is V11() real ext-real Element of REAL
x2 `2 is V11() real ext-real Element of REAL
- (x2 `1) is V11() real ext-real Element of REAL
(x2 `1) / (x2 `2) is V11() real ext-real Element of REAL
((x2 `1) / (x2 `2)) ^2 is V11() real ext-real Element of REAL
K37(((x2 `1) / (x2 `2)),((x2 `1) / (x2 `2))) is V11() real ext-real set
1 + (((x2 `1) / (x2 `2)) ^2) is V11() real ext-real Element of REAL
sqrt (1 + (((x2 `1) / (x2 `2)) ^2)) is V11() real ext-real Element of REAL
- (x2 `2) is V11() real ext-real Element of REAL
- (- (x2 `1)) is V11() real ext-real Element of REAL
(- (x2 `2)) * (sqrt (1 + (((x2 `1) / (x2 `2)) ^2))) is V11() real ext-real Element of REAL
(x2 `1) * (sqrt (1 + (((x2 `1) / (x2 `2)) ^2))) is V11() real ext-real Element of REAL
- (KXN `2) is V11() real ext-real Element of REAL
(Sq_Circ ") . (p2 . h) is set
Sq_Circ . KXN is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(Sq_Circ ") . x2 is set
(x2 `2) * (sqrt (1 + (((x2 `1) / (x2 `2)) ^2))) is V11() real ext-real Element of REAL
|[((x2 `1) * (sqrt (1 + (((x2 `1) / (x2 `2)) ^2)))),((x2 `2) * (sqrt (1 + (((x2 `1) / (x2 `2)) ^2))))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|[((KXN `1) / (sqrt (1 + (((KXN `1) / (KXN `2)) ^2)))),((KXN `2) / (sqrt (1 + (((KXN `1) / (KXN `2)) ^2))))]| `1 is V11() real ext-real Element of REAL
|.x2.| ^2 is V11() real ext-real Element of REAL
K37(|.x2.|,|.x2.|) is V11() real ext-real non negative set
((KXN `2) / (sqrt (1 + (((KXN `1) / (KXN `2)) ^2)))) ^2 is V11() real ext-real Element of REAL
K37(((KXN `2) / (sqrt (1 + (((KXN `1) / (KXN `2)) ^2)))),((KXN `2) / (sqrt (1 + (((KXN `1) / (KXN `2)) ^2))))) is V11() real ext-real set
((KXN `1) / (sqrt (1 + (((KXN `1) / (KXN `2)) ^2)))) ^2 is V11() real ext-real Element of REAL
K37(((KXN `1) / (sqrt (1 + (((KXN `1) / (KXN `2)) ^2)))),((KXN `1) / (sqrt (1 + (((KXN `1) / (KXN `2)) ^2))))) is V11() real ext-real set
(((KXN `2) / (sqrt (1 + (((KXN `1) / (KXN `2)) ^2)))) ^2) + (((KXN `1) / (sqrt (1 + (((KXN `1) / (KXN `2)) ^2)))) ^2) is V11() real ext-real Element of REAL
(KXN `2) ^2 is V11() real ext-real Element of REAL
K37((KXN `2),(KXN `2)) is V11() real ext-real set
(sqrt (1 + (((KXN `1) / (KXN `2)) ^2))) ^2 is V11() real ext-real Element of REAL
K37((sqrt (1 + (((KXN `1) / (KXN `2)) ^2))),(sqrt (1 + (((KXN `1) / (KXN `2)) ^2)))) is V11() real ext-real set
((KXN `2) ^2) / ((sqrt (1 + (((KXN `1) / (KXN `2)) ^2))) ^2) is V11() real ext-real Element of REAL
(((KXN `2) ^2) / ((sqrt (1 + (((KXN `1) / (KXN `2)) ^2))) ^2)) + (((KXN `1) / (sqrt (1 + (((KXN `1) / (KXN `2)) ^2)))) ^2) is V11() real ext-real Element of REAL
(KXN `1) ^2 is V11() real ext-real Element of REAL
K37((KXN `1),(KXN `1)) is V11() real ext-real set
((KXN `1) ^2) / ((sqrt (1 + (((KXN `1) / (KXN `2)) ^2))) ^2) is V11() real ext-real Element of REAL
(((KXN `2) ^2) / ((sqrt (1 + (((KXN `1) / (KXN `2)) ^2))) ^2)) + (((KXN `1) ^2) / ((sqrt (1 + (((KXN `1) / (KXN `2)) ^2))) ^2)) is V11() real ext-real Element of REAL
((KXN `2) ^2) / (1 + (((KXN `1) / (KXN `2)) ^2)) is V11() real ext-real Element of REAL
(((KXN `2) ^2) / (1 + (((KXN `1) / (KXN `2)) ^2))) + (((KXN `1) ^2) / ((sqrt (1 + (((KXN `1) / (KXN `2)) ^2))) ^2)) is V11() real ext-real Element of REAL
((KXN `1) ^2) / (1 + (((KXN `1) / (KXN `2)) ^2)) is V11() real ext-real Element of REAL
(((KXN `2) ^2) / (1 + (((KXN `1) / (KXN `2)) ^2))) + (((KXN `1) ^2) / (1 + (((KXN `1) / (KXN `2)) ^2))) is V11() real ext-real Element of REAL
((KXN `2) ^2) + ((KXN `1) ^2) is V11() real ext-real Element of REAL
(((KXN `2) ^2) + ((KXN `1) ^2)) / (1 + (((KXN `1) / (KXN `2)) ^2)) is V11() real ext-real Element of REAL
((((KXN `2) ^2) + ((KXN `1) ^2)) / (1 + (((KXN `1) / (KXN `2)) ^2))) * (1 + (((KXN `1) / (KXN `2)) ^2)) is V11() real ext-real Element of REAL
1 * (1 + (((KXN `1) / (KXN `2)) ^2)) is V11() real ext-real Element of REAL
(((KXN `2) ^2) + ((KXN `1) ^2)) - 1 is V11() real ext-real Element of REAL
((KXN `1) ^2) / ((KXN `2) ^2) is V11() real ext-real Element of REAL
((((KXN `2) ^2) + ((KXN `1) ^2)) - 1) * ((KXN `2) ^2) is V11() real ext-real Element of REAL
((KXN `2) ^2) - 1 is V11() real ext-real Element of REAL
(((KXN `2) ^2) - 1) * (((KXN `2) ^2) + ((KXN `1) ^2)) is V11() real ext-real Element of REAL
(KXN `2) - 1 is V11() real ext-real Element of REAL
(KXN `2) + 1 is V11() real ext-real Element of REAL
((KXN `2) - 1) * ((KXN `2) + 1) is V11() real ext-real Element of REAL
z3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.z3.| is V11() real ext-real non negative Element of REAL
z3 `2 is V11() real ext-real Element of REAL
z3 `1 is V11() real ext-real Element of REAL
- (z3 `1) is V11() real ext-real Element of REAL
(Sq_Circ ") . (p2 . g) is set
Sq_Circ . h1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
- (- (z3 `1)) is V11() real ext-real Element of REAL
- (z3 `2) is V11() real ext-real Element of REAL
(Sq_Circ ") . z3 is set
(z3 `1) / (z3 `2) is V11() real ext-real Element of REAL
((z3 `1) / (z3 `2)) ^2 is V11() real ext-real Element of REAL
K37(((z3 `1) / (z3 `2)),((z3 `1) / (z3 `2))) is V11() real ext-real set
1 + (((z3 `1) / (z3 `2)) ^2) is V11() real ext-real Element of REAL
sqrt (1 + (((z3 `1) / (z3 `2)) ^2)) is V11() real ext-real Element of REAL
(z3 `1) * (sqrt (1 + (((z3 `1) / (z3 `2)) ^2))) is V11() real ext-real Element of REAL
(z3 `2) * (sqrt (1 + (((z3 `1) / (z3 `2)) ^2))) is V11() real ext-real Element of REAL
|[((z3 `1) * (sqrt (1 + (((z3 `1) / (z3 `2)) ^2)))),((z3 `2) * (sqrt (1 + (((z3 `1) / (z3 `2)) ^2))))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(- (z3 `2)) * (sqrt (1 + (((z3 `1) / (z3 `2)) ^2))) is V11() real ext-real Element of REAL
- (h1 `2) is V11() real ext-real Element of REAL
|[((h1 `1) / (sqrt (1 + (((h1 `1) / (h1 `2)) ^2)))),((h1 `2) / (sqrt (1 + (((h1 `1) / (h1 `2)) ^2))))]| `1 is V11() real ext-real Element of REAL
|.z3.| ^2 is V11() real ext-real Element of REAL
K37(|.z3.|,|.z3.|) is V11() real ext-real non negative set
((h1 `2) / (sqrt (1 + (((h1 `1) / (h1 `2)) ^2)))) ^2 is V11() real ext-real Element of REAL
K37(((h1 `2) / (sqrt (1 + (((h1 `1) / (h1 `2)) ^2)))),((h1 `2) / (sqrt (1 + (((h1 `1) / (h1 `2)) ^2))))) is V11() real ext-real set
((h1 `1) / (sqrt (1 + (((h1 `1) / (h1 `2)) ^2)))) ^2 is V11() real ext-real Element of REAL
K37(((h1 `1) / (sqrt (1 + (((h1 `1) / (h1 `2)) ^2)))),((h1 `1) / (sqrt (1 + (((h1 `1) / (h1 `2)) ^2))))) is V11() real ext-real set
(((h1 `2) / (sqrt (1 + (((h1 `1) / (h1 `2)) ^2)))) ^2) + (((h1 `1) / (sqrt (1 + (((h1 `1) / (h1 `2)) ^2)))) ^2) is V11() real ext-real Element of REAL
(h1 `2) ^2 is V11() real ext-real Element of REAL
K37((h1 `2),(h1 `2)) is V11() real ext-real set
(sqrt (1 + (((h1 `1) / (h1 `2)) ^2))) ^2 is V11() real ext-real Element of REAL
K37((sqrt (1 + (((h1 `1) / (h1 `2)) ^2))),(sqrt (1 + (((h1 `1) / (h1 `2)) ^2)))) is V11() real ext-real set
((h1 `2) ^2) / ((sqrt (1 + (((h1 `1) / (h1 `2)) ^2))) ^2) is V11() real ext-real Element of REAL
(((h1 `2) ^2) / ((sqrt (1 + (((h1 `1) / (h1 `2)) ^2))) ^2)) + (((h1 `1) / (sqrt (1 + (((h1 `1) / (h1 `2)) ^2)))) ^2) is V11() real ext-real Element of REAL
(h1 `1) ^2 is V11() real ext-real Element of REAL
K37((h1 `1),(h1 `1)) is V11() real ext-real set
((h1 `1) ^2) / ((sqrt (1 + (((h1 `1) / (h1 `2)) ^2))) ^2) is V11() real ext-real Element of REAL
(((h1 `2) ^2) / ((sqrt (1 + (((h1 `1) / (h1 `2)) ^2))) ^2)) + (((h1 `1) ^2) / ((sqrt (1 + (((h1 `1) / (h1 `2)) ^2))) ^2)) is V11() real ext-real Element of REAL
((h1 `2) ^2) / (1 + (((h1 `1) / (h1 `2)) ^2)) is V11() real ext-real Element of REAL
(((h1 `2) ^2) / (1 + (((h1 `1) / (h1 `2)) ^2))) + (((h1 `1) ^2) / ((sqrt (1 + (((h1 `1) / (h1 `2)) ^2))) ^2)) is V11() real ext-real Element of REAL
((h1 `1) ^2) / (1 + (((h1 `1) / (h1 `2)) ^2)) is V11() real ext-real Element of REAL
(((h1 `2) ^2) / (1 + (((h1 `1) / (h1 `2)) ^2))) + (((h1 `1) ^2) / (1 + (((h1 `1) / (h1 `2)) ^2))) is V11() real ext-real Element of REAL
((h1 `2) ^2) + ((h1 `1) ^2) is V11() real ext-real Element of REAL
(((h1 `2) ^2) + ((h1 `1) ^2)) / (1 + (((h1 `1) / (h1 `2)) ^2)) is V11() real ext-real Element of REAL
((((h1 `2) ^2) + ((h1 `1) ^2)) / (1 + (((h1 `1) / (h1 `2)) ^2))) * (1 + (((h1 `1) / (h1 `2)) ^2)) is V11() real ext-real Element of REAL
1 * (1 + (((h1 `1) / (h1 `2)) ^2)) is V11() real ext-real Element of REAL
(((h1 `2) ^2) + ((h1 `1) ^2)) - 1 is V11() real ext-real Element of REAL
((h1 `1) ^2) / ((h1 `2) ^2) is V11() real ext-real Element of REAL
((((h1 `2) ^2) + ((h1 `1) ^2)) - 1) * ((h1 `2) ^2) is V11() real ext-real Element of REAL
((h1 `2) ^2) - 1 is V11() real ext-real Element of REAL
(((h1 `2) ^2) - 1) * (((h1 `2) ^2) + ((h1 `1) ^2)) is V11() real ext-real Element of REAL
(h1 `2) - 1 is V11() real ext-real Element of REAL
(h1 `2) + 1 is V11() real ext-real Element of REAL
((h1 `2) - 1) * ((h1 `2) + 1) is V11() real ext-real Element of REAL
(I `1) - 1 is V11() real ext-real Element of REAL
(I `1) + 1 is V11() real ext-real Element of REAL
((I `1) - 1) * ((I `1) + 1) is V11() real ext-real Element of REAL
dom p1 is V142() V143() V144() Element of K6( the carrier of I[01])
h1 is V11() real ext-real Element of the carrier of I[01]
g2 . h1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(g2 . h1) `1 is V11() real ext-real Element of REAL
(g2 . h1) `2 is V11() real ext-real Element of REAL
f2 . h1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(f2 . h1) `1 is V11() real ext-real Element of REAL
(f2 . h1) `2 is V11() real ext-real Element of REAL
p1 . h1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
p2 . h1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.I.| is V11() real ext-real non negative Element of REAL
(Sq_Circ ") . (p2 . h1) is set
I `2 is V11() real ext-real Element of REAL
I `1 is V11() real ext-real Element of REAL
- (I `1) is V11() real ext-real Element of REAL
(Sq_Circ ") . I is set
(I `2) / (I `1) is V11() real ext-real Element of REAL
((I `2) / (I `1)) ^2 is V11() real ext-real Element of REAL
K37(((I `2) / (I `1)),((I `2) / (I `1))) is V11() real ext-real set
1 + (((I `2) / (I `1)) ^2) is V11() real ext-real Element of REAL
sqrt (1 + (((I `2) / (I `1)) ^2)) is V11() real ext-real Element of REAL
(I `1) * (sqrt (1 + (((I `2) / (I `1)) ^2))) is V11() real ext-real Element of REAL
(I `2) * (sqrt (1 + (((I `2) / (I `1)) ^2))) is V11() real ext-real Element of REAL
|[((I `1) * (sqrt (1 + (((I `2) / (I `1)) ^2)))),((I `2) * (sqrt (1 + (((I `2) / (I `1)) ^2))))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KXP is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KXP `1 is V11() real ext-real Element of REAL
(KXP `1) ^2 is V11() real ext-real Element of REAL
K37((KXP `1),(KXP `1)) is V11() real ext-real set
|.I.| ^2 is V11() real ext-real Element of REAL
K37(|.I.|,|.I.|) is V11() real ext-real non negative set
KXP `2 is V11() real ext-real Element of REAL
(KXP `2) ^2 is V11() real ext-real Element of REAL
K37((KXP `2),(KXP `2)) is V11() real ext-real set
(- (I `1)) * (sqrt (1 + (((I `2) / (I `1)) ^2))) is V11() real ext-real Element of REAL
- (KXP `1) is V11() real ext-real Element of REAL
Sq_Circ . KXP is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(KXP `2) / (KXP `1) is V11() real ext-real Element of REAL
((KXP `2) / (KXP `1)) ^2 is V11() real ext-real Element of REAL
K37(((KXP `2) / (KXP `1)),((KXP `2) / (KXP `1))) is V11() real ext-real set
1 + (((KXP `2) / (KXP `1)) ^2) is V11() real ext-real Element of REAL
sqrt (1 + (((KXP `2) / (KXP `1)) ^2)) is V11() real ext-real Element of REAL
(KXP `1) / (sqrt (1 + (((KXP `2) / (KXP `1)) ^2))) is V11() real ext-real Element of REAL
(KXP `2) / (sqrt (1 + (((KXP `2) / (KXP `1)) ^2))) is V11() real ext-real Element of REAL
|[((KXP `1) / (sqrt (1 + (((KXP `2) / (KXP `1)) ^2)))),((KXP `2) / (sqrt (1 + (((KXP `2) / (KXP `1)) ^2))))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|[((KXP `1) / (sqrt (1 + (((KXP `2) / (KXP `1)) ^2)))),((KXP `2) / (sqrt (1 + (((KXP `2) / (KXP `1)) ^2))))]| `1 is V11() real ext-real Element of REAL
|[((KXP `1) / (sqrt (1 + (((KXP `2) / (KXP `1)) ^2)))),((KXP `2) / (sqrt (1 + (((KXP `2) / (KXP `1)) ^2))))]| `2 is V11() real ext-real Element of REAL
((KXP `1) / (sqrt (1 + (((KXP `2) / (KXP `1)) ^2)))) ^2 is V11() real ext-real Element of REAL
K37(((KXP `1) / (sqrt (1 + (((KXP `2) / (KXP `1)) ^2)))),((KXP `1) / (sqrt (1 + (((KXP `2) / (KXP `1)) ^2))))) is V11() real ext-real set
((KXP `2) / (sqrt (1 + (((KXP `2) / (KXP `1)) ^2)))) ^2 is V11() real ext-real Element of REAL
K37(((KXP `2) / (sqrt (1 + (((KXP `2) / (KXP `1)) ^2)))),((KXP `2) / (sqrt (1 + (((KXP `2) / (KXP `1)) ^2))))) is V11() real ext-real set
(((KXP `1) / (sqrt (1 + (((KXP `2) / (KXP `1)) ^2)))) ^2) + (((KXP `2) / (sqrt (1 + (((KXP `2) / (KXP `1)) ^2)))) ^2) is V11() real ext-real Element of REAL
(sqrt (1 + (((KXP `2) / (KXP `1)) ^2))) ^2 is V11() real ext-real Element of REAL
K37((sqrt (1 + (((KXP `2) / (KXP `1)) ^2))),(sqrt (1 + (((KXP `2) / (KXP `1)) ^2)))) is V11() real ext-real set
((KXP `1) ^2) / ((sqrt (1 + (((KXP `2) / (KXP `1)) ^2))) ^2) is V11() real ext-real Element of REAL
(((KXP `1) ^2) / ((sqrt (1 + (((KXP `2) / (KXP `1)) ^2))) ^2)) + (((KXP `2) / (sqrt (1 + (((KXP `2) / (KXP `1)) ^2)))) ^2) is V11() real ext-real Element of REAL
((KXP `2) ^2) / ((sqrt (1 + (((KXP `2) / (KXP `1)) ^2))) ^2) is V11() real ext-real Element of REAL
(((KXP `1) ^2) / ((sqrt (1 + (((KXP `2) / (KXP `1)) ^2))) ^2)) + (((KXP `2) ^2) / ((sqrt (1 + (((KXP `2) / (KXP `1)) ^2))) ^2)) is V11() real ext-real Element of REAL
((KXP `1) ^2) / (1 + (((KXP `2) / (KXP `1)) ^2)) is V11() real ext-real Element of REAL
(((KXP `1) ^2) / (1 + (((KXP `2) / (KXP `1)) ^2))) + (((KXP `2) ^2) / ((sqrt (1 + (((KXP `2) / (KXP `1)) ^2))) ^2)) is V11() real ext-real Element of REAL
((KXP `2) ^2) / (1 + (((KXP `2) / (KXP `1)) ^2)) is V11() real ext-real Element of REAL
(((KXP `1) ^2) / (1 + (((KXP `2) / (KXP `1)) ^2))) + (((KXP `2) ^2) / (1 + (((KXP `2) / (KXP `1)) ^2))) is V11() real ext-real Element of REAL
((KXP `1) ^2) + ((KXP `2) ^2) is V11() real ext-real Element of REAL
(((KXP `1) ^2) + ((KXP `2) ^2)) / (1 + (((KXP `2) / (KXP `1)) ^2)) is V11() real ext-real Element of REAL
1 * (1 + (((KXP `2) / (KXP `1)) ^2)) is V11() real ext-real Element of REAL
((((KXP `1) ^2) + ((KXP `2) ^2)) / (1 + (((KXP `2) / (KXP `1)) ^2))) * (1 + (((KXP `2) / (KXP `1)) ^2)) is V11() real ext-real Element of REAL
((KXP `2) ^2) / ((KXP `1) ^2) is V11() real ext-real Element of REAL
1 + (((KXP `2) ^2) / ((KXP `1) ^2)) is V11() real ext-real Element of REAL
(1 + (((KXP `2) ^2) / ((KXP `1) ^2))) - 1 is V11() real ext-real Element of REAL
(((KXP `1) ^2) + ((KXP `2) ^2)) - 1 is V11() real ext-real Element of REAL
(((KXP `2) ^2) / ((KXP `1) ^2)) * ((KXP `1) ^2) is V11() real ext-real Element of REAL
((((KXP `1) ^2) + ((KXP `2) ^2)) - 1) * ((KXP `1) ^2) is V11() real ext-real Element of REAL
((KXP `2) ^2) - 1 is V11() real ext-real Element of REAL
((KXP `1) ^2) + (((KXP `2) ^2) - 1) is V11() real ext-real Element of REAL
(((KXP `1) ^2) + (((KXP `2) ^2) - 1)) * ((KXP `1) ^2) is V11() real ext-real Element of REAL
((KXP `2) ^2) - ((KXP `2) ^2) is V11() real ext-real Element of REAL
((KXP `1) ^2) * ((KXP `1) ^2) is V11() real ext-real Element of REAL
((KXP `1) ^2) * (((KXP `2) ^2) - 1) is V11() real ext-real Element of REAL
(((KXP `1) ^2) * ((KXP `1) ^2)) + (((KXP `1) ^2) * (((KXP `2) ^2) - 1)) is V11() real ext-real Element of REAL
((((KXP `1) ^2) * ((KXP `1) ^2)) + (((KXP `1) ^2) * (((KXP `2) ^2) - 1))) - ((KXP `2) ^2) is V11() real ext-real Element of REAL
((KXP `1) ^2) - 1 is V11() real ext-real Element of REAL
(((KXP `1) ^2) - 1) * (((KXP `1) ^2) + ((KXP `2) ^2)) is V11() real ext-real Element of REAL
(KXP `1) - 1 is V11() real ext-real Element of REAL
(KXP `1) + 1 is V11() real ext-real Element of REAL
((KXP `1) - 1) * ((KXP `1) + 1) is V11() real ext-real Element of REAL
I `2 is V11() real ext-real Element of REAL
I `1 is V11() real ext-real Element of REAL
- (I `1) is V11() real ext-real Element of REAL
(Sq_Circ ") . I is set
(I `1) / (I `2) is V11() real ext-real Element of REAL
((I `1) / (I `2)) ^2 is V11() real ext-real Element of REAL
K37(((I `1) / (I `2)),((I `1) / (I `2))) is V11() real ext-real set
1 + (((I `1) / (I `2)) ^2) is V11() real ext-real Element of REAL
sqrt (1 + (((I `1) / (I `2)) ^2)) is V11() real ext-real Element of REAL
(I `1) * (sqrt (1 + (((I `1) / (I `2)) ^2))) is V11() real ext-real Element of REAL
(I `2) * (sqrt (1 + (((I `1) / (I `2)) ^2))) is V11() real ext-real Element of REAL
|[((I `1) * (sqrt (1 + (((I `1) / (I `2)) ^2)))),((I `2) * (sqrt (1 + (((I `1) / (I `2)) ^2))))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KXP is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KXP `2 is V11() real ext-real Element of REAL
KXP `1 is V11() real ext-real Element of REAL
- (I `2) is V11() real ext-real Element of REAL
(- (I `2)) * (sqrt (1 + (((I `1) / (I `2)) ^2))) is V11() real ext-real Element of REAL
- (KXP `2) is V11() real ext-real Element of REAL
Sq_Circ . KXP is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(KXP `1) / (KXP `2) is V11() real ext-real Element of REAL
((KXP `1) / (KXP `2)) ^2 is V11() real ext-real Element of REAL
K37(((KXP `1) / (KXP `2)),((KXP `1) / (KXP `2))) is V11() real ext-real set
1 + (((KXP `1) / (KXP `2)) ^2) is V11() real ext-real Element of REAL
sqrt (1 + (((KXP `1) / (KXP `2)) ^2)) is V11() real ext-real Element of REAL
(KXP `1) / (sqrt (1 + (((KXP `1) / (KXP `2)) ^2))) is V11() real ext-real Element of REAL
(KXP `2) / (sqrt (1 + (((KXP `1) / (KXP `2)) ^2))) is V11() real ext-real Element of REAL
|[((KXP `1) / (sqrt (1 + (((KXP `1) / (KXP `2)) ^2)))),((KXP `2) / (sqrt (1 + (((KXP `1) / (KXP `2)) ^2))))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.I.| ^2 is V11() real ext-real Element of REAL
K37(|.I.|,|.I.|) is V11() real ext-real non negative set
|[((KXP `1) / (sqrt (1 + (((KXP `1) / (KXP `2)) ^2)))),((KXP `2) / (sqrt (1 + (((KXP `1) / (KXP `2)) ^2))))]| `1 is V11() real ext-real Element of REAL
(KXP `1) ^2 is V11() real ext-real Element of REAL
K37((KXP `1),(KXP `1)) is V11() real ext-real set
(KXP `2) ^2 is V11() real ext-real Element of REAL
K37((KXP `2),(KXP `2)) is V11() real ext-real set
|[((KXP `1) / (sqrt (1 + (((KXP `1) / (KXP `2)) ^2)))),((KXP `2) / (sqrt (1 + (((KXP `1) / (KXP `2)) ^2))))]| `2 is V11() real ext-real Element of REAL
((KXP `2) / (sqrt (1 + (((KXP `1) / (KXP `2)) ^2)))) ^2 is V11() real ext-real Element of REAL
K37(((KXP `2) / (sqrt (1 + (((KXP `1) / (KXP `2)) ^2)))),((KXP `2) / (sqrt (1 + (((KXP `1) / (KXP `2)) ^2))))) is V11() real ext-real set
((KXP `1) / (sqrt (1 + (((KXP `1) / (KXP `2)) ^2)))) ^2 is V11() real ext-real Element of REAL
K37(((KXP `1) / (sqrt (1 + (((KXP `1) / (KXP `2)) ^2)))),((KXP `1) / (sqrt (1 + (((KXP `1) / (KXP `2)) ^2))))) is V11() real ext-real set
(((KXP `2) / (sqrt (1 + (((KXP `1) / (KXP `2)) ^2)))) ^2) + (((KXP `1) / (sqrt (1 + (((KXP `1) / (KXP `2)) ^2)))) ^2) is V11() real ext-real Element of REAL
(sqrt (1 + (((KXP `1) / (KXP `2)) ^2))) ^2 is V11() real ext-real Element of REAL
K37((sqrt (1 + (((KXP `1) / (KXP `2)) ^2))),(sqrt (1 + (((KXP `1) / (KXP `2)) ^2)))) is V11() real ext-real set
((KXP `2) ^2) / ((sqrt (1 + (((KXP `1) / (KXP `2)) ^2))) ^2) is V11() real ext-real Element of REAL
(((KXP `2) ^2) / ((sqrt (1 + (((KXP `1) / (KXP `2)) ^2))) ^2)) + (((KXP `1) / (sqrt (1 + (((KXP `1) / (KXP `2)) ^2)))) ^2) is V11() real ext-real Element of REAL
((KXP `1) ^2) / ((sqrt (1 + (((KXP `1) / (KXP `2)) ^2))) ^2) is V11() real ext-real Element of REAL
(((KXP `2) ^2) / ((sqrt (1 + (((KXP `1) / (KXP `2)) ^2))) ^2)) + (((KXP `1) ^2) / ((sqrt (1 + (((KXP `1) / (KXP `2)) ^2))) ^2)) is V11() real ext-real Element of REAL
((KXP `2) ^2) / (1 + (((KXP `1) / (KXP `2)) ^2)) is V11() real ext-real Element of REAL
(((KXP `2) ^2) / (1 + (((KXP `1) / (KXP `2)) ^2))) + (((KXP `1) ^2) / ((sqrt (1 + (((KXP `1) / (KXP `2)) ^2))) ^2)) is V11() real ext-real Element of REAL
((KXP `1) ^2) / (1 + (((KXP `1) / (KXP `2)) ^2)) is V11() real ext-real Element of REAL
(((KXP `2) ^2) / (1 + (((KXP `1) / (KXP `2)) ^2))) + (((KXP `1) ^2) / (1 + (((KXP `1) / (KXP `2)) ^2))) is V11() real ext-real Element of REAL
((KXP `2) ^2) + ((KXP `1) ^2) is V11() real ext-real Element of REAL
(((KXP `2) ^2) + ((KXP `1) ^2)) / (1 + (((KXP `1) / (KXP `2)) ^2)) is V11() real ext-real Element of REAL
1 * (1 + (((KXP `1) / (KXP `2)) ^2)) is V11() real ext-real Element of REAL
((((KXP `2) ^2) + ((KXP `1) ^2)) / (1 + (((KXP `1) / (KXP `2)) ^2))) * (1 + (((KXP `1) / (KXP `2)) ^2)) is V11() real ext-real Element of REAL
((KXP `1) ^2) / ((KXP `2) ^2) is V11() real ext-real Element of REAL
1 + (((KXP `1) ^2) / ((KXP `2) ^2)) is V11() real ext-real Element of REAL
(1 + (((KXP `1) ^2) / ((KXP `2) ^2))) - 1 is V11() real ext-real Element of REAL
(((KXP `2) ^2) + ((KXP `1) ^2)) - 1 is V11() real ext-real Element of REAL
(((KXP `1) ^2) / ((KXP `2) ^2)) * ((KXP `2) ^2) is V11() real ext-real Element of REAL
((((KXP `2) ^2) + ((KXP `1) ^2)) - 1) * ((KXP `2) ^2) is V11() real ext-real Element of REAL
((KXP `1) ^2) - 1 is V11() real ext-real Element of REAL
((KXP `2) ^2) + (((KXP `1) ^2) - 1) is V11() real ext-real Element of REAL
(((KXP `2) ^2) + (((KXP `1) ^2) - 1)) * ((KXP `2) ^2) is V11() real ext-real Element of REAL
((KXP `1) ^2) - ((KXP `1) ^2) is V11() real ext-real Element of REAL
((KXP `2) ^2) * ((KXP `2) ^2) is V11() real ext-real Element of REAL
((KXP `2) ^2) * (((KXP `1) ^2) - 1) is V11() real ext-real Element of REAL
(((KXP `2) ^2) * ((KXP `2) ^2)) + (((KXP `2) ^2) * (((KXP `1) ^2) - 1)) is V11() real ext-real Element of REAL
((((KXP `2) ^2) * ((KXP `2) ^2)) + (((KXP `2) ^2) * (((KXP `1) ^2) - 1))) - ((KXP `1) ^2) is V11() real ext-real Element of REAL
((KXP `2) ^2) - 1 is V11() real ext-real Element of REAL
(((KXP `2) ^2) - 1) * (((KXP `2) ^2) + ((KXP `1) ^2)) is V11() real ext-real Element of REAL
(KXP `2) - 1 is V11() real ext-real Element of REAL
(KXP `2) + 1 is V11() real ext-real Element of REAL
((KXP `2) - 1) * ((KXP `2) + 1) is V11() real ext-real Element of REAL
I `2 is V11() real ext-real Element of REAL
I `1 is V11() real ext-real Element of REAL
- (I `1) is V11() real ext-real Element of REAL
I `2 is V11() real ext-real Element of REAL
I `1 is V11() real ext-real Element of REAL
- (I `1) is V11() real ext-real Element of REAL
(Sq_Circ ") . (p1 . h1) is set
O `2 is V11() real ext-real Element of REAL
O `1 is V11() real ext-real Element of REAL
- (O `1) is V11() real ext-real Element of REAL
(Sq_Circ ") . O is set
(O `2) / (O `1) is V11() real ext-real Element of REAL
((O `2) / (O `1)) ^2 is V11() real ext-real Element of REAL
K37(((O `2) / (O `1)),((O `2) / (O `1))) is V11() real ext-real set
1 + (((O `2) / (O `1)) ^2) is V11() real ext-real Element of REAL
sqrt (1 + (((O `2) / (O `1)) ^2)) is V11() real ext-real Element of REAL
(O `1) * (sqrt (1 + (((O `2) / (O `1)) ^2))) is V11() real ext-real Element of REAL
(O `2) * (sqrt (1 + (((O `2) / (O `1)) ^2))) is V11() real ext-real Element of REAL
|[((O `1) * (sqrt (1 + (((O `2) / (O `1)) ^2)))),((O `2) * (sqrt (1 + (((O `2) / (O `1)) ^2))))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KXP is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KXP `1 is V11() real ext-real Element of REAL
KXP `2 is V11() real ext-real Element of REAL
(- (O `1)) * (sqrt (1 + (((O `2) / (O `1)) ^2))) is V11() real ext-real Element of REAL
- (KXP `1) is V11() real ext-real Element of REAL
|.O.| ^2 is V11() real ext-real Element of REAL
K37(|.O.|,|.O.|) is V11() real ext-real non negative set
(KXP `1) ^2 is V11() real ext-real Element of REAL
K37((KXP `1),(KXP `1)) is V11() real ext-real set
(KXP `2) / (KXP `1) is V11() real ext-real Element of REAL
((KXP `2) / (KXP `1)) ^2 is V11() real ext-real Element of REAL
K37(((KXP `2) / (KXP `1)),((KXP `2) / (KXP `1))) is V11() real ext-real set
1 + (((KXP `2) / (KXP `1)) ^2) is V11() real ext-real Element of REAL
sqrt (1 + (((KXP `2) / (KXP `1)) ^2)) is V11() real ext-real Element of REAL
(KXP `1) / (sqrt (1 + (((KXP `2) / (KXP `1)) ^2))) is V11() real ext-real Element of REAL
(KXP `2) / (sqrt (1 + (((KXP `2) / (KXP `1)) ^2))) is V11() real ext-real Element of REAL
|[((KXP `1) / (sqrt (1 + (((KXP `2) / (KXP `1)) ^2)))),((KXP `2) / (sqrt (1 + (((KXP `2) / (KXP `1)) ^2))))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|[((KXP `1) / (sqrt (1 + (((KXP `2) / (KXP `1)) ^2)))),((KXP `2) / (sqrt (1 + (((KXP `2) / (KXP `1)) ^2))))]| `2 is V11() real ext-real Element of REAL
(KXP `2) ^2 is V11() real ext-real Element of REAL
K37((KXP `2),(KXP `2)) is V11() real ext-real set
Sq_Circ . KXP is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|[((KXP `1) / (sqrt (1 + (((KXP `2) / (KXP `1)) ^2)))),((KXP `2) / (sqrt (1 + (((KXP `2) / (KXP `1)) ^2))))]| `1 is V11() real ext-real Element of REAL
((KXP `1) / (sqrt (1 + (((KXP `2) / (KXP `1)) ^2)))) ^2 is V11() real ext-real Element of REAL
K37(((KXP `1) / (sqrt (1 + (((KXP `2) / (KXP `1)) ^2)))),((KXP `1) / (sqrt (1 + (((KXP `2) / (KXP `1)) ^2))))) is V11() real ext-real set
((KXP `2) / (sqrt (1 + (((KXP `2) / (KXP `1)) ^2)))) ^2 is V11() real ext-real Element of REAL
K37(((KXP `2) / (sqrt (1 + (((KXP `2) / (KXP `1)) ^2)))),((KXP `2) / (sqrt (1 + (((KXP `2) / (KXP `1)) ^2))))) is V11() real ext-real set
(((KXP `1) / (sqrt (1 + (((KXP `2) / (KXP `1)) ^2)))) ^2) + (((KXP `2) / (sqrt (1 + (((KXP `2) / (KXP `1)) ^2)))) ^2) is V11() real ext-real Element of REAL
(sqrt (1 + (((KXP `2) / (KXP `1)) ^2))) ^2 is V11() real ext-real Element of REAL
K37((sqrt (1 + (((KXP `2) / (KXP `1)) ^2))),(sqrt (1 + (((KXP `2) / (KXP `1)) ^2)))) is V11() real ext-real set
((KXP `1) ^2) / ((sqrt (1 + (((KXP `2) / (KXP `1)) ^2))) ^2) is V11() real ext-real Element of REAL
(((KXP `1) ^2) / ((sqrt (1 + (((KXP `2) / (KXP `1)) ^2))) ^2)) + (((KXP `2) / (sqrt (1 + (((KXP `2) / (KXP `1)) ^2)))) ^2) is V11() real ext-real Element of REAL
((KXP `2) ^2) / ((sqrt (1 + (((KXP `2) / (KXP `1)) ^2))) ^2) is V11() real ext-real Element of REAL
(((KXP `1) ^2) / ((sqrt (1 + (((KXP `2) / (KXP `1)) ^2))) ^2)) + (((KXP `2) ^2) / ((sqrt (1 + (((KXP `2) / (KXP `1)) ^2))) ^2)) is V11() real ext-real Element of REAL
((KXP `1) ^2) / (1 + (((KXP `2) / (KXP `1)) ^2)) is V11() real ext-real Element of REAL
(((KXP `1) ^2) / (1 + (((KXP `2) / (KXP `1)) ^2))) + (((KXP `2) ^2) / ((sqrt (1 + (((KXP `2) / (KXP `1)) ^2))) ^2)) is V11() real ext-real Element of REAL
((KXP `2) ^2) / (1 + (((KXP `2) / (KXP `1)) ^2)) is V11() real ext-real Element of REAL
(((KXP `1) ^2) / (1 + (((KXP `2) / (KXP `1)) ^2))) + (((KXP `2) ^2) / (1 + (((KXP `2) / (KXP `1)) ^2))) is V11() real ext-real Element of REAL
((KXP `1) ^2) + ((KXP `2) ^2) is V11() real ext-real Element of REAL
(((KXP `1) ^2) + ((KXP `2) ^2)) / (1 + (((KXP `2) / (KXP `1)) ^2)) is V11() real ext-real Element of REAL
1 * (1 + (((KXP `2) / (KXP `1)) ^2)) is V11() real ext-real Element of REAL
((((KXP `1) ^2) + ((KXP `2) ^2)) / (1 + (((KXP `2) / (KXP `1)) ^2))) * (1 + (((KXP `2) / (KXP `1)) ^2)) is V11() real ext-real Element of REAL
((KXP `2) ^2) / ((KXP `1) ^2) is V11() real ext-real Element of REAL
1 + (((KXP `2) ^2) / ((KXP `1) ^2)) is V11() real ext-real Element of REAL
(1 + (((KXP `2) ^2) / ((KXP `1) ^2))) - 1 is V11() real ext-real Element of REAL
(((KXP `1) ^2) + ((KXP `2) ^2)) - 1 is V11() real ext-real Element of REAL
(((KXP `2) ^2) / ((KXP `1) ^2)) * ((KXP `1) ^2) is V11() real ext-real Element of REAL
((((KXP `1) ^2) + ((KXP `2) ^2)) - 1) * ((KXP `1) ^2) is V11() real ext-real Element of REAL
((KXP `2) ^2) - 1 is V11() real ext-real Element of REAL
((KXP `1) ^2) + (((KXP `2) ^2) - 1) is V11() real ext-real Element of REAL
(((KXP `1) ^2) + (((KXP `2) ^2) - 1)) * ((KXP `1) ^2) is V11() real ext-real Element of REAL
((KXP `2) ^2) - ((KXP `2) ^2) is V11() real ext-real Element of REAL
((KXP `1) ^2) * ((KXP `1) ^2) is V11() real ext-real Element of REAL
((KXP `1) ^2) * (((KXP `2) ^2) - 1) is V11() real ext-real Element of REAL
(((KXP `1) ^2) * ((KXP `1) ^2)) + (((KXP `1) ^2) * (((KXP `2) ^2) - 1)) is V11() real ext-real Element of REAL
((((KXP `1) ^2) * ((KXP `1) ^2)) + (((KXP `1) ^2) * (((KXP `2) ^2) - 1))) - ((KXP `2) ^2) is V11() real ext-real Element of REAL
((KXP `1) ^2) - 1 is V11() real ext-real Element of REAL
(((KXP `1) ^2) - 1) * (((KXP `1) ^2) + ((KXP `2) ^2)) is V11() real ext-real Element of REAL
(KXP `1) - 1 is V11() real ext-real Element of REAL
(KXP `1) + 1 is V11() real ext-real Element of REAL
((KXP `1) - 1) * ((KXP `1) + 1) is V11() real ext-real Element of REAL
O `2 is V11() real ext-real Element of REAL
O `1 is V11() real ext-real Element of REAL
- (O `1) is V11() real ext-real Element of REAL
(Sq_Circ ") . O is set
(O `1) / (O `2) is V11() real ext-real Element of REAL
((O `1) / (O `2)) ^2 is V11() real ext-real Element of REAL
K37(((O `1) / (O `2)),((O `1) / (O `2))) is V11() real ext-real set
1 + (((O `1) / (O `2)) ^2) is V11() real ext-real Element of REAL
sqrt (1 + (((O `1) / (O `2)) ^2)) is V11() real ext-real Element of REAL
(O `1) * (sqrt (1 + (((O `1) / (O `2)) ^2))) is V11() real ext-real Element of REAL
(O `2) * (sqrt (1 + (((O `1) / (O `2)) ^2))) is V11() real ext-real Element of REAL
|[((O `1) * (sqrt (1 + (((O `1) / (O `2)) ^2)))),((O `2) * (sqrt (1 + (((O `1) / (O `2)) ^2))))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KXP is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KXP `2 is V11() real ext-real Element of REAL
KXP `1 is V11() real ext-real Element of REAL
- (O `2) is V11() real ext-real Element of REAL
(- (O `2)) * (sqrt (1 + (((O `1) / (O `2)) ^2))) is V11() real ext-real Element of REAL
- (KXP `2) is V11() real ext-real Element of REAL
Sq_Circ . KXP is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(KXP `1) / (KXP `2) is V11() real ext-real Element of REAL
((KXP `1) / (KXP `2)) ^2 is V11() real ext-real Element of REAL
K37(((KXP `1) / (KXP `2)),((KXP `1) / (KXP `2))) is V11() real ext-real set
1 + (((KXP `1) / (KXP `2)) ^2) is V11() real ext-real Element of REAL
sqrt (1 + (((KXP `1) / (KXP `2)) ^2)) is V11() real ext-real Element of REAL
(KXP `1) / (sqrt (1 + (((KXP `1) / (KXP `2)) ^2))) is V11() real ext-real Element of REAL
(KXP `2) / (sqrt (1 + (((KXP `1) / (KXP `2)) ^2))) is V11() real ext-real Element of REAL
|[((KXP `1) / (sqrt (1 + (((KXP `1) / (KXP `2)) ^2)))),((KXP `2) / (sqrt (1 + (((KXP `1) / (KXP `2)) ^2))))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| ^2 is V11() real ext-real Element of REAL
K37(|.O.|,|.O.|) is V11() real ext-real non negative set
|[((KXP `1) / (sqrt (1 + (((KXP `1) / (KXP `2)) ^2)))),((KXP `2) / (sqrt (1 + (((KXP `1) / (KXP `2)) ^2))))]| `1 is V11() real ext-real Element of REAL
(KXP `1) ^2 is V11() real ext-real Element of REAL
K37((KXP `1),(KXP `1)) is V11() real ext-real set
(KXP `2) ^2 is V11() real ext-real Element of REAL
K37((KXP `2),(KXP `2)) is V11() real ext-real set
|[((KXP `1) / (sqrt (1 + (((KXP `1) / (KXP `2)) ^2)))),((KXP `2) / (sqrt (1 + (((KXP `1) / (KXP `2)) ^2))))]| `2 is V11() real ext-real Element of REAL
((KXP `2) / (sqrt (1 + (((KXP `1) / (KXP `2)) ^2)))) ^2 is V11() real ext-real Element of REAL
K37(((KXP `2) / (sqrt (1 + (((KXP `1) / (KXP `2)) ^2)))),((KXP `2) / (sqrt (1 + (((KXP `1) / (KXP `2)) ^2))))) is V11() real ext-real set
((KXP `1) / (sqrt (1 + (((KXP `1) / (KXP `2)) ^2)))) ^2 is V11() real ext-real Element of REAL
K37(((KXP `1) / (sqrt (1 + (((KXP `1) / (KXP `2)) ^2)))),((KXP `1) / (sqrt (1 + (((KXP `1) / (KXP `2)) ^2))))) is V11() real ext-real set
(((KXP `2) / (sqrt (1 + (((KXP `1) / (KXP `2)) ^2)))) ^2) + (((KXP `1) / (sqrt (1 + (((KXP `1) / (KXP `2)) ^2)))) ^2) is V11() real ext-real Element of REAL
(sqrt (1 + (((KXP `1) / (KXP `2)) ^2))) ^2 is V11() real ext-real Element of REAL
K37((sqrt (1 + (((KXP `1) / (KXP `2)) ^2))),(sqrt (1 + (((KXP `1) / (KXP `2)) ^2)))) is V11() real ext-real set
((KXP `2) ^2) / ((sqrt (1 + (((KXP `1) / (KXP `2)) ^2))) ^2) is V11() real ext-real Element of REAL
(((KXP `2) ^2) / ((sqrt (1 + (((KXP `1) / (KXP `2)) ^2))) ^2)) + (((KXP `1) / (sqrt (1 + (((KXP `1) / (KXP `2)) ^2)))) ^2) is V11() real ext-real Element of REAL
((KXP `1) ^2) / ((sqrt (1 + (((KXP `1) / (KXP `2)) ^2))) ^2) is V11() real ext-real Element of REAL
(((KXP `2) ^2) / ((sqrt (1 + (((KXP `1) / (KXP `2)) ^2))) ^2)) + (((KXP `1) ^2) / ((sqrt (1 + (((KXP `1) / (KXP `2)) ^2))) ^2)) is V11() real ext-real Element of REAL
((KXP `2) ^2) / (1 + (((KXP `1) / (KXP `2)) ^2)) is V11() real ext-real Element of REAL
(((KXP `2) ^2) / (1 + (((KXP `1) / (KXP `2)) ^2))) + (((KXP `1) ^2) / ((sqrt (1 + (((KXP `1) / (KXP `2)) ^2))) ^2)) is V11() real ext-real Element of REAL
((KXP `1) ^2) / (1 + (((KXP `1) / (KXP `2)) ^2)) is V11() real ext-real Element of REAL
(((KXP `2) ^2) / (1 + (((KXP `1) / (KXP `2)) ^2))) + (((KXP `1) ^2) / (1 + (((KXP `1) / (KXP `2)) ^2))) is V11() real ext-real Element of REAL
((KXP `2) ^2) + ((KXP `1) ^2) is V11() real ext-real Element of REAL
(((KXP `2) ^2) + ((KXP `1) ^2)) / (1 + (((KXP `1) / (KXP `2)) ^2)) is V11() real ext-real Element of REAL
1 * (1 + (((KXP `1) / (KXP `2)) ^2)) is V11() real ext-real Element of REAL
((((KXP `2) ^2) + ((KXP `1) ^2)) / (1 + (((KXP `1) / (KXP `2)) ^2))) * (1 + (((KXP `1) / (KXP `2)) ^2)) is V11() real ext-real Element of REAL
((KXP `1) ^2) / ((KXP `2) ^2) is V11() real ext-real Element of REAL
1 + (((KXP `1) ^2) / ((KXP `2) ^2)) is V11() real ext-real Element of REAL
(1 + (((KXP `1) ^2) / ((KXP `2) ^2))) - 1 is V11() real ext-real Element of REAL
(((KXP `2) ^2) + ((KXP `1) ^2)) - 1 is V11() real ext-real Element of REAL
(((KXP `1) ^2) / ((KXP `2) ^2)) * ((KXP `2) ^2) is V11() real ext-real Element of REAL
((((KXP `2) ^2) + ((KXP `1) ^2)) - 1) * ((KXP `2) ^2) is V11() real ext-real Element of REAL
((KXP `1) ^2) - 1 is V11() real ext-real Element of REAL
((KXP `2) ^2) + (((KXP `1) ^2) - 1) is V11() real ext-real Element of REAL
(((KXP `2) ^2) + (((KXP `1) ^2) - 1)) * ((KXP `2) ^2) is V11() real ext-real Element of REAL
((KXP `1) ^2) - ((KXP `1) ^2) is V11() real ext-real Element of REAL
((KXP `2) ^2) * ((KXP `2) ^2) is V11() real ext-real Element of REAL
((KXP `2) ^2) * (((KXP `1) ^2) - 1) is V11() real ext-real Element of REAL
(((KXP `2) ^2) * ((KXP `2) ^2)) + (((KXP `2) ^2) * (((KXP `1) ^2) - 1)) is V11() real ext-real Element of REAL
((((KXP `2) ^2) * ((KXP `2) ^2)) + (((KXP `2) ^2) * (((KXP `1) ^2) - 1))) - ((KXP `1) ^2) is V11() real ext-real Element of REAL
((KXP `2) ^2) - 1 is V11() real ext-real Element of REAL
(((KXP `2) ^2) - 1) * (((KXP `2) ^2) + ((KXP `1) ^2)) is V11() real ext-real Element of REAL
(KXP `2) - 1 is V11() real ext-real Element of REAL
(KXP `2) + 1 is V11() real ext-real Element of REAL
((KXP `2) - 1) * ((KXP `2) + 1) is V11() real ext-real Element of REAL
O `2 is V11() real ext-real Element of REAL
O `1 is V11() real ext-real Element of REAL
- (O `1) is V11() real ext-real Element of REAL
O `2 is V11() real ext-real Element of REAL
O `1 is V11() real ext-real Element of REAL
- (O `1) is V11() real ext-real Element of REAL
(g2 . g) `2 is V11() real ext-real Element of REAL
(g2 . h) `2 is V11() real ext-real Element of REAL
(f2 . g) `1 is V11() real ext-real Element of REAL
(f2 . h) `1 is V11() real ext-real Element of REAL
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
I `1 is V11() real ext-real Element of REAL
I `2 is V11() real ext-real Element of REAL
(I `2) / (I `1) is V11() real ext-real Element of REAL
((I `2) / (I `1)) ^2 is V11() real ext-real Element of REAL
K37(((I `2) / (I `1)),((I `2) / (I `1))) is V11() real ext-real set
1 + (((I `2) / (I `1)) ^2) is V11() real ext-real Element of REAL
sqrt (1 + (((I `2) / (I `1)) ^2)) is V11() real ext-real Element of REAL
(I `1) / (sqrt (1 + (((I `2) / (I `1)) ^2))) is V11() real ext-real Element of REAL
(I `2) / (sqrt (1 + (((I `2) / (I `1)) ^2))) is V11() real ext-real Element of REAL
|[((I `1) / (sqrt (1 + (((I `2) / (I `1)) ^2)))),((I `2) / (sqrt (1 + (((I `2) / (I `1)) ^2))))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|[((I `1) / (sqrt (1 + (((I `2) / (I `1)) ^2)))),((I `2) / (sqrt (1 + (((I `2) / (I `1)) ^2))))]| `1 is V11() real ext-real Element of REAL
|[((I `1) / (sqrt (1 + (((I `2) / (I `1)) ^2)))),((I `2) / (sqrt (1 + (((I `2) / (I `1)) ^2))))]| `2 is V11() real ext-real Element of REAL
KXN is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.KXN.| is V11() real ext-real non negative Element of REAL
KXN `1 is V11() real ext-real Element of REAL
KXN `2 is V11() real ext-real Element of REAL
- (KXN `1) is V11() real ext-real Element of REAL
(Sq_Circ ") . (p1 . g) is set
Sq_Circ . I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(KXN `2) / (KXN `1) is V11() real ext-real Element of REAL
((KXN `2) / (KXN `1)) ^2 is V11() real ext-real Element of REAL
K37(((KXN `2) / (KXN `1)),((KXN `2) / (KXN `1))) is V11() real ext-real set
1 + (((KXN `2) / (KXN `1)) ^2) is V11() real ext-real Element of REAL
sqrt (1 + (((KXN `2) / (KXN `1)) ^2)) is V11() real ext-real Element of REAL
(Sq_Circ ") . KXN is set
(KXN `1) * (sqrt (1 + (((KXN `2) / (KXN `1)) ^2))) is V11() real ext-real Element of REAL
(KXN `2) * (sqrt (1 + (((KXN `2) / (KXN `1)) ^2))) is V11() real ext-real Element of REAL
|[((KXN `1) * (sqrt (1 + (((KXN `2) / (KXN `1)) ^2)))),((KXN `2) * (sqrt (1 + (((KXN `2) / (KXN `1)) ^2))))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(- (KXN `1)) * (sqrt (1 + (((KXN `2) / (KXN `1)) ^2))) is V11() real ext-real Element of REAL
- (I `1) is V11() real ext-real Element of REAL
|.KXN.| ^2 is V11() real ext-real Element of REAL
K37(|.KXN.|,|.KXN.|) is V11() real ext-real non negative set
((I `1) / (sqrt (1 + (((I `2) / (I `1)) ^2)))) ^2 is V11() real ext-real Element of REAL
K37(((I `1) / (sqrt (1 + (((I `2) / (I `1)) ^2)))),((I `1) / (sqrt (1 + (((I `2) / (I `1)) ^2))))) is V11() real ext-real set
((I `2) / (sqrt (1 + (((I `2) / (I `1)) ^2)))) ^2 is V11() real ext-real Element of REAL
K37(((I `2) / (sqrt (1 + (((I `2) / (I `1)) ^2)))),((I `2) / (sqrt (1 + (((I `2) / (I `1)) ^2))))) is V11() real ext-real set
(((I `1) / (sqrt (1 + (((I `2) / (I `1)) ^2)))) ^2) + (((I `2) / (sqrt (1 + (((I `2) / (I `1)) ^2)))) ^2) is V11() real ext-real Element of REAL
(I `1) ^2 is V11() real ext-real Element of REAL
K37((I `1),(I `1)) is V11() real ext-real set
(sqrt (1 + (((I `2) / (I `1)) ^2))) ^2 is V11() real ext-real Element of REAL
K37((sqrt (1 + (((I `2) / (I `1)) ^2))),(sqrt (1 + (((I `2) / (I `1)) ^2)))) is V11() real ext-real set
((I `1) ^2) / ((sqrt (1 + (((I `2) / (I `1)) ^2))) ^2) is V11() real ext-real Element of REAL
(((I `1) ^2) / ((sqrt (1 + (((I `2) / (I `1)) ^2))) ^2)) + (((I `2) / (sqrt (1 + (((I `2) / (I `1)) ^2)))) ^2) is V11() real ext-real Element of REAL
(I `2) ^2 is V11() real ext-real Element of REAL
K37((I `2),(I `2)) is V11() real ext-real set
((I `2) ^2) / ((sqrt (1 + (((I `2) / (I `1)) ^2))) ^2) is V11() real ext-real Element of REAL
(((I `1) ^2) / ((sqrt (1 + (((I `2) / (I `1)) ^2))) ^2)) + (((I `2) ^2) / ((sqrt (1 + (((I `2) / (I `1)) ^2))) ^2)) is V11() real ext-real Element of REAL
((I `1) ^2) / (1 + (((I `2) / (I `1)) ^2)) is V11() real ext-real Element of REAL
(((I `1) ^2) / (1 + (((I `2) / (I `1)) ^2))) + (((I `2) ^2) / ((sqrt (1 + (((I `2) / (I `1)) ^2))) ^2)) is V11() real ext-real Element of REAL
((I `2) ^2) / (1 + (((I `2) / (I `1)) ^2)) is V11() real ext-real Element of REAL
(((I `1) ^2) / (1 + (((I `2) / (I `1)) ^2))) + (((I `2) ^2) / (1 + (((I `2) / (I `1)) ^2))) is V11() real ext-real Element of REAL
((I `1) ^2) + ((I `2) ^2) is V11() real ext-real Element of REAL
(((I `1) ^2) + ((I `2) ^2)) / (1 + (((I `2) / (I `1)) ^2)) is V11() real ext-real Element of REAL
((((I `1) ^2) + ((I `2) ^2)) / (1 + (((I `2) / (I `1)) ^2))) * (1 + (((I `2) / (I `1)) ^2)) is V11() real ext-real Element of REAL
1 * (1 + (((I `2) / (I `1)) ^2)) is V11() real ext-real Element of REAL
(((I `1) ^2) + ((I `2) ^2)) - 1 is V11() real ext-real Element of REAL
((I `2) ^2) / ((I `1) ^2) is V11() real ext-real Element of REAL
((((I `1) ^2) + ((I `2) ^2)) - 1) * ((I `1) ^2) is V11() real ext-real Element of REAL
((I `1) ^2) - 1 is V11() real ext-real Element of REAL
(((I `1) ^2) - 1) * (((I `1) ^2) + ((I `2) ^2)) is V11() real ext-real Element of REAL
(I `1) - 1 is V11() real ext-real Element of REAL
(I `1) + 1 is V11() real ext-real Element of REAL
((I `1) - 1) * ((I `1) + 1) is V11() real ext-real Element of REAL
0 - 1 is non empty V11() real ext-real non positive negative Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
O `2 is V11() real ext-real Element of REAL
O `1 is V11() real ext-real Element of REAL
(O `2) / (O `1) is V11() real ext-real Element of REAL
((O `2) / (O `1)) ^2 is V11() real ext-real Element of REAL
K37(((O `2) / (O `1)),((O `2) / (O `1))) is V11() real ext-real set
1 + (((O `2) / (O `1)) ^2) is V11() real ext-real Element of REAL
sqrt (1 + (((O `2) / (O `1)) ^2)) is V11() real ext-real Element of REAL
(O `1) / (sqrt (1 + (((O `2) / (O `1)) ^2))) is V11() real ext-real Element of REAL
(O `2) / (sqrt (1 + (((O `2) / (O `1)) ^2))) is V11() real ext-real Element of REAL
|[((O `1) / (sqrt (1 + (((O `2) / (O `1)) ^2)))),((O `2) / (sqrt (1 + (((O `2) / (O `1)) ^2))))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|[((O `1) / (sqrt (1 + (((O `2) / (O `1)) ^2)))),((O `2) / (sqrt (1 + (((O `2) / (O `1)) ^2))))]| `1 is V11() real ext-real Element of REAL
|[((O `1) / (sqrt (1 + (((O `2) / (O `1)) ^2)))),((O `2) / (sqrt (1 + (((O `2) / (O `1)) ^2))))]| `2 is V11() real ext-real Element of REAL
h1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
h1 `1 is V11() real ext-real Element of REAL
h1 `2 is V11() real ext-real Element of REAL
(h1 `1) / (h1 `2) is V11() real ext-real Element of REAL
((h1 `1) / (h1 `2)) ^2 is V11() real ext-real Element of REAL
K37(((h1 `1) / (h1 `2)),((h1 `1) / (h1 `2))) is V11() real ext-real set
KYN is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.KYN.| is V11() real ext-real non negative Element of REAL
KYN `2 is V11() real ext-real Element of REAL
KYN `1 is V11() real ext-real Element of REAL
- (KYN `1) is V11() real ext-real Element of REAL
(Sq_Circ ") . (p1 . h) is set
Sq_Circ . O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(Sq_Circ ") . KYN is set
(KYN `2) / (KYN `1) is V11() real ext-real Element of REAL
((KYN `2) / (KYN `1)) ^2 is V11() real ext-real Element of REAL
K37(((KYN `2) / (KYN `1)),((KYN `2) / (KYN `1))) is V11() real ext-real set
1 + (((KYN `2) / (KYN `1)) ^2) is V11() real ext-real Element of REAL
sqrt (1 + (((KYN `2) / (KYN `1)) ^2)) is V11() real ext-real Element of REAL
(KYN `1) * (sqrt (1 + (((KYN `2) / (KYN `1)) ^2))) is V11() real ext-real Element of REAL
(KYN `2) * (sqrt (1 + (((KYN `2) / (KYN `1)) ^2))) is V11() real ext-real Element of REAL
|[((KYN `1) * (sqrt (1 + (((KYN `2) / (KYN `1)) ^2)))),((KYN `2) * (sqrt (1 + (((KYN `2) / (KYN `1)) ^2))))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(- (KYN `1)) * (sqrt (1 + (((KYN `2) / (KYN `1)) ^2))) is V11() real ext-real Element of REAL
- (O `1) is V11() real ext-real Element of REAL
|.KYN.| ^2 is V11() real ext-real Element of REAL
K37(|.KYN.|,|.KYN.|) is V11() real ext-real non negative set
((O `1) / (sqrt (1 + (((O `2) / (O `1)) ^2)))) ^2 is V11() real ext-real Element of REAL
K37(((O `1) / (sqrt (1 + (((O `2) / (O `1)) ^2)))),((O `1) / (sqrt (1 + (((O `2) / (O `1)) ^2))))) is V11() real ext-real set
((O `2) / (sqrt (1 + (((O `2) / (O `1)) ^2)))) ^2 is V11() real ext-real Element of REAL
K37(((O `2) / (sqrt (1 + (((O `2) / (O `1)) ^2)))),((O `2) / (sqrt (1 + (((O `2) / (O `1)) ^2))))) is V11() real ext-real set
(((O `1) / (sqrt (1 + (((O `2) / (O `1)) ^2)))) ^2) + (((O `2) / (sqrt (1 + (((O `2) / (O `1)) ^2)))) ^2) is V11() real ext-real Element of REAL
(O `1) ^2 is V11() real ext-real Element of REAL
K37((O `1),(O `1)) is V11() real ext-real set
(sqrt (1 + (((O `2) / (O `1)) ^2))) ^2 is V11() real ext-real Element of REAL
K37((sqrt (1 + (((O `2) / (O `1)) ^2))),(sqrt (1 + (((O `2) / (O `1)) ^2)))) is V11() real ext-real set
((O `1) ^2) / ((sqrt (1 + (((O `2) / (O `1)) ^2))) ^2) is V11() real ext-real Element of REAL
(((O `1) ^2) / ((sqrt (1 + (((O `2) / (O `1)) ^2))) ^2)) + (((O `2) / (sqrt (1 + (((O `2) / (O `1)) ^2)))) ^2) is V11() real ext-real Element of REAL
(O `2) ^2 is V11() real ext-real Element of REAL
K37((O `2),(O `2)) is V11() real ext-real set
((O `2) ^2) / ((sqrt (1 + (((O `2) / (O `1)) ^2))) ^2) is V11() real ext-real Element of REAL
(((O `1) ^2) / ((sqrt (1 + (((O `2) / (O `1)) ^2))) ^2)) + (((O `2) ^2) / ((sqrt (1 + (((O `2) / (O `1)) ^2))) ^2)) is V11() real ext-real Element of REAL
((O `1) ^2) / (1 + (((O `2) / (O `1)) ^2)) is V11() real ext-real Element of REAL
(((O `1) ^2) / (1 + (((O `2) / (O `1)) ^2))) + (((O `2) ^2) / ((sqrt (1 + (((O `2) / (O `1)) ^2))) ^2)) is V11() real ext-real Element of REAL
((O `2) ^2) / (1 + (((O `2) / (O `1)) ^2)) is V11() real ext-real Element of REAL
(((O `1) ^2) / (1 + (((O `2) / (O `1)) ^2))) + (((O `2) ^2) / (1 + (((O `2) / (O `1)) ^2))) is V11() real ext-real Element of REAL
((O `1) ^2) + ((O `2) ^2) is V11() real ext-real Element of REAL
(((O `1) ^2) + ((O `2) ^2)) / (1 + (((O `2) / (O `1)) ^2)) is V11() real ext-real Element of REAL
((((O `1) ^2) + ((O `2) ^2)) / (1 + (((O `2) / (O `1)) ^2))) * (1 + (((O `2) / (O `1)) ^2)) is V11() real ext-real Element of REAL
1 * (1 + (((O `2) / (O `1)) ^2)) is V11() real ext-real Element of REAL
(((O `1) ^2) + ((O `2) ^2)) - 1 is V11() real ext-real Element of REAL
((O `2) ^2) / ((O `1) ^2) is V11() real ext-real Element of REAL
((((O `1) ^2) + ((O `2) ^2)) - 1) * ((O `1) ^2) is V11() real ext-real Element of REAL
((O `1) ^2) - 1 is V11() real ext-real Element of REAL
(((O `1) ^2) - 1) * (((O `1) ^2) + ((O `2) ^2)) is V11() real ext-real Element of REAL
(O `1) - 1 is V11() real ext-real Element of REAL
(O `1) + 1 is V11() real ext-real Element of REAL
((O `1) - 1) * ((O `1) + 1) is V11() real ext-real Element of REAL
1 + (((h1 `1) / (h1 `2)) ^2) is V11() real ext-real Element of REAL
sqrt (1 + (((h1 `1) / (h1 `2)) ^2)) is V11() real ext-real Element of REAL
(h1 `1) / (sqrt (1 + (((h1 `1) / (h1 `2)) ^2))) is V11() real ext-real Element of REAL
(h1 `2) / (sqrt (1 + (((h1 `1) / (h1 `2)) ^2))) is V11() real ext-real Element of REAL
|[((h1 `1) / (sqrt (1 + (((h1 `1) / (h1 `2)) ^2)))),((h1 `2) / (sqrt (1 + (((h1 `1) / (h1 `2)) ^2))))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|[((h1 `1) / (sqrt (1 + (((h1 `1) / (h1 `2)) ^2)))),((h1 `2) / (sqrt (1 + (((h1 `1) / (h1 `2)) ^2))))]| `2 is V11() real ext-real Element of REAL
|[((h1 `1) / (sqrt (1 + (((h1 `1) / (h1 `2)) ^2)))),((h1 `2) / (sqrt (1 + (((h1 `1) / (h1 `2)) ^2))))]| `1 is V11() real ext-real Element of REAL
x2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.x2.| is V11() real ext-real non negative Element of REAL
x2 `2 is V11() real ext-real Element of REAL
x2 `1 is V11() real ext-real Element of REAL
- (x2 `1) is V11() real ext-real Element of REAL
(Sq_Circ ") . (p2 . g) is set
Sq_Circ . h1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
- (- (x2 `1)) is V11() real ext-real Element of REAL
- (x2 `2) is V11() real ext-real Element of REAL
(Sq_Circ ") . x2 is set
(x2 `1) / (x2 `2) is V11() real ext-real Element of REAL
((x2 `1) / (x2 `2)) ^2 is V11() real ext-real Element of REAL
K37(((x2 `1) / (x2 `2)),((x2 `1) / (x2 `2))) is V11() real ext-real set
1 + (((x2 `1) / (x2 `2)) ^2) is V11() real ext-real Element of REAL
sqrt (1 + (((x2 `1) / (x2 `2)) ^2)) is V11() real ext-real Element of REAL
(x2 `1) * (sqrt (1 + (((x2 `1) / (x2 `2)) ^2))) is V11() real ext-real Element of REAL
(x2 `2) * (sqrt (1 + (((x2 `1) / (x2 `2)) ^2))) is V11() real ext-real Element of REAL
|[((x2 `1) * (sqrt (1 + (((x2 `1) / (x2 `2)) ^2)))),((x2 `2) * (sqrt (1 + (((x2 `1) / (x2 `2)) ^2))))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(- (x2 `2)) * (sqrt (1 + (((x2 `1) / (x2 `2)) ^2))) is V11() real ext-real Element of REAL
- (h1 `2) is V11() real ext-real Element of REAL
|.x2.| ^2 is V11() real ext-real Element of REAL
K37(|.x2.|,|.x2.|) is V11() real ext-real non negative set
((h1 `2) / (sqrt (1 + (((h1 `1) / (h1 `2)) ^2)))) ^2 is V11() real ext-real Element of REAL
K37(((h1 `2) / (sqrt (1 + (((h1 `1) / (h1 `2)) ^2)))),((h1 `2) / (sqrt (1 + (((h1 `1) / (h1 `2)) ^2))))) is V11() real ext-real set
((h1 `1) / (sqrt (1 + (((h1 `1) / (h1 `2)) ^2)))) ^2 is V11() real ext-real Element of REAL
K37(((h1 `1) / (sqrt (1 + (((h1 `1) / (h1 `2)) ^2)))),((h1 `1) / (sqrt (1 + (((h1 `1) / (h1 `2)) ^2))))) is V11() real ext-real set
(((h1 `2) / (sqrt (1 + (((h1 `1) / (h1 `2)) ^2)))) ^2) + (((h1 `1) / (sqrt (1 + (((h1 `1) / (h1 `2)) ^2)))) ^2) is V11() real ext-real Element of REAL
(h1 `2) ^2 is V11() real ext-real Element of REAL
K37((h1 `2),(h1 `2)) is V11() real ext-real set
(sqrt (1 + (((h1 `1) / (h1 `2)) ^2))) ^2 is V11() real ext-real Element of REAL
K37((sqrt (1 + (((h1 `1) / (h1 `2)) ^2))),(sqrt (1 + (((h1 `1) / (h1 `2)) ^2)))) is V11() real ext-real set
((h1 `2) ^2) / ((sqrt (1 + (((h1 `1) / (h1 `2)) ^2))) ^2) is V11() real ext-real Element of REAL
(((h1 `2) ^2) / ((sqrt (1 + (((h1 `1) / (h1 `2)) ^2))) ^2)) + (((h1 `1) / (sqrt (1 + (((h1 `1) / (h1 `2)) ^2)))) ^2) is V11() real ext-real Element of REAL
(h1 `1) ^2 is V11() real ext-real Element of REAL
K37((h1 `1),(h1 `1)) is V11() real ext-real set
((h1 `1) ^2) / ((sqrt (1 + (((h1 `1) / (h1 `2)) ^2))) ^2) is V11() real ext-real Element of REAL
(((h1 `2) ^2) / ((sqrt (1 + (((h1 `1) / (h1 `2)) ^2))) ^2)) + (((h1 `1) ^2) / ((sqrt (1 + (((h1 `1) / (h1 `2)) ^2))) ^2)) is V11() real ext-real Element of REAL
((h1 `2) ^2) / (1 + (((h1 `1) / (h1 `2)) ^2)) is V11() real ext-real Element of REAL
(((h1 `2) ^2) / (1 + (((h1 `1) / (h1 `2)) ^2))) + (((h1 `1) ^2) / ((sqrt (1 + (((h1 `1) / (h1 `2)) ^2))) ^2)) is V11() real ext-real Element of REAL
((h1 `1) ^2) / (1 + (((h1 `1) / (h1 `2)) ^2)) is V11() real ext-real Element of REAL
(((h1 `2) ^2) / (1 + (((h1 `1) / (h1 `2)) ^2))) + (((h1 `1) ^2) / (1 + (((h1 `1) / (h1 `2)) ^2))) is V11() real ext-real Element of REAL
((h1 `2) ^2) + ((h1 `1) ^2) is V11() real ext-real Element of REAL
(((h1 `2) ^2) + ((h1 `1) ^2)) / (1 + (((h1 `1) / (h1 `2)) ^2)) is V11() real ext-real Element of REAL
((((h1 `2) ^2) + ((h1 `1) ^2)) / (1 + (((h1 `1) / (h1 `2)) ^2))) * (1 + (((h1 `1) / (h1 `2)) ^2)) is V11() real ext-real Element of REAL
1 * (1 + (((h1 `1) / (h1 `2)) ^2)) is V11() real ext-real Element of REAL
(((h1 `2) ^2) + ((h1 `1) ^2)) - 1 is V11() real ext-real Element of REAL
((h1 `1) ^2) / ((h1 `2) ^2) is V11() real ext-real Element of REAL
((((h1 `2) ^2) + ((h1 `1) ^2)) - 1) * ((h1 `2) ^2) is V11() real ext-real Element of REAL
((h1 `2) ^2) - 1 is V11() real ext-real Element of REAL
(((h1 `2) ^2) - 1) * (((h1 `2) ^2) + ((h1 `1) ^2)) is V11() real ext-real Element of REAL
(h1 `2) - 1 is V11() real ext-real Element of REAL
(h1 `2) + 1 is V11() real ext-real Element of REAL
((h1 `2) - 1) * ((h1 `2) + 1) is V11() real ext-real Element of REAL
KYP is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KYP `1 is V11() real ext-real Element of REAL
KYP `2 is V11() real ext-real Element of REAL
(KYP `1) / (KYP `2) is V11() real ext-real Element of REAL
((KYP `1) / (KYP `2)) ^2 is V11() real ext-real Element of REAL
K37(((KYP `1) / (KYP `2)),((KYP `1) / (KYP `2))) is V11() real ext-real set
1 + (((KYP `1) / (KYP `2)) ^2) is V11() real ext-real Element of REAL
sqrt (1 + (((KYP `1) / (KYP `2)) ^2)) is V11() real ext-real Element of REAL
(KYP `1) / (sqrt (1 + (((KYP `1) / (KYP `2)) ^2))) is V11() real ext-real Element of REAL
(KYP `2) / (sqrt (1 + (((KYP `1) / (KYP `2)) ^2))) is V11() real ext-real Element of REAL
|[((KYP `1) / (sqrt (1 + (((KYP `1) / (KYP `2)) ^2)))),((KYP `2) / (sqrt (1 + (((KYP `1) / (KYP `2)) ^2))))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|[((KYP `1) / (sqrt (1 + (((KYP `1) / (KYP `2)) ^2)))),((KYP `2) / (sqrt (1 + (((KYP `1) / (KYP `2)) ^2))))]| `2 is V11() real ext-real Element of REAL
|[((KYP `1) / (sqrt (1 + (((KYP `1) / (KYP `2)) ^2)))),((KYP `2) / (sqrt (1 + (((KYP `1) / (KYP `2)) ^2))))]| `1 is V11() real ext-real Element of REAL
z3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.z3.| is V11() real ext-real non negative Element of REAL
z3 `1 is V11() real ext-real Element of REAL
z3 `2 is V11() real ext-real Element of REAL
- (z3 `1) is V11() real ext-real Element of REAL
- (z3 `2) is V11() real ext-real Element of REAL
- (- (z3 `1)) is V11() real ext-real Element of REAL
(Sq_Circ ") . (p2 . h) is set
Sq_Circ . KYP is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(Sq_Circ ") . z3 is set
(z3 `1) / (z3 `2) is V11() real ext-real Element of REAL
((z3 `1) / (z3 `2)) ^2 is V11() real ext-real Element of REAL
K37(((z3 `1) / (z3 `2)),((z3 `1) / (z3 `2))) is V11() real ext-real set
1 + (((z3 `1) / (z3 `2)) ^2) is V11() real ext-real Element of REAL
sqrt (1 + (((z3 `1) / (z3 `2)) ^2)) is V11() real ext-real Element of REAL
(z3 `1) * (sqrt (1 + (((z3 `1) / (z3 `2)) ^2))) is V11() real ext-real Element of REAL
(z3 `2) * (sqrt (1 + (((z3 `1) / (z3 `2)) ^2))) is V11() real ext-real Element of REAL
|[((z3 `1) * (sqrt (1 + (((z3 `1) / (z3 `2)) ^2)))),((z3 `2) * (sqrt (1 + (((z3 `1) / (z3 `2)) ^2))))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(- (z3 `2)) * (sqrt (1 + (((z3 `1) / (z3 `2)) ^2))) is V11() real ext-real Element of REAL
- (KYP `2) is V11() real ext-real Element of REAL
|.z3.| ^2 is V11() real ext-real Element of REAL
K37(|.z3.|,|.z3.|) is V11() real ext-real non negative set
((KYP `2) / (sqrt (1 + (((KYP `1) / (KYP `2)) ^2)))) ^2 is V11() real ext-real Element of REAL
K37(((KYP `2) / (sqrt (1 + (((KYP `1) / (KYP `2)) ^2)))),((KYP `2) / (sqrt (1 + (((KYP `1) / (KYP `2)) ^2))))) is V11() real ext-real set
((KYP `1) / (sqrt (1 + (((KYP `1) / (KYP `2)) ^2)))) ^2 is V11() real ext-real Element of REAL
K37(((KYP `1) / (sqrt (1 + (((KYP `1) / (KYP `2)) ^2)))),((KYP `1) / (sqrt (1 + (((KYP `1) / (KYP `2)) ^2))))) is V11() real ext-real set
(((KYP `2) / (sqrt (1 + (((KYP `1) / (KYP `2)) ^2)))) ^2) + (((KYP `1) / (sqrt (1 + (((KYP `1) / (KYP `2)) ^2)))) ^2) is V11() real ext-real Element of REAL
(KYP `2) ^2 is V11() real ext-real Element of REAL
K37((KYP `2),(KYP `2)) is V11() real ext-real set
(sqrt (1 + (((KYP `1) / (KYP `2)) ^2))) ^2 is V11() real ext-real Element of REAL
K37((sqrt (1 + (((KYP `1) / (KYP `2)) ^2))),(sqrt (1 + (((KYP `1) / (KYP `2)) ^2)))) is V11() real ext-real set
((KYP `2) ^2) / ((sqrt (1 + (((KYP `1) / (KYP `2)) ^2))) ^2) is V11() real ext-real Element of REAL
(((KYP `2) ^2) / ((sqrt (1 + (((KYP `1) / (KYP `2)) ^2))) ^2)) + (((KYP `1) / (sqrt (1 + (((KYP `1) / (KYP `2)) ^2)))) ^2) is V11() real ext-real Element of REAL
(KYP `1) ^2 is V11() real ext-real Element of REAL
K37((KYP `1),(KYP `1)) is V11() real ext-real set
((KYP `1) ^2) / ((sqrt (1 + (((KYP `1) / (KYP `2)) ^2))) ^2) is V11() real ext-real Element of REAL
(((KYP `2) ^2) / ((sqrt (1 + (((KYP `1) / (KYP `2)) ^2))) ^2)) + (((KYP `1) ^2) / ((sqrt (1 + (((KYP `1) / (KYP `2)) ^2))) ^2)) is V11() real ext-real Element of REAL
((KYP `2) ^2) / (1 + (((KYP `1) / (KYP `2)) ^2)) is V11() real ext-real Element of REAL
(((KYP `2) ^2) / (1 + (((KYP `1) / (KYP `2)) ^2))) + (((KYP `1) ^2) / ((sqrt (1 + (((KYP `1) / (KYP `2)) ^2))) ^2)) is V11() real ext-real Element of REAL
((KYP `1) ^2) / (1 + (((KYP `1) / (KYP `2)) ^2)) is V11() real ext-real Element of REAL
(((KYP `2) ^2) / (1 + (((KYP `1) / (KYP `2)) ^2))) + (((KYP `1) ^2) / (1 + (((KYP `1) / (KYP `2)) ^2))) is V11() real ext-real Element of REAL
((KYP `2) ^2) + ((KYP `1) ^2) is V11() real ext-real Element of REAL
(((KYP `2) ^2) + ((KYP `1) ^2)) / (1 + (((KYP `1) / (KYP `2)) ^2)) is V11() real ext-real Element of REAL
((((KYP `2) ^2) + ((KYP `1) ^2)) / (1 + (((KYP `1) / (KYP `2)) ^2))) * (1 + (((KYP `1) / (KYP `2)) ^2)) is V11() real ext-real Element of REAL
1 * (1 + (((KYP `1) / (KYP `2)) ^2)) is V11() real ext-real Element of REAL
(((KYP `2) ^2) + ((KYP `1) ^2)) - 1 is V11() real ext-real Element of REAL
((KYP `1) ^2) / ((KYP `2) ^2) is V11() real ext-real Element of REAL
((((KYP `2) ^2) + ((KYP `1) ^2)) - 1) * ((KYP `2) ^2) is V11() real ext-real Element of REAL
((KYP `2) ^2) - 1 is V11() real ext-real Element of REAL
(((KYP `2) ^2) - 1) * (((KYP `2) ^2) + ((KYP `1) ^2)) is V11() real ext-real Element of REAL
(KYP `2) - 1 is V11() real ext-real Element of REAL
(KYP `2) + 1 is V11() real ext-real Element of REAL
((KYP `2) - 1) * ((KYP `2) + 1) is V11() real ext-real Element of REAL
rng g2 is functional Element of K6( the carrier of (TOP-REAL 2))
rng f2 is functional Element of K6( the carrier of (TOP-REAL 2))
h1 is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
h1 is set
O is set
g2 . O is Relation-like Function-like set
I is set
f2 . I is Relation-like Function-like set
dom (Sq_Circ ") is set
p2 . I is Relation-like Function-like set
(Sq_Circ ") . (p2 . I) is set
p1 . O is Relation-like Function-like set
(Sq_Circ ") . (p1 . O) is set
p1 is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p2 is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng p1 is functional Element of K6( the carrier of (TOP-REAL 2))
rng p2 is functional Element of K6( the carrier of (TOP-REAL 2))
p3 is functional Element of K6( the carrier of (TOP-REAL 2))
p4 is functional Element of K6( the carrier of (TOP-REAL 2))
P is functional Element of K6( the carrier of (TOP-REAL 2))
C0 is functional Element of K6( the carrier of (TOP-REAL 2))
f is functional Element of K6( the carrier of (TOP-REAL 2))
g is V11() real ext-real Element of the carrier of I[01]
h is V11() real ext-real Element of the carrier of I[01]
p1 . g is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p1 . h is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 . g is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 . h is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 . 1 is Relation-like Function-like set
p2 . 0 is Relation-like Function-like set
f2 is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 . 0 is Relation-like Function-like set
f2 . 1 is Relation-like Function-like set
rng f2 is functional Element of K6( the carrier of (TOP-REAL 2))
|[(- 1),0]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|[1,0]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|[0,1]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|[0,(- 1)]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p4 is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p3 . 0 is Relation-like Function-like set
p3 . 1 is Relation-like Function-like set
p4 . 1 is Relation-like Function-like set
p4 . 0 is Relation-like Function-like set
rng p3 is functional Element of K6( the carrier of (TOP-REAL 2))
rng p4 is functional Element of K6( the carrier of (TOP-REAL 2))
P is functional Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : S1[b1] } is set
|[0,1]| `1 is V11() real ext-real Element of REAL
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : S2[b1] } is set
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : S3[b1] } is set
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : S4[b1] } is set
|[0,(- 1)]| `1 is V11() real ext-real Element of REAL
|[0,(- 1)]| `2 is V11() real ext-real Element of REAL
|.|[0,(- 1)]|.| is V11() real ext-real non negative Element of REAL
0 ^2 is V11() real ext-real Element of REAL
K37(0,0) is empty V11() real ext-real non positive non negative Function-like functional V142() V143() V144() V145() V146() V147() V148() V201() V204() set
(- 1) ^2 is V11() real ext-real Element of REAL
K37((- 1),(- 1)) is V11() real ext-real non negative set
(0 ^2) + ((- 1) ^2) is V11() real ext-real Element of REAL
sqrt ((0 ^2) + ((- 1) ^2)) is V11() real ext-real Element of REAL
- (|[0,(- 1)]| `1) is V11() real ext-real Element of REAL
p2 is V11() real ext-real Element of the carrier of I[01]
p4 . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
h is functional Element of K6( the carrier of (TOP-REAL 2))
|[(- 1),0]| `1 is V11() real ext-real Element of REAL
|[(- 1),0]| `2 is V11() real ext-real Element of REAL
- (|[(- 1),0]| `1) is V11() real ext-real Element of REAL
|[0,1]| `2 is V11() real ext-real Element of REAL
|.|[0,1]|.| is V11() real ext-real non negative Element of REAL
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
(0 ^2) + (1 ^2) is V11() real ext-real Element of REAL
sqrt ((0 ^2) + (1 ^2)) is V11() real ext-real Element of REAL
- (|[0,1]| `1) is V11() real ext-real Element of REAL
p1 is V11() real ext-real Element of the carrier of I[01]
p4 . p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g is functional Element of K6( the carrier of (TOP-REAL 2))
|[1,0]| `1 is V11() real ext-real Element of REAL
|[1,0]| `2 is V11() real ext-real Element of REAL
|.|[1,0]|.| is V11() real ext-real non negative Element of REAL
(1 ^2) + (0 ^2) is V11() real ext-real Element of REAL
sqrt ((1 ^2) + (0 ^2)) is V11() real ext-real Element of REAL
p3 . p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
C0 is functional Element of K6( the carrier of (TOP-REAL 2))
|.|[(- 1),0]|.| is V11() real ext-real non negative Element of REAL
((- 1) ^2) + (0 ^2) is V11() real ext-real Element of REAL
sqrt (((- 1) ^2) + (0 ^2)) is V11() real ext-real Element of REAL
p3 . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
f is functional Element of K6( the carrier of (TOP-REAL 2))
p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.p1.| is V11() real ext-real non negative Element of REAL
p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.p2.| is V11() real ext-real non negative Element of REAL
p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.p3.| is V11() real ext-real non negative Element of REAL
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.p4.| is V11() real ext-real non negative Element of REAL
P is functional Element of K6( the carrier of (TOP-REAL 2))
C0 is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
C0 .: P is functional Element of K6( the carrier of (TOP-REAL 2))
C0 . p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
C0 . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
C0 . p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
C0 . p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
C0 is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
C0 .: P is functional Element of K6( the carrier of (TOP-REAL 2))
C0 . p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
C0 . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
C0 . p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
C0 . p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
f is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f . 0 is Relation-like Function-like set
f . 1 is Relation-like Function-like set
g . 0 is Relation-like Function-like set
g . 1 is Relation-like Function-like set
rng f is functional Element of K6( the carrier of (TOP-REAL 2))
rng g is functional Element of K6( the carrier of (TOP-REAL 2))
C0 * f is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
h is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
dom h is V142() V143() V144() Element of K6( the carrier of I[01])
h . 0 is Relation-like Function-like set
C0 * g is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
dom f2 is V142() V143() V144() Element of K6( the carrier of I[01])
f2 . 0 is Relation-like Function-like set
f2 . 1 is Relation-like Function-like set
rng h is functional Element of K6( the carrier of (TOP-REAL 2))
g2 is set
dom C0 is functional Element of K6( the carrier of (TOP-REAL 2))
h1 is set
h . h1 is Relation-like Function-like set
dom f is V142() V143() V144() Element of K6( the carrier of I[01])
f . h1 is Relation-like Function-like set
C0 . (f . h1) is Relation-like Function-like set
rng f2 is functional Element of K6( the carrier of (TOP-REAL 2))
g2 is set
dom C0 is functional Element of K6( the carrier of (TOP-REAL 2))
h1 is set
f2 . h1 is Relation-like Function-like set
dom g is V142() V143() V144() Element of K6( the carrier of I[01])
g . h1 is Relation-like Function-like set
C0 . (g . h1) is Relation-like Function-like set
h . 1 is Relation-like Function-like set
g2 is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
g2 .: P is functional Element of K6( the carrier of (TOP-REAL 2))
g2 . p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g2 . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g2 . p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g2 . p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g2 is set
h1 is set
h . h1 is Relation-like Function-like set
dom f is V142() V143() V144() Element of K6( the carrier of I[01])
f . h1 is Relation-like Function-like set
O is set
f2 . O is Relation-like Function-like set
g . O is Relation-like Function-like set
C0 . (g . O) is Relation-like Function-like set
dom C0 is functional Element of K6( the carrier of (TOP-REAL 2))
dom g is V142() V143() V144() Element of K6( the carrier of I[01])
C0 . (f . h1) is Relation-like Function-like set
p1 is V11() real ext-real Element of REAL
p1 -FanMorphN is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
(p1 -FanMorphN) . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
|.p2.| is V11() real ext-real non negative Element of REAL
(p2 `1) / |.p2.| is V11() real ext-real Element of REAL
p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
|.p2.| is V11() real ext-real non negative Element of REAL
(p2 `1) / |.p2.| is V11() real ext-real Element of REAL
p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
|.p2.| is V11() real ext-real non negative Element of REAL
(p2 `1) / |.p2.| is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
|.p2.| is V11() real ext-real non negative Element of REAL
(p2 `1) / |.p2.| is V11() real ext-real Element of REAL
p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p1 is V11() real ext-real Element of REAL
p1 -FanMorphN is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
(p1 -FanMorphN) . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p1 is V11() real ext-real Element of REAL
p1 -FanMorphN is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
|.p2.| is V11() real ext-real non negative Element of REAL
(p2 `1) / |.p2.| is V11() real ext-real Element of REAL
(p1 -FanMorphN) . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
|.p2.| ^2 is V11() real ext-real Element of REAL
K37(|.p2.|,|.p2.|) is V11() real ext-real non negative set
(p2 `1) ^2 is V11() real ext-real Element of REAL
K37((p2 `1),(p2 `1)) is V11() real ext-real set
0 ^2 is V11() real ext-real Element of REAL
K37(0,0) is empty V11() real ext-real non positive non negative Function-like functional V142() V143() V144() V145() V146() V147() V148() V201() V204() set
((p2 `1) ^2) + (0 ^2) is V11() real ext-real Element of REAL
- (p2 `1) is V11() real ext-real Element of REAL
p1 is V11() real ext-real Element of REAL
p1 -FanMorphN is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
|.p2.| is V11() real ext-real non negative Element of REAL
|.p3.| is V11() real ext-real non negative Element of REAL
p3 `1 is V11() real ext-real Element of REAL
(p3 `1) / |.p3.| is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
(p2 `1) / |.p2.| is V11() real ext-real Element of REAL
(p1 -FanMorphN) . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(p1 -FanMorphN) . p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P `1 is V11() real ext-real Element of REAL
|.P.| is V11() real ext-real non negative Element of REAL
(P `1) / |.P.| is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
|.p4.| is V11() real ext-real non negative Element of REAL
(p4 `1) / |.p4.| is V11() real ext-real Element of REAL
|.p2.| ^2 is V11() real ext-real Element of REAL
K37(|.p2.|,|.p2.|) is V11() real ext-real non negative set
(p2 `1) ^2 is V11() real ext-real Element of REAL
K37((p2 `1),(p2 `1)) is V11() real ext-real set
(p2 `2) ^2 is V11() real ext-real Element of REAL
K37((p2 `2),(p2 `2)) is V11() real ext-real set
((p2 `1) ^2) + ((p2 `2) ^2) is V11() real ext-real Element of REAL
(|.p2.| ^2) - ((p2 `1) ^2) is V11() real ext-real Element of REAL
0 + ((p2 `1) ^2) is V11() real ext-real Element of REAL
((|.p2.| ^2) - ((p2 `1) ^2)) + ((p2 `1) ^2) is V11() real ext-real Element of REAL
- |.p2.| is V11() real ext-real non positive Element of REAL
(- |.p2.|) / |.p2.| is V11() real ext-real non positive Element of REAL
- (p3 `1) is V11() real ext-real Element of REAL
(- (p3 `1)) / |.p3.| is V11() real ext-real Element of REAL
|.p3.| ^2 is V11() real ext-real Element of REAL
K37(|.p3.|,|.p3.|) is V11() real ext-real non negative set
(p3 `1) ^2 is V11() real ext-real Element of REAL
K37((p3 `1),(p3 `1)) is V11() real ext-real set
0 ^2 is V11() real ext-real Element of REAL
K37(0,0) is empty V11() real ext-real non positive non negative Function-like functional V142() V143() V144() V145() V146() V147() V148() V201() V204() set
((p3 `1) ^2) + (0 ^2) is V11() real ext-real Element of REAL
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P `1 is V11() real ext-real Element of REAL
|.P.| is V11() real ext-real non negative Element of REAL
(P `1) / |.P.| is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
|.p4.| is V11() real ext-real non negative Element of REAL
(p4 `1) / |.p4.| is V11() real ext-real Element of REAL
|.p4.| ^2 is V11() real ext-real Element of REAL
K37(|.p4.|,|.p4.|) is V11() real ext-real non negative set
(p4 `1) ^2 is V11() real ext-real Element of REAL
K37((p4 `1),(p4 `1)) is V11() real ext-real set
p4 `2 is V11() real ext-real Element of REAL
(p4 `2) ^2 is V11() real ext-real Element of REAL
K37((p4 `2),(p4 `2)) is V11() real ext-real set
((p4 `1) ^2) + ((p4 `2) ^2) is V11() real ext-real Element of REAL
1 * |.p4.| is V11() real ext-real non negative Element of REAL
(|.p4.| ^2) - ((p4 `1) ^2) is V11() real ext-real Element of REAL
0 + ((p4 `1) ^2) is V11() real ext-real Element of REAL
((|.p4.| ^2) - ((p4 `1) ^2)) + ((p4 `1) ^2) is V11() real ext-real Element of REAL
|.p4.| / |.p4.| is V11() real ext-real non negative Element of REAL
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P `1 is V11() real ext-real Element of REAL
|.P.| is V11() real ext-real non negative Element of REAL
(P `1) / |.P.| is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
|.p4.| is V11() real ext-real non negative Element of REAL
(p4 `1) / |.p4.| is V11() real ext-real Element of REAL
|.p3.| ^2 is V11() real ext-real Element of REAL
K37(|.p3.|,|.p3.|) is V11() real ext-real non negative set
(p3 `1) ^2 is V11() real ext-real Element of REAL
K37((p3 `1),(p3 `1)) is V11() real ext-real set
(p3 `2) ^2 is V11() real ext-real Element of REAL
K37((p3 `2),(p3 `2)) is V11() real ext-real set
((p3 `1) ^2) + ((p3 `2) ^2) is V11() real ext-real Element of REAL
(|.p3.| ^2) - ((p3 `1) ^2) is V11() real ext-real Element of REAL
0 + ((p3 `1) ^2) is V11() real ext-real Element of REAL
((|.p3.| ^2) - ((p3 `1) ^2)) + ((p3 `1) ^2) is V11() real ext-real Element of REAL
|.p3.| / |.p3.| is V11() real ext-real non negative Element of REAL
|.p2.| ^2 is V11() real ext-real Element of REAL
K37(|.p2.|,|.p2.|) is V11() real ext-real non negative set
(p2 `1) ^2 is V11() real ext-real Element of REAL
K37((p2 `1),(p2 `1)) is V11() real ext-real set
0 ^2 is V11() real ext-real Element of REAL
K37(0,0) is empty V11() real ext-real non positive non negative Function-like functional V142() V143() V144() V145() V146() V147() V148() V201() V204() set
((p2 `1) ^2) + (0 ^2) is V11() real ext-real Element of REAL
- (p2 `1) is V11() real ext-real Element of REAL
(- (p2 `1)) / |.p2.| is V11() real ext-real Element of REAL
- ((p2 `1) / |.p2.|) is V11() real ext-real Element of REAL
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P `1 is V11() real ext-real Element of REAL
|.P.| is V11() real ext-real non negative Element of REAL
(P `1) / |.P.| is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
|.p4.| is V11() real ext-real non negative Element of REAL
(p4 `1) / |.p4.| is V11() real ext-real Element of REAL
|.P.| ^2 is V11() real ext-real Element of REAL
K37(|.P.|,|.P.|) is V11() real ext-real non negative set
(P `1) ^2 is V11() real ext-real Element of REAL
K37((P `1),(P `1)) is V11() real ext-real set
P `2 is V11() real ext-real Element of REAL
(P `2) ^2 is V11() real ext-real Element of REAL
K37((P `2),(P `2)) is V11() real ext-real set
((P `1) ^2) + ((P `2) ^2) is V11() real ext-real Element of REAL
(|.P.| ^2) - ((P `1) ^2) is V11() real ext-real Element of REAL
0 + ((P `1) ^2) is V11() real ext-real Element of REAL
((|.P.| ^2) - ((P `1) ^2)) + ((P `1) ^2) is V11() real ext-real Element of REAL
- |.P.| is V11() real ext-real non positive Element of REAL
(- |.P.|) / |.P.| is V11() real ext-real non positive Element of REAL
(- 1) * |.P.| is V11() real ext-real non positive Element of REAL
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P `1 is V11() real ext-real Element of REAL
|.P.| is V11() real ext-real non negative Element of REAL
(P `1) / |.P.| is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
|.p4.| is V11() real ext-real non negative Element of REAL
(p4 `1) / |.p4.| is V11() real ext-real Element of REAL
p1 is V11() real ext-real Element of REAL
p1 -FanMorphE is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
(p1 -FanMorphE) . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
|.p2.| is V11() real ext-real non negative Element of REAL
(p2 `2) / |.p2.| is V11() real ext-real Element of REAL
p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
|.p2.| is V11() real ext-real non negative Element of REAL
(p2 `2) / |.p2.| is V11() real ext-real Element of REAL
p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
|.p2.| is V11() real ext-real non negative Element of REAL
(p2 `2) / |.p2.| is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
|.p2.| is V11() real ext-real non negative Element of REAL
(p2 `2) / |.p2.| is V11() real ext-real Element of REAL
p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p1 is V11() real ext-real Element of REAL
p1 -FanMorphE is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
|.p2.| is V11() real ext-real non negative Element of REAL
(p2 `2) / |.p2.| is V11() real ext-real Element of REAL
(p1 -FanMorphE) . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
|.p2.| ^2 is V11() real ext-real Element of REAL
K37(|.p2.|,|.p2.|) is V11() real ext-real non negative set
(p2 `2) ^2 is V11() real ext-real Element of REAL
K37((p2 `2),(p2 `2)) is V11() real ext-real set
0 ^2 is V11() real ext-real Element of REAL
K37(0,0) is empty V11() real ext-real non positive non negative Function-like functional V142() V143() V144() V145() V146() V147() V148() V201() V204() set
((p2 `2) ^2) + (0 ^2) is V11() real ext-real Element of REAL
- (p2 `2) is V11() real ext-real Element of REAL
p1 is V11() real ext-real Element of REAL
p1 -FanMorphE is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
|.p2.| is V11() real ext-real non negative Element of REAL
|.p3.| is V11() real ext-real non negative Element of REAL
p3 `2 is V11() real ext-real Element of REAL
(p3 `2) / |.p3.| is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
(p2 `2) / |.p2.| is V11() real ext-real Element of REAL
(p1 -FanMorphE) . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(p1 -FanMorphE) . p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P `2 is V11() real ext-real Element of REAL
|.P.| is V11() real ext-real non negative Element of REAL
(P `2) / |.P.| is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
|.p4.| is V11() real ext-real non negative Element of REAL
(p4 `2) / |.p4.| is V11() real ext-real Element of REAL
|.p2.| ^2 is V11() real ext-real Element of REAL
K37(|.p2.|,|.p2.|) is V11() real ext-real non negative set
(p2 `2) ^2 is V11() real ext-real Element of REAL
K37((p2 `2),(p2 `2)) is V11() real ext-real set
(p2 `1) ^2 is V11() real ext-real Element of REAL
K37((p2 `1),(p2 `1)) is V11() real ext-real set
((p2 `2) ^2) + ((p2 `1) ^2) is V11() real ext-real Element of REAL
(|.p2.| ^2) - ((p2 `2) ^2) is V11() real ext-real Element of REAL
0 + ((p2 `2) ^2) is V11() real ext-real Element of REAL
((|.p2.| ^2) - ((p2 `2) ^2)) + ((p2 `2) ^2) is V11() real ext-real Element of REAL
- |.p2.| is V11() real ext-real non positive Element of REAL
(- |.p2.|) / |.p2.| is V11() real ext-real non positive Element of REAL
- (p3 `2) is V11() real ext-real Element of REAL
(- (p3 `2)) / |.p3.| is V11() real ext-real Element of REAL
|.p3.| ^2 is V11() real ext-real Element of REAL
K37(|.p3.|,|.p3.|) is V11() real ext-real non negative set
(p3 `2) ^2 is V11() real ext-real Element of REAL
K37((p3 `2),(p3 `2)) is V11() real ext-real set
0 ^2 is V11() real ext-real Element of REAL
K37(0,0) is empty V11() real ext-real non positive non negative Function-like functional V142() V143() V144() V145() V146() V147() V148() V201() V204() set
((p3 `2) ^2) + (0 ^2) is V11() real ext-real Element of REAL
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P `2 is V11() real ext-real Element of REAL
|.P.| is V11() real ext-real non negative Element of REAL
(P `2) / |.P.| is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
|.p4.| is V11() real ext-real non negative Element of REAL
(p4 `2) / |.p4.| is V11() real ext-real Element of REAL
|.p4.| ^2 is V11() real ext-real Element of REAL
K37(|.p4.|,|.p4.|) is V11() real ext-real non negative set
(p4 `2) ^2 is V11() real ext-real Element of REAL
K37((p4 `2),(p4 `2)) is V11() real ext-real set
p4 `1 is V11() real ext-real Element of REAL
(p4 `1) ^2 is V11() real ext-real Element of REAL
K37((p4 `1),(p4 `1)) is V11() real ext-real set
((p4 `2) ^2) + ((p4 `1) ^2) is V11() real ext-real Element of REAL
1 * |.p4.| is V11() real ext-real non negative Element of REAL
(|.p4.| ^2) - ((p4 `2) ^2) is V11() real ext-real Element of REAL
0 + ((p4 `2) ^2) is V11() real ext-real Element of REAL
((|.p4.| ^2) - ((p4 `2) ^2)) + ((p4 `2) ^2) is V11() real ext-real Element of REAL
|.p4.| / |.p4.| is V11() real ext-real non negative Element of REAL
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P `2 is V11() real ext-real Element of REAL
|.P.| is V11() real ext-real non negative Element of REAL
(P `2) / |.P.| is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
|.p4.| is V11() real ext-real non negative Element of REAL
(p4 `2) / |.p4.| is V11() real ext-real Element of REAL
|.p3.| ^2 is V11() real ext-real Element of REAL
K37(|.p3.|,|.p3.|) is V11() real ext-real non negative set
(p3 `2) ^2 is V11() real ext-real Element of REAL
K37((p3 `2),(p3 `2)) is V11() real ext-real set
(p3 `1) ^2 is V11() real ext-real Element of REAL
K37((p3 `1),(p3 `1)) is V11() real ext-real set
((p3 `2) ^2) + ((p3 `1) ^2) is V11() real ext-real Element of REAL
(|.p3.| ^2) - ((p3 `2) ^2) is V11() real ext-real Element of REAL
0 + ((p3 `2) ^2) is V11() real ext-real Element of REAL
((|.p3.| ^2) - ((p3 `2) ^2)) + ((p3 `2) ^2) is V11() real ext-real Element of REAL
|.p3.| / |.p3.| is V11() real ext-real non negative Element of REAL
|.p2.| ^2 is V11() real ext-real Element of REAL
K37(|.p2.|,|.p2.|) is V11() real ext-real non negative set
(p2 `2) ^2 is V11() real ext-real Element of REAL
K37((p2 `2),(p2 `2)) is V11() real ext-real set
0 ^2 is V11() real ext-real Element of REAL
K37(0,0) is empty V11() real ext-real non positive non negative Function-like functional V142() V143() V144() V145() V146() V147() V148() V201() V204() set
((p2 `2) ^2) + (0 ^2) is V11() real ext-real Element of REAL
- (p2 `2) is V11() real ext-real Element of REAL
(- (p2 `2)) / |.p2.| is V11() real ext-real Element of REAL
- ((p2 `2) / |.p2.|) is V11() real ext-real Element of REAL
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P `2 is V11() real ext-real Element of REAL
|.P.| is V11() real ext-real non negative Element of REAL
(P `2) / |.P.| is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
|.p4.| is V11() real ext-real non negative Element of REAL
(p4 `2) / |.p4.| is V11() real ext-real Element of REAL
|.P.| ^2 is V11() real ext-real Element of REAL
K37(|.P.|,|.P.|) is V11() real ext-real non negative set
(P `2) ^2 is V11() real ext-real Element of REAL
K37((P `2),(P `2)) is V11() real ext-real set
P `1 is V11() real ext-real Element of REAL
(P `1) ^2 is V11() real ext-real Element of REAL
K37((P `1),(P `1)) is V11() real ext-real set
((P `2) ^2) + ((P `1) ^2) is V11() real ext-real Element of REAL
(|.P.| ^2) - ((P `2) ^2) is V11() real ext-real Element of REAL
0 + ((P `2) ^2) is V11() real ext-real Element of REAL
((|.P.| ^2) - ((P `2) ^2)) + ((P `2) ^2) is V11() real ext-real Element of REAL
- |.P.| is V11() real ext-real non positive Element of REAL
(- |.P.|) / |.P.| is V11() real ext-real non positive Element of REAL
(- 1) * |.P.| is V11() real ext-real non positive Element of REAL
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P `2 is V11() real ext-real Element of REAL
|.P.| is V11() real ext-real non negative Element of REAL
(P `2) / |.P.| is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
|.p4.| is V11() real ext-real non negative Element of REAL
(p4 `2) / |.p4.| is V11() real ext-real Element of REAL
p1 is V11() real ext-real Element of REAL
p1 -FanMorphS is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
(p1 -FanMorphS) . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
|.p2.| is V11() real ext-real non negative Element of REAL
(p2 `1) / |.p2.| is V11() real ext-real Element of REAL
p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
|.p2.| is V11() real ext-real non negative Element of REAL
(p2 `1) / |.p2.| is V11() real ext-real Element of REAL
p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
|.p2.| is V11() real ext-real non negative Element of REAL
(p2 `1) / |.p2.| is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
|.p2.| is V11() real ext-real non negative Element of REAL
(p2 `1) / |.p2.| is V11() real ext-real Element of REAL
p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p1 is V11() real ext-real Element of REAL
p1 -FanMorphS is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
|.p2.| is V11() real ext-real non negative Element of REAL
(p2 `1) / |.p2.| is V11() real ext-real Element of REAL
(p1 -FanMorphS) . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p1 ^2 is V11() real ext-real Element of REAL
K37(p1,p1) is V11() real ext-real set
1 - (p1 ^2) is V11() real ext-real Element of REAL
sqrt (1 - (p1 ^2)) is V11() real ext-real Element of REAL
- (sqrt (1 - (p1 ^2))) is V11() real ext-real Element of REAL
|[p1,(- (sqrt (1 - (p1 ^2))))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.p3.| is V11() real ext-real non negative Element of REAL
|.p3.| * |[p1,(- (sqrt (1 - (p1 ^2))))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
1 / |.p3.| is V11() real ext-real non negative Element of REAL
(1 / |.p3.|) * p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(p1 -FanMorphS) . (|.p3.| * |[p1,(- (sqrt (1 - (p1 ^2))))]|) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|[0,(- 1)]| `1 is V11() real ext-real Element of REAL
|[0,(- 1)]| `2 is V11() real ext-real Element of REAL
|.p3.| * |[0,(- 1)]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.p3.| * 0 is empty V11() real ext-real non positive non negative Function-like functional V142() V143() V144() V145() V146() V147() V148() V201() V204() Element of REAL
|.p3.| * (- 1) is V11() real ext-real non positive Element of REAL
|[(|.p3.| * 0),(|.p3.| * (- 1))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
- |.p3.| is V11() real ext-real non positive Element of REAL
|[0,(- |.p3.|)]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|[p1,(- (sqrt (1 - (p1 ^2))))]| `1 is V11() real ext-real Element of REAL
|[p1,(- (sqrt (1 - (p1 ^2))))]| `2 is V11() real ext-real Element of REAL
|.p3.| * p1 is V11() real ext-real Element of REAL
|.p3.| * (- (sqrt (1 - (p1 ^2)))) is V11() real ext-real Element of REAL
|[(|.p3.| * p1),(|.p3.| * (- (sqrt (1 - (p1 ^2)))))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(|.p3.| * |[p1,(- (sqrt (1 - (p1 ^2))))]|) `1 is V11() real ext-real Element of REAL
|.p3.| ^2 is V11() real ext-real Element of REAL
K37(|.p3.|,|.p3.|) is V11() real ext-real non negative set
(p3 `2) ^2 is V11() real ext-real Element of REAL
K37((p3 `2),(p3 `2)) is V11() real ext-real set
0 ^2 is V11() real ext-real Element of REAL
K37(0,0) is empty V11() real ext-real non positive non negative Function-like functional V142() V143() V144() V145() V146() V147() V148() V201() V204() set
((p3 `2) ^2) + (0 ^2) is V11() real ext-real Element of REAL
(|.p3.| * |[p1,(- (sqrt (1 - (p1 ^2))))]|) `2 is V11() real ext-real Element of REAL
(sqrt (1 - (p1 ^2))) * |.p3.| is V11() real ext-real Element of REAL
- ((sqrt (1 - (p1 ^2))) * |.p3.|) is V11() real ext-real Element of REAL
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
- (- ((sqrt (1 - (p1 ^2))) * |.p3.|)) is V11() real ext-real Element of REAL
|.p3.| * ((1 / |.p3.|) * p3) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.p3.| * (1 / |.p3.|) is V11() real ext-real non negative Element of REAL
(|.p3.| * (1 / |.p3.|)) * p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
1 * p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(1 / |.p3.|) * (p3 `1) is V11() real ext-real Element of REAL
(1 / |.p3.|) * (p3 `2) is V11() real ext-real Element of REAL
|[((1 / |.p3.|) * (p3 `1)),((1 / |.p3.|) * (p3 `2))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
((1 / |.p3.|) * p3) `2 is V11() real ext-real Element of REAL
- (|.p3.| * (1 / |.p3.|)) is V11() real ext-real non positive Element of REAL
|.(|.p3.| * |[p1,(- (sqrt (1 - (p1 ^2))))]|).| is V11() real ext-real non negative Element of REAL
abs |.p3.| is V11() real ext-real Element of REAL
|.|[p1,(- (sqrt (1 - (p1 ^2))))]|.| is V11() real ext-real non negative Element of REAL
(abs |.p3.|) * |.|[p1,(- (sqrt (1 - (p1 ^2))))]|.| is V11() real ext-real Element of REAL
(- (sqrt (1 - (p1 ^2)))) ^2 is V11() real ext-real Element of REAL
K37((- (sqrt (1 - (p1 ^2)))),(- (sqrt (1 - (p1 ^2))))) is V11() real ext-real set
(p1 ^2) + ((- (sqrt (1 - (p1 ^2)))) ^2) is V11() real ext-real Element of REAL
sqrt ((p1 ^2) + ((- (sqrt (1 - (p1 ^2)))) ^2)) is V11() real ext-real Element of REAL
(abs |.p3.|) * (sqrt ((p1 ^2) + ((- (sqrt (1 - (p1 ^2)))) ^2))) is V11() real ext-real Element of REAL
(sqrt (1 - (p1 ^2))) ^2 is V11() real ext-real Element of REAL
K37((sqrt (1 - (p1 ^2))),(sqrt (1 - (p1 ^2)))) is V11() real ext-real set
(p1 ^2) + ((sqrt (1 - (p1 ^2))) ^2) is V11() real ext-real Element of REAL
sqrt ((p1 ^2) + ((sqrt (1 - (p1 ^2))) ^2)) is V11() real ext-real Element of REAL
(abs |.p3.|) * (sqrt ((p1 ^2) + ((sqrt (1 - (p1 ^2))) ^2))) is V11() real ext-real Element of REAL
(p1 ^2) + (1 - (p1 ^2)) is V11() real ext-real Element of REAL
sqrt ((p1 ^2) + (1 - (p1 ^2))) is V11() real ext-real Element of REAL
(abs |.p3.|) * (sqrt ((p1 ^2) + (1 - (p1 ^2)))) is V11() real ext-real Element of REAL
|.((p1 -FanMorphS) . (|.p3.| * |[p1,(- (sqrt (1 - (p1 ^2))))]|)).| is V11() real ext-real non negative Element of REAL
((|.p3.| * |[p1,(- (sqrt (1 - (p1 ^2))))]|) `1) / |.(|.p3.| * |[p1,(- (sqrt (1 - (p1 ^2))))]|).| is V11() real ext-real Element of REAL
((p1 -FanMorphS) . (|.p3.| * |[p1,(- (sqrt (1 - (p1 ^2))))]|)) `1 is V11() real ext-real Element of REAL
|.((p1 -FanMorphS) . (|.p3.| * |[p1,(- (sqrt (1 - (p1 ^2))))]|)).| ^2 is V11() real ext-real Element of REAL
K37(|.((p1 -FanMorphS) . (|.p3.| * |[p1,(- (sqrt (1 - (p1 ^2))))]|)).|,|.((p1 -FanMorphS) . (|.p3.| * |[p1,(- (sqrt (1 - (p1 ^2))))]|)).|) is V11() real ext-real non negative set
((p1 -FanMorphS) . (|.p3.| * |[p1,(- (sqrt (1 - (p1 ^2))))]|)) `2 is V11() real ext-real Element of REAL
(((p1 -FanMorphS) . (|.p3.| * |[p1,(- (sqrt (1 - (p1 ^2))))]|)) `2) ^2 is V11() real ext-real Element of REAL
K37((((p1 -FanMorphS) . (|.p3.| * |[p1,(- (sqrt (1 - (p1 ^2))))]|)) `2),(((p1 -FanMorphS) . (|.p3.| * |[p1,(- (sqrt (1 - (p1 ^2))))]|)) `2)) is V11() real ext-real set
((((p1 -FanMorphS) . (|.p3.| * |[p1,(- (sqrt (1 - (p1 ^2))))]|)) `2) ^2) + (0 ^2) is V11() real ext-real Element of REAL
- |.((p1 -FanMorphS) . (|.p3.| * |[p1,(- (sqrt (1 - (p1 ^2))))]|)).| is V11() real ext-real non positive Element of REAL
dom (p1 -FanMorphS) is functional Element of K6( the carrier of (TOP-REAL 2))
p1 is V11() real ext-real Element of REAL
p1 -FanMorphS is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
|.p2.| is V11() real ext-real non negative Element of REAL
|.p3.| is V11() real ext-real non negative Element of REAL
p3 `1 is V11() real ext-real Element of REAL
(p3 `1) / |.p3.| is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
(p2 `1) / |.p2.| is V11() real ext-real Element of REAL
(p1 -FanMorphS) . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(p1 -FanMorphS) . p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P `1 is V11() real ext-real Element of REAL
|.P.| is V11() real ext-real non negative Element of REAL
(P `1) / |.P.| is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
|.p4.| is V11() real ext-real non negative Element of REAL
(p4 `1) / |.p4.| is V11() real ext-real Element of REAL
|.p2.| ^2 is V11() real ext-real Element of REAL
K37(|.p2.|,|.p2.|) is V11() real ext-real non negative set
(p2 `1) ^2 is V11() real ext-real Element of REAL
K37((p2 `1),(p2 `1)) is V11() real ext-real set
(p2 `2) ^2 is V11() real ext-real Element of REAL
K37((p2 `2),(p2 `2)) is V11() real ext-real set
((p2 `1) ^2) + ((p2 `2) ^2) is V11() real ext-real Element of REAL
(|.p2.| ^2) - ((p2 `1) ^2) is V11() real ext-real Element of REAL
0 + ((p2 `1) ^2) is V11() real ext-real Element of REAL
((|.p2.| ^2) - ((p2 `1) ^2)) + ((p2 `1) ^2) is V11() real ext-real Element of REAL
- |.p2.| is V11() real ext-real non positive Element of REAL
(- |.p2.|) / |.p2.| is V11() real ext-real non positive Element of REAL
- (p3 `1) is V11() real ext-real Element of REAL
(- (p3 `1)) / |.p3.| is V11() real ext-real Element of REAL
|.p3.| ^2 is V11() real ext-real Element of REAL
K37(|.p3.|,|.p3.|) is V11() real ext-real non negative set
(p3 `1) ^2 is V11() real ext-real Element of REAL
K37((p3 `1),(p3 `1)) is V11() real ext-real set
0 ^2 is V11() real ext-real Element of REAL
K37(0,0) is empty V11() real ext-real non positive non negative Function-like functional V142() V143() V144() V145() V146() V147() V148() V201() V204() set
((p3 `1) ^2) + (0 ^2) is V11() real ext-real Element of REAL
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P `1 is V11() real ext-real Element of REAL
|.P.| is V11() real ext-real non negative Element of REAL
(P `1) / |.P.| is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
|.p4.| is V11() real ext-real non negative Element of REAL
(p4 `1) / |.p4.| is V11() real ext-real Element of REAL
|.p4.| ^2 is V11() real ext-real Element of REAL
K37(|.p4.|,|.p4.|) is V11() real ext-real non negative set
(p4 `1) ^2 is V11() real ext-real Element of REAL
K37((p4 `1),(p4 `1)) is V11() real ext-real set
p4 `2 is V11() real ext-real Element of REAL
(p4 `2) ^2 is V11() real ext-real Element of REAL
K37((p4 `2),(p4 `2)) is V11() real ext-real set
((p4 `1) ^2) + ((p4 `2) ^2) is V11() real ext-real Element of REAL
1 * |.p4.| is V11() real ext-real non negative Element of REAL
(|.p4.| ^2) - ((p4 `1) ^2) is V11() real ext-real Element of REAL
0 + ((p4 `1) ^2) is V11() real ext-real Element of REAL
((|.p4.| ^2) - ((p4 `1) ^2)) + ((p4 `1) ^2) is V11() real ext-real Element of REAL
|.p4.| / |.p4.| is V11() real ext-real non negative Element of REAL
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P `1 is V11() real ext-real Element of REAL
|.P.| is V11() real ext-real non negative Element of REAL
(P `1) / |.P.| is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
|.p4.| is V11() real ext-real non negative Element of REAL
(p4 `1) / |.p4.| is V11() real ext-real Element of REAL
|.p3.| ^2 is V11() real ext-real Element of REAL
K37(|.p3.|,|.p3.|) is V11() real ext-real non negative set
(p3 `1) ^2 is V11() real ext-real Element of REAL
K37((p3 `1),(p3 `1)) is V11() real ext-real set
(p3 `2) ^2 is V11() real ext-real Element of REAL
K37((p3 `2),(p3 `2)) is V11() real ext-real set
((p3 `1) ^2) + ((p3 `2) ^2) is V11() real ext-real Element of REAL
(|.p3.| ^2) - ((p3 `1) ^2) is V11() real ext-real Element of REAL
0 + ((p3 `1) ^2) is V11() real ext-real Element of REAL
((|.p3.| ^2) - ((p3 `1) ^2)) + ((p3 `1) ^2) is V11() real ext-real Element of REAL
|.p3.| / |.p3.| is V11() real ext-real non negative Element of REAL
|.p2.| ^2 is V11() real ext-real Element of REAL
K37(|.p2.|,|.p2.|) is V11() real ext-real non negative set
(p2 `1) ^2 is V11() real ext-real Element of REAL
K37((p2 `1),(p2 `1)) is V11() real ext-real set
0 ^2 is V11() real ext-real Element of REAL
K37(0,0) is empty V11() real ext-real non positive non negative Function-like functional V142() V143() V144() V145() V146() V147() V148() V201() V204() set
((p2 `1) ^2) + (0 ^2) is V11() real ext-real Element of REAL
- (p2 `1) is V11() real ext-real Element of REAL
(- (p2 `1)) / |.p2.| is V11() real ext-real Element of REAL
- ((p2 `1) / |.p2.|) is V11() real ext-real Element of REAL
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P `1 is V11() real ext-real Element of REAL
|.P.| is V11() real ext-real non negative Element of REAL
(P `1) / |.P.| is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
|.p4.| is V11() real ext-real non negative Element of REAL
(p4 `1) / |.p4.| is V11() real ext-real Element of REAL
|.P.| ^2 is V11() real ext-real Element of REAL
K37(|.P.|,|.P.|) is V11() real ext-real non negative set
(P `1) ^2 is V11() real ext-real Element of REAL
K37((P `1),(P `1)) is V11() real ext-real set
P `2 is V11() real ext-real Element of REAL
(P `2) ^2 is V11() real ext-real Element of REAL
K37((P `2),(P `2)) is V11() real ext-real set
((P `1) ^2) + ((P `2) ^2) is V11() real ext-real Element of REAL
(|.P.| ^2) - ((P `1) ^2) is V11() real ext-real Element of REAL
0 + ((P `1) ^2) is V11() real ext-real Element of REAL
((|.P.| ^2) - ((P `1) ^2)) + ((P `1) ^2) is V11() real ext-real Element of REAL
- |.P.| is V11() real ext-real non positive Element of REAL
(- |.P.|) / |.P.| is V11() real ext-real non positive Element of REAL
(- 1) * |.P.| is V11() real ext-real non positive Element of REAL
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P `1 is V11() real ext-real Element of REAL
|.P.| is V11() real ext-real non negative Element of REAL
(P `1) / |.P.| is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
|.p4.| is V11() real ext-real non negative Element of REAL
(p4 `1) / |.p4.| is V11() real ext-real Element of REAL
p1 is non empty functional closed compact Element of K6( the carrier of (TOP-REAL 2))
[.(- 1),1.] is V142() V143() V144() V204() Element of K6(REAL)
proj1 .: p1 is V142() V143() V144() Element of K6(REAL)
p2 is set
{ b1 where b1 is V11() real ext-real Element of REAL : ( - 1 <= b1 & b1 <= 1 ) } is set
p3 is V11() real ext-real Element of REAL
p3 ^2 is V11() real ext-real Element of REAL
K37(p3,p3) is V11() real ext-real set
1 - (p3 ^2) is V11() real ext-real Element of REAL
sqrt (1 - (p3 ^2)) is V11() real ext-real Element of REAL
|[p3,(sqrt (1 - (p3 ^2)))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
|[p3,(sqrt (1 - (p3 ^2)))]| `1 is V11() real ext-real Element of REAL
|[p3,(sqrt (1 - (p3 ^2)))]| `2 is V11() real ext-real Element of REAL
|.|[p3,(sqrt (1 - (p3 ^2)))]|.| is V11() real ext-real non negative Element of REAL
(sqrt (1 - (p3 ^2))) ^2 is V11() real ext-real Element of REAL
K37((sqrt (1 - (p3 ^2))),(sqrt (1 - (p3 ^2)))) is V11() real ext-real set
(p3 ^2) + ((sqrt (1 - (p3 ^2))) ^2) is V11() real ext-real Element of REAL
sqrt ((p3 ^2) + ((sqrt (1 - (p3 ^2))) ^2)) is V11() real ext-real Element of REAL
(p3 ^2) + (1 - (p3 ^2)) is V11() real ext-real Element of REAL
sqrt ((p3 ^2) + (1 - (p3 ^2))) is V11() real ext-real Element of REAL
dom proj1 is functional Element of K6( the carrier of (TOP-REAL 2))
proj1 . |[p3,(sqrt (1 - (p3 ^2)))]| is V11() real ext-real Element of REAL
p2 is set
dom proj1 is functional Element of K6( the carrier of (TOP-REAL 2))
p3 is set
proj1 . p3 is set
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
(p4 `1) ^2 is V11() real ext-real Element of REAL
K37((p4 `1),(p4 `1)) is V11() real ext-real set
p4 `2 is V11() real ext-real Element of REAL
(p4 `2) ^2 is V11() real ext-real Element of REAL
K37((p4 `2),(p4 `2)) is V11() real ext-real set
((p4 `1) ^2) + ((p4 `2) ^2) is V11() real ext-real Element of REAL
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.P.| is V11() real ext-real non negative Element of REAL
0 + ((p4 `1) ^2) is V11() real ext-real Element of REAL
1 - ((p4 `1) ^2) is V11() real ext-real Element of REAL
(1 - ((p4 `1) ^2)) + ((p4 `1) ^2) is V11() real ext-real Element of REAL
proj2 .: p1 is V142() V143() V144() Element of K6(REAL)
p2 is set
{ b1 where b1 is V11() real ext-real Element of REAL : ( - 1 <= b1 & b1 <= 1 ) } is set
p3 is V11() real ext-real Element of REAL
p3 ^2 is V11() real ext-real Element of REAL
K37(p3,p3) is V11() real ext-real set
1 - (p3 ^2) is V11() real ext-real Element of REAL
sqrt (1 - (p3 ^2)) is V11() real ext-real Element of REAL
|[(sqrt (1 - (p3 ^2))),p3]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
|[(sqrt (1 - (p3 ^2))),p3]| `2 is V11() real ext-real Element of REAL
|[(sqrt (1 - (p3 ^2))),p3]| `1 is V11() real ext-real Element of REAL
|.|[(sqrt (1 - (p3 ^2))),p3]|.| is V11() real ext-real non negative Element of REAL
(sqrt (1 - (p3 ^2))) ^2 is V11() real ext-real Element of REAL
K37((sqrt (1 - (p3 ^2))),(sqrt (1 - (p3 ^2)))) is V11() real ext-real set
((sqrt (1 - (p3 ^2))) ^2) + (p3 ^2) is V11() real ext-real Element of REAL
sqrt (((sqrt (1 - (p3 ^2))) ^2) + (p3 ^2)) is V11() real ext-real Element of REAL
(1 - (p3 ^2)) + (p3 ^2) is V11() real ext-real Element of REAL
sqrt ((1 - (p3 ^2)) + (p3 ^2)) is V11() real ext-real Element of REAL
dom proj2 is functional Element of K6( the carrier of (TOP-REAL 2))
proj2 . |[(sqrt (1 - (p3 ^2))),p3]| is V11() real ext-real Element of REAL
p2 is set
dom proj2 is functional Element of K6( the carrier of (TOP-REAL 2))
p3 is set
proj2 . p3 is set
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
(p4 `1) ^2 is V11() real ext-real Element of REAL
K37((p4 `1),(p4 `1)) is V11() real ext-real set
p4 `2 is V11() real ext-real Element of REAL
(p4 `2) ^2 is V11() real ext-real Element of REAL
K37((p4 `2),(p4 `2)) is V11() real ext-real set
((p4 `1) ^2) + ((p4 `2) ^2) is V11() real ext-real Element of REAL
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.P.| is V11() real ext-real non negative Element of REAL
0 + ((p4 `2) ^2) is V11() real ext-real Element of REAL
1 - ((p4 `2) ^2) is V11() real ext-real Element of REAL
(1 - ((p4 `2) ^2)) + ((p4 `2) ^2) is V11() real ext-real Element of REAL
p1 is non empty functional closed compact Element of K6( the carrier of (TOP-REAL 2))
W-bound p1 is V11() real ext-real Element of REAL
proj1 .: p1 is V142() V143() V144() Element of K6(REAL)
(TOP-REAL 2) | p1 is non empty strict TopSpace-like T_0 T_1 T_2 compact SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | p1) is non empty set
proj1 | p1 is Relation-like the carrier of ((TOP-REAL 2) | p1) -defined REAL -valued Function-like quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | p1),REAL))
K7( the carrier of ((TOP-REAL 2) | p1),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | p1),REAL)) is set
(proj1 | p1) .: p1 is V142() V143() V144() Element of K6(REAL)
lower_bound ((proj1 | p1) .: p1) is V11() real ext-real Element of REAL
lower_bound (proj1 | p1) is V11() real ext-real Element of REAL
p1 is non empty functional closed compact Element of K6( the carrier of (TOP-REAL 2))
W-bound p1 is V11() real ext-real Element of REAL
E-bound p1 is V11() real ext-real Element of REAL
S-bound p1 is V11() real ext-real Element of REAL
N-bound p1 is V11() real ext-real Element of REAL
(TOP-REAL 2) | p1 is non empty strict TopSpace-like T_0 T_1 T_2 compact SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | p1) is non empty set
proj1 .: p1 is V142() V143() V144() Element of K6(REAL)
proj1 | p1 is Relation-like the carrier of ((TOP-REAL 2) | p1) -defined REAL -valued Function-like quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | p1),REAL))
K7( the carrier of ((TOP-REAL 2) | p1),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | p1),REAL)) is set
(proj1 | p1) .: p1 is V142() V143() V144() Element of K6(REAL)
(proj1 | p1) .: the carrier of ((TOP-REAL 2) | p1) is V142() V143() V144() Element of K6(REAL)
upper_bound ((proj1 | p1) .: the carrier of ((TOP-REAL 2) | p1)) is V11() real ext-real Element of REAL
upper_bound (proj1 | p1) is V11() real ext-real Element of REAL
proj2 .: p1 is V142() V143() V144() Element of K6(REAL)
proj2 | p1 is Relation-like the carrier of ((TOP-REAL 2) | p1) -defined REAL -valued Function-like quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | p1),REAL))
(proj2 | p1) .: p1 is V142() V143() V144() Element of K6(REAL)
lower_bound ((proj2 | p1) .: p1) is V11() real ext-real Element of REAL
lower_bound (proj2 | p1) is V11() real ext-real Element of REAL
upper_bound ((proj2 | p1) .: p1) is V11() real ext-real Element of REAL
upper_bound (proj2 | p1) is V11() real ext-real Element of REAL
p1 is non empty functional closed compact Element of K6( the carrier of (TOP-REAL 2))
W-min p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(TOP-REAL 2) | p1 is non empty strict TopSpace-like T_0 T_1 T_2 compact SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | p1) is non empty set
W-bound p1 is V11() real ext-real Element of REAL
proj2 .: p1 is V142() V143() V144() Element of K6(REAL)
proj2 | p1 is Relation-like the carrier of ((TOP-REAL 2) | p1) -defined REAL -valued Function-like quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | p1),REAL))
K7( the carrier of ((TOP-REAL 2) | p1),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | p1),REAL)) is set
(proj2 | p1) .: p1 is V142() V143() V144() Element of K6(REAL)
upper_bound ((proj2 | p1) .: p1) is V11() real ext-real Element of REAL
upper_bound (proj2 | p1) is V11() real ext-real Element of REAL
N-bound p1 is V11() real ext-real Element of REAL
NW-corner p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|[(- 1),1]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
lower_bound ((proj2 | p1) .: p1) is V11() real ext-real Element of REAL
lower_bound (proj2 | p1) is V11() real ext-real Element of REAL
S-bound p1 is V11() real ext-real Element of REAL
SW-corner p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|[(- 1),(- 1)]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner p1),(NW-corner p1)) is functional Element of K6( the carrier of (TOP-REAL 2))
{ (((1 - b1) * (SW-corner p1)) + (b1 * (NW-corner p1))) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
(LSeg ((SW-corner p1),(NW-corner p1))) /\ p1 is functional Element of K6( the carrier of (TOP-REAL 2))
{|[(- 1),0]|} is non empty functional set
p2 is set
p3 is V11() real ext-real Element of REAL
1 - p3 is V11() real ext-real Element of REAL
(1 - p3) * (SW-corner p1) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 * (NW-corner p1) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
((1 - p3) * (SW-corner p1)) + (p3 * (NW-corner p1)) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(1 - p3) * (- 1) is V11() real ext-real Element of REAL
|[((1 - p3) * (- 1)),((1 - p3) * (- 1))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 * |[(- 1),1]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|[((1 - p3) * (- 1)),((1 - p3) * (- 1))]| + (p3 * |[(- 1),1]|) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 * (- 1) is V11() real ext-real Element of REAL
p3 * 1 is V11() real ext-real Element of REAL
|[(p3 * (- 1)),(p3 * 1)]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|[((1 - p3) * (- 1)),((1 - p3) * (- 1))]| + |[(p3 * (- 1)),(p3 * 1)]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
((1 - p3) * (- 1)) + (p3 * (- 1)) is V11() real ext-real Element of REAL
((1 - p3) * (- 1)) + (p3 * 1) is V11() real ext-real Element of REAL
|[(((1 - p3) * (- 1)) + (p3 * (- 1))),(((1 - p3) * (- 1)) + (p3 * 1))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
(- 1) ^2 is V11() real ext-real Element of REAL
K37((- 1),(- 1)) is V11() real ext-real non negative set
p4 `2 is V11() real ext-real Element of REAL
(p4 `2) ^2 is V11() real ext-real Element of REAL
K37((p4 `2),(p4 `2)) is V11() real ext-real set
((- 1) ^2) + ((p4 `2) ^2) is V11() real ext-real Element of REAL
sqrt (((- 1) ^2) + ((p4 `2) ^2)) is V11() real ext-real Element of REAL
1 + ((p4 `2) ^2) is V11() real ext-real Element of REAL
sqrt (1 + ((p4 `2) ^2)) is V11() real ext-real Element of REAL
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.P.| is V11() real ext-real non negative Element of REAL
((1 - p3) * (- 1)) + p3 is V11() real ext-real Element of REAL
p3 is set
|[(- 1),0]| `2 is V11() real ext-real Element of REAL
|[(- 1),0]| `1 is V11() real ext-real Element of REAL
|.|[(- 1),0]|.| is V11() real ext-real non negative Element of REAL
(- 1) ^2 is V11() real ext-real Element of REAL
K37((- 1),(- 1)) is V11() real ext-real non negative set
0 ^2 is V11() real ext-real Element of REAL
K37(0,0) is empty V11() real ext-real non positive non negative Function-like functional V142() V143() V144() V145() V146() V147() V148() V201() V204() set
((- 1) ^2) + (0 ^2) is V11() real ext-real Element of REAL
sqrt (((- 1) ^2) + (0 ^2)) is V11() real ext-real Element of REAL
1 / 2 is V11() real ext-real non negative Element of REAL
(1 / 2) * (- 1) is V11() real ext-real non positive Element of REAL
((1 / 2) * (- 1)) + ((1 / 2) * (- 1)) is V11() real ext-real non positive Element of REAL
(1 / 2) * 1 is V11() real ext-real non negative Element of REAL
((1 / 2) * (- 1)) + ((1 / 2) * 1) is V11() real ext-real Element of REAL
|[(((1 / 2) * (- 1)) + ((1 / 2) * (- 1))),(((1 / 2) * (- 1)) + ((1 / 2) * 1))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|[((1 / 2) * (- 1)),((1 / 2) * (- 1))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|[((1 / 2) * (- 1)),((1 / 2) * 1)]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|[((1 / 2) * (- 1)),((1 / 2) * (- 1))]| + |[((1 / 2) * (- 1)),((1 / 2) * 1)]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(1 / 2) * |[(- 1),1]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|[((1 / 2) * (- 1)),((1 / 2) * (- 1))]| + ((1 / 2) * |[(- 1),1]|) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(1 / 2) * |[(- 1),(- 1)]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
1 - (1 / 2) is V11() real ext-real Element of REAL
(1 - (1 / 2)) * |[(- 1),1]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
((1 / 2) * |[(- 1),(- 1)]|) + ((1 - (1 / 2)) * |[(- 1),1]|) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
W-most p1 is functional Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most p1) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (W-most p1)) is set
proj2 | (W-most p1) is Relation-like the carrier of ((TOP-REAL 2) | (W-most p1)) -defined REAL -valued Function-like quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most p1)),REAL))
K7( the carrier of ((TOP-REAL 2) | (W-most p1)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most p1)),REAL)) is set
(proj2 | (W-most p1)) .: the carrier of ((TOP-REAL 2) | (W-most p1)) is V142() V143() V144() Element of K6(REAL)
(proj2 | (W-most p1)) .: (W-most p1) is V142() V143() V144() Element of K6(REAL)
Im (proj2,|[(- 1),0]|) is set
proj2 .: {|[(- 1),0]|} is set
proj2 . |[(- 1),0]| is V11() real ext-real Element of REAL
{(proj2 . |[(- 1),0]|)} is non empty V142() V143() V144() Element of K6(REAL)
|[(- 1),0]| `2 is V11() real ext-real Element of REAL
{(|[(- 1),0]| `2)} is non empty V142() V143() V144() Element of K6(REAL)
{0} is non empty V142() V143() V144() V145() V146() V147() V199() V201() Element of K6(REAL)
lower_bound ((proj2 | (W-most p1)) .: the carrier of ((TOP-REAL 2) | (W-most p1))) is V11() real ext-real Element of REAL
lower_bound (proj2 | (W-most p1)) is V11() real ext-real Element of REAL
p1 is non empty functional closed compact Element of K6( the carrier of (TOP-REAL 2))
E-max p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(TOP-REAL 2) | p1 is non empty strict TopSpace-like T_0 T_1 T_2 compact SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | p1) is non empty set
E-bound p1 is V11() real ext-real Element of REAL
proj2 .: p1 is V142() V143() V144() Element of K6(REAL)
proj2 | p1 is Relation-like the carrier of ((TOP-REAL 2) | p1) -defined REAL -valued Function-like quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | p1),REAL))
K7( the carrier of ((TOP-REAL 2) | p1),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | p1),REAL)) is set
(proj2 | p1) .: p1 is V142() V143() V144() Element of K6(REAL)
upper_bound ((proj2 | p1) .: p1) is V11() real ext-real Element of REAL
upper_bound (proj2 | p1) is V11() real ext-real Element of REAL
N-bound p1 is V11() real ext-real Element of REAL
NE-corner p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|[1,1]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
lower_bound ((proj2 | p1) .: p1) is V11() real ext-real Element of REAL
lower_bound (proj2 | p1) is V11() real ext-real Element of REAL
S-bound p1 is V11() real ext-real Element of REAL
SE-corner p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|[1,(- 1)]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner p1),(NE-corner p1)) is functional Element of K6( the carrier of (TOP-REAL 2))
{ (((1 - b1) * (SE-corner p1)) + (b1 * (NE-corner p1))) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
(LSeg ((SE-corner p1),(NE-corner p1))) /\ p1 is functional Element of K6( the carrier of (TOP-REAL 2))
{|[1,0]|} is non empty functional set
p2 is set
p3 is V11() real ext-real Element of REAL
1 - p3 is V11() real ext-real Element of REAL
(1 - p3) * (SE-corner p1) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 * (NE-corner p1) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
((1 - p3) * (SE-corner p1)) + (p3 * (NE-corner p1)) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(1 - p3) * 1 is V11() real ext-real Element of REAL
(1 - p3) * (- 1) is V11() real ext-real Element of REAL
|[((1 - p3) * 1),((1 - p3) * (- 1))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 * |[1,1]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|[((1 - p3) * 1),((1 - p3) * (- 1))]| + (p3 * |[1,1]|) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 * 1 is V11() real ext-real Element of REAL
|[(p3 * 1),(p3 * 1)]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|[((1 - p3) * 1),((1 - p3) * (- 1))]| + |[(p3 * 1),(p3 * 1)]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(1 - p3) + p3 is V11() real ext-real Element of REAL
((1 - p3) + p3) * 1 is V11() real ext-real Element of REAL
((1 - p3) * (- 1)) + (p3 * 1) is V11() real ext-real Element of REAL
|[(((1 - p3) + p3) * 1),(((1 - p3) * (- 1)) + (p3 * 1))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
(p4 `2) ^2 is V11() real ext-real Element of REAL
K37((p4 `2),(p4 `2)) is V11() real ext-real set
1 + ((p4 `2) ^2) is V11() real ext-real Element of REAL
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.P.| is V11() real ext-real non negative Element of REAL
((1 - p3) * (- 1)) + p3 is V11() real ext-real Element of REAL
p3 is set
|[1,0]| `2 is V11() real ext-real Element of REAL
|[1,0]| `1 is V11() real ext-real Element of REAL
|.|[1,0]|.| is V11() real ext-real non negative Element of REAL
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
0 ^2 is V11() real ext-real Element of REAL
K37(0,0) is empty V11() real ext-real non positive non negative Function-like functional V142() V143() V144() V145() V146() V147() V148() V201() V204() set
(1 ^2) + (0 ^2) is V11() real ext-real Element of REAL
sqrt ((1 ^2) + (0 ^2)) is V11() real ext-real Element of REAL
1 / 2 is V11() real ext-real non negative Element of REAL
(1 / 2) * 1 is V11() real ext-real non negative Element of REAL
((1 / 2) * 1) + ((1 / 2) * 1) is V11() real ext-real non negative Element of REAL
(1 / 2) * (- 1) is V11() real ext-real non positive Element of REAL
((1 / 2) * (- 1)) + ((1 / 2) * 1) is V11() real ext-real Element of REAL
|[(((1 / 2) * 1) + ((1 / 2) * 1)),(((1 / 2) * (- 1)) + ((1 / 2) * 1))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|[((1 / 2) * 1),((1 / 2) * (- 1))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|[((1 / 2) * 1),((1 / 2) * 1)]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|[((1 / 2) * 1),((1 / 2) * (- 1))]| + |[((1 / 2) * 1),((1 / 2) * 1)]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(1 / 2) * |[1,1]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|[((1 / 2) * 1),((1 / 2) * (- 1))]| + ((1 / 2) * |[1,1]|) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(1 / 2) * |[1,(- 1)]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
1 - (1 / 2) is V11() real ext-real Element of REAL
(1 - (1 / 2)) * |[1,1]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
((1 / 2) * |[1,(- 1)]|) + ((1 - (1 / 2)) * |[1,1]|) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
E-most p1 is functional Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most p1) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (E-most p1)) is set
proj2 | (E-most p1) is Relation-like the carrier of ((TOP-REAL 2) | (E-most p1)) -defined REAL -valued Function-like quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most p1)),REAL))
K7( the carrier of ((TOP-REAL 2) | (E-most p1)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most p1)),REAL)) is set
(proj2 | (E-most p1)) .: the carrier of ((TOP-REAL 2) | (E-most p1)) is V142() V143() V144() Element of K6(REAL)
(proj2 | (E-most p1)) .: (E-most p1) is V142() V143() V144() Element of K6(REAL)
Im (proj2,|[1,0]|) is set
proj2 .: {|[1,0]|} is set
proj2 . |[1,0]| is V11() real ext-real Element of REAL
{(proj2 . |[1,0]|)} is non empty V142() V143() V144() Element of K6(REAL)
|[1,0]| `2 is V11() real ext-real Element of REAL
{(|[1,0]| `2)} is non empty V142() V143() V144() Element of K6(REAL)
{0} is non empty V142() V143() V144() V145() V146() V147() V199() V201() Element of K6(REAL)
upper_bound ((proj2 | (E-most p1)) .: the carrier of ((TOP-REAL 2) | (E-most p1))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (E-most p1)) is V11() real ext-real Element of REAL
K7( the carrier of (TOP-REAL 2), the carrier of R^1) is set
K6(K7( the carrier of (TOP-REAL 2), the carrier of R^1)) is set
p1 is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of R^1))
the topology of (TOP-REAL 2) is non empty open Element of K6(K6( the carrier of (TOP-REAL 2)))
K6(K6( the carrier of (TOP-REAL 2))) is set
TopStruct(# the carrier of (TOP-REAL 2), the topology of (TOP-REAL 2) #) is non empty strict TopSpace-like TopStruct
the carrier of TopStruct(# the carrier of (TOP-REAL 2), the topology of (TOP-REAL 2) #) is non empty set
K7( the carrier of TopStruct(# the carrier of (TOP-REAL 2), the topology of (TOP-REAL 2) #), the carrier of R^1) is set
K6(K7( the carrier of TopStruct(# the carrier of (TOP-REAL 2), the topology of (TOP-REAL 2) #), the carrier of R^1)) is set
[#] (TOP-REAL 2) is non empty non proper functional closed Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | ([#] (TOP-REAL 2)) is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
p2 is non empty Relation-like the carrier of TopStruct(# the carrier of (TOP-REAL 2), the topology of (TOP-REAL 2) #) -defined the carrier of R^1 -valued Function-like V29( the carrier of TopStruct(# the carrier of (TOP-REAL 2), the topology of (TOP-REAL 2) #)) quasi_total Element of K6(K7( the carrier of TopStruct(# the carrier of (TOP-REAL 2), the topology of (TOP-REAL 2) #), the carrier of R^1))
p1 is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of R^1))
the topology of (TOP-REAL 2) is non empty open Element of K6(K6( the carrier of (TOP-REAL 2)))
K6(K6( the carrier of (TOP-REAL 2))) is set
TopStruct(# the carrier of (TOP-REAL 2), the topology of (TOP-REAL 2) #) is non empty strict TopSpace-like TopStruct
the carrier of TopStruct(# the carrier of (TOP-REAL 2), the topology of (TOP-REAL 2) #) is non empty set
K7( the carrier of TopStruct(# the carrier of (TOP-REAL 2), the topology of (TOP-REAL 2) #), the carrier of R^1) is set
K6(K7( the carrier of TopStruct(# the carrier of (TOP-REAL 2), the topology of (TOP-REAL 2) #), the carrier of R^1)) is set
[#] (TOP-REAL 2) is non empty non proper functional closed Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | ([#] (TOP-REAL 2)) is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
p2 is non empty Relation-like the carrier of TopStruct(# the carrier of (TOP-REAL 2), the topology of (TOP-REAL 2) #) -defined the carrier of R^1 -valued Function-like V29( the carrier of TopStruct(# the carrier of (TOP-REAL 2), the topology of (TOP-REAL 2) #)) quasi_total Element of K6(K7( the carrier of TopStruct(# the carrier of (TOP-REAL 2), the topology of (TOP-REAL 2) #), the carrier of R^1))
p1 is non empty functional closed compact Element of K6( the carrier of (TOP-REAL 2))
Upper_Arc p1 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
Lower_Arc p1 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
p2 is non empty functional closed compact Element of K6( the carrier of (TOP-REAL 2))
Upper_Arc p2 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : ( b1 in p2 & 0 <= b1 `2 ) } is set
Lower_Arc p2 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
Vertical_Line 0 is functional Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : b1 `1 = 0 } is set
W-min p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
E-max p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
First_Point ((Upper_Arc p2),(W-min p2),(E-max p2),(Vertical_Line 0)) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
Last_Point ((Lower_Arc p2),(E-max p2),(W-min p2),(Vertical_Line 0)) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
LSeg (|[0,(- 1)]|,|[0,1]|) is functional Element of K6( the carrier of (TOP-REAL 2))
{ (((1 - b1) * |[0,(- 1)]|) + (b1 * |[0,1]|)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
h is set
f2 is V11() real ext-real Element of REAL
1 - f2 is V11() real ext-real Element of REAL
(1 - f2) * |[0,(- 1)]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
f2 * |[0,1]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
((1 - f2) * |[0,(- 1)]|) + (f2 * |[0,1]|) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(((1 - f2) * |[0,(- 1)]|) + (f2 * |[0,1]|)) `1 is V11() real ext-real Element of REAL
((1 - f2) * |[0,(- 1)]|) `1 is V11() real ext-real Element of REAL
(f2 * |[0,1]|) `1 is V11() real ext-real Element of REAL
(((1 - f2) * |[0,(- 1)]|) `1) + ((f2 * |[0,1]|) `1) is V11() real ext-real Element of REAL
|[0,(- 1)]| `1 is V11() real ext-real Element of REAL
(1 - f2) * (|[0,(- 1)]| `1) is V11() real ext-real Element of REAL
((1 - f2) * (|[0,(- 1)]| `1)) + ((f2 * |[0,1]|) `1) is V11() real ext-real Element of REAL
|[0,1]| `1 is V11() real ext-real Element of REAL
f2 * (|[0,1]| `1) is V11() real ext-real Element of REAL
((1 - f2) * (|[0,(- 1)]| `1)) + (f2 * (|[0,1]| `1)) is V11() real ext-real Element of REAL
(1 - f2) * 0 is V11() real ext-real Element of REAL
((1 - f2) * 0) + (f2 * (|[0,1]| `1)) is V11() real ext-real Element of REAL
f2 * 0 is V11() real ext-real Element of REAL
((1 - f2) * 0) + (f2 * 0) is V11() real ext-real Element of REAL
h is non empty functional Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | h is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | h) is non empty set
K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | h)) is set
K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | h))) is set
f2 is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | h) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | h)))
f2 . 0 is set
f2 . 1 is set
dom f2 is V142() V143() V144() Element of K6( the carrier of I[01])
p1 is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of R^1))
dom p1 is functional Element of K6( the carrier of (TOP-REAL 2))
{(W-min p2),(E-max p2)} is non empty functional set
W-bound p2 is V11() real ext-real Element of REAL
E-bound p2 is V11() real ext-real Element of REAL
(W-bound p2) + (E-bound p2) is V11() real ext-real Element of REAL
((W-bound p2) + (E-bound p2)) / 2 is V11() real ext-real Element of REAL
Vertical_Line (((W-bound p2) + (E-bound p2)) / 2) is functional Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : b1 `1 = ((W-bound p2) + (E-bound p2)) / 2 } is set
First_Point ((Upper_Arc p2),(W-min p2),(E-max p2),(Vertical_Line (((W-bound p2) + (E-bound p2)) / 2))) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(First_Point ((Upper_Arc p2),(W-min p2),(E-max p2),(Vertical_Line (((W-bound p2) + (E-bound p2)) / 2)))) `2 is V11() real ext-real Element of REAL
g2 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
(Upper_Arc p2) /\ g2 is functional Element of K6( the carrier of (TOP-REAL 2))
(Upper_Arc p2) \/ g2 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
Last_Point (g2,(E-max p2),(W-min p2),(Vertical_Line (((W-bound p2) + (E-bound p2)) / 2))) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(Last_Point (g2,(E-max p2),(W-min p2),(Vertical_Line (((W-bound p2) + (E-bound p2)) / 2)))) `2 is V11() real ext-real Element of REAL
rng f2 is Element of K6( the carrier of ((TOP-REAL 2) | h))
K6( the carrier of ((TOP-REAL 2) | h)) is set
[#] ((TOP-REAL 2) | h) is non empty non proper closed Element of K6( the carrier of ((TOP-REAL 2) | h))
S-bound p2 is V11() real ext-real Element of REAL
N-bound p2 is V11() real ext-real Element of REAL
g2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p1 . g2 is V11() real ext-real Element of the carrier of R^1
proj2 . g2 is V11() real ext-real Element of REAL
Last_Point ((Lower_Arc p2),(E-max p2),(W-min p2),(Vertical_Line (((W-bound p2) + (E-bound p2)) / 2))) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(Last_Point ((Lower_Arc p2),(E-max p2),(W-min p2),(Vertical_Line (((W-bound p2) + (E-bound p2)) / 2)))) `2 is V11() real ext-real Element of REAL
(Upper_Arc p2) /\ (Vertical_Line 0) is functional Element of K6( the carrier of (TOP-REAL 2))
g2 is set
f2 . g2 is set
{ b1 where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
h1 is V11() real ext-real Element of REAL
{|[0,(- 1)]|,|[0,1]|} is non empty functional set
O is set
I is non empty functional Element of K6( the carrier of (TOP-REAL 2))
(Upper_Arc p2) /\ I is functional Element of K6( the carrier of (TOP-REAL 2))
(Upper_Arc p2) \/ I is non empty functional Element of K6( the carrier of (TOP-REAL 2))
Last_Point (I,(E-max p2),(W-min p2),(Vertical_Line (((W-bound p2) + (E-bound p2)) / 2))) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(Last_Point (I,(E-max p2),(W-min p2),(Vertical_Line (((W-bound p2) + (E-bound p2)) / 2)))) `2 is V11() real ext-real Element of REAL
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.I.| is V11() real ext-real non negative Element of REAL
0 ^2 is V11() real ext-real Element of REAL
K37(0,0) is empty V11() real ext-real non positive non negative Function-like functional V142() V143() V144() V145() V146() V147() V148() V201() V204() set
I `2 is V11() real ext-real Element of REAL
(I `2) ^2 is V11() real ext-real Element of REAL
K37((I `2),(I `2)) is V11() real ext-real set
(0 ^2) + ((I `2) ^2) is V11() real ext-real Element of REAL
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
KXP is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KXP `1 is V11() real ext-real Element of REAL
KXP is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KXP `1 is V11() real ext-real Element of REAL
(First_Point ((Upper_Arc p2),(W-min p2),(E-max p2),(Vertical_Line 0))) `2 is V11() real ext-real Element of REAL
p1 * f2 is Relation-like the carrier of I[01] -defined the carrier of R^1 -valued Function-like Element of K6(K7( the carrier of I[01], the carrier of R^1))
K7( the carrier of I[01], the carrier of R^1) is set
K6(K7( the carrier of I[01], the carrier of R^1)) is set
rng (p1 * f2) is V142() V143() V144() Element of K6( the carrier of R^1)
dom (p1 * f2) is V142() V143() V144() Element of K6( the carrier of I[01])
KXP is V11() real ext-real Element of REAL
f2 . KXP is set
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
I `2 is V11() real ext-real Element of REAL
KXP is V11() real ext-real Element of REAL
f2 . KXP is set
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
I `2 is V11() real ext-real Element of REAL
KXN is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KXN `2 is V11() real ext-real Element of REAL
KXN is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KXN `2 is V11() real ext-real Element of REAL
KYP is set
f2 . KYP is set
(p1 * f2) . KXP is set
p1 . I is V11() real ext-real Element of the carrier of R^1
KYN is V11() real ext-real Element of REAL
(p1 * f2) . KYN is set
p1 . KXN is V11() real ext-real Element of the carrier of R^1
[.KYN,KXP.] is V142() V143() V144() V204() Element of K6(REAL)
x2 is non empty V142() V143() V144() Element of K6( the carrier of I[01])
z3 is V142() V143() V144() Element of K6( the carrier of I[01])
I[01] | z3 is strict TopSpace-like V196() SubSpace of I[01]
the carrier of (I[01] | z3) is V142() V143() V144() set
K7( the carrier of (I[01] | z3), the carrier of R^1) is set
K6(K7( the carrier of (I[01] | z3), the carrier of R^1)) is set
O is non empty Relation-like the carrier of I[01] -defined the carrier of R^1 -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of R^1))
O | z3 is Relation-like the carrier of I[01] -defined the carrier of R^1 -valued Function-like Element of K6(K7( the carrier of I[01], the carrier of R^1))
(KXN `2) * (I `2) is V11() real ext-real Element of REAL
{ b1 where b1 is V11() real ext-real Element of REAL : ( KYN <= b1 & b1 <= KXP ) } is set
z2 is Relation-like the carrier of (I[01] | z3) -defined the carrier of R^1 -valued Function-like V29( the carrier of (I[01] | z3)) quasi_total Element of K6(K7( the carrier of (I[01] | z3), the carrier of R^1))
z2 . KXP is set
z2 . KYN is set
Closed-Interval-TSpace (KYN,KXP) is non empty strict TopSpace-like V196() SubSpace of R^1
I[01] | x2 is non empty strict TopSpace-like V196() SubSpace of I[01]
f4 is V11() real ext-real Element of REAL
z2 . f4 is set
f2 . f4 is set
g is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.g.| is V11() real ext-real non negative Element of REAL
g `2 is V11() real ext-real Element of REAL
p1 . (f2 . f4) is set
O . f4 is set
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
g `1 is V11() real ext-real Element of REAL
(g `1) ^2 is V11() real ext-real Element of REAL
K37((g `1),(g `1)) is V11() real ext-real set
0 ^2 is V11() real ext-real Element of REAL
K37(0,0) is empty V11() real ext-real non positive non negative Function-like functional V142() V143() V144() V145() V146() V147() V148() V201() V204() set
((g `1) ^2) + (0 ^2) is V11() real ext-real Element of REAL
[.KXP,KYN.] is V142() V143() V144() V204() Element of K6(REAL)
x2 is non empty V142() V143() V144() Element of K6( the carrier of I[01])
z3 is V142() V143() V144() Element of K6( the carrier of I[01])
I[01] | z3 is strict TopSpace-like V196() SubSpace of I[01]
the carrier of (I[01] | z3) is V142() V143() V144() set
K7( the carrier of (I[01] | z3), the carrier of R^1) is set
K6(K7( the carrier of (I[01] | z3), the carrier of R^1)) is set
O is non empty Relation-like the carrier of I[01] -defined the carrier of R^1 -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of R^1))
O | z3 is Relation-like the carrier of I[01] -defined the carrier of R^1 -valued Function-like Element of K6(K7( the carrier of I[01], the carrier of R^1))
(KXN `2) * (I `2) is V11() real ext-real Element of REAL
{ b1 where b1 is V11() real ext-real Element of REAL : ( KXP <= b1 & b1 <= KYN ) } is set
z2 is Relation-like the carrier of (I[01] | z3) -defined the carrier of R^1 -valued Function-like V29( the carrier of (I[01] | z3)) quasi_total Element of K6(K7( the carrier of (I[01] | z3), the carrier of R^1))
z2 . KXP is set
z2 . KYN is set
Closed-Interval-TSpace (KXP,KYN) is non empty strict TopSpace-like V196() SubSpace of R^1
I[01] | x2 is non empty strict TopSpace-like V196() SubSpace of I[01]
f4 is V11() real ext-real Element of REAL
z2 . f4 is set
f2 . f4 is set
g is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.g.| is V11() real ext-real non negative Element of REAL
g `2 is V11() real ext-real Element of REAL
p1 . (f2 . f4) is set
(p1 * f2) . f4 is set
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
g `1 is V11() real ext-real Element of REAL
(g `1) ^2 is V11() real ext-real Element of REAL
K37((g `1),(g `1)) is V11() real ext-real set
0 ^2 is V11() real ext-real Element of REAL
K37(0,0) is empty V11() real ext-real non positive non negative Function-like functional V142() V143() V144() V145() V146() V147() V148() V201() V204() set
((g `1) ^2) + (0 ^2) is V11() real ext-real Element of REAL
KXN is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KXN `2 is V11() real ext-real Element of REAL
I is non empty functional Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | I is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | I) is non empty set
K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | I)) is set
K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | I))) is set
KXP is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | I) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | I)))
KXP . 0 is set
KXP . 1 is set
dom KXP is V142() V143() V144() Element of K6( the carrier of I[01])
p1 * KXP is Relation-like the carrier of I[01] -defined the carrier of R^1 -valued Function-like Element of K6(K7( the carrier of I[01], the carrier of R^1))
rng (p1 * KXP) is V142() V143() V144() Element of K6( the carrier of R^1)
rng KXP is Element of K6( the carrier of ((TOP-REAL 2) | I))
K6( the carrier of ((TOP-REAL 2) | I)) is set
dom (p1 * KXP) is V142() V143() V144() Element of K6( the carrier of I[01])
(Upper_Arc p2) \/ (Lower_Arc p2) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
(Lower_Arc p2) /\ (Vertical_Line 0) is functional Element of K6( the carrier of (TOP-REAL 2))
KYP is set
KYN is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.KYN.| is V11() real ext-real non negative Element of REAL
0 ^2 is V11() real ext-real Element of REAL
K37(0,0) is empty V11() real ext-real non positive non negative Function-like functional V142() V143() V144() V145() V146() V147() V148() V201() V204() set
KYN `2 is V11() real ext-real Element of REAL
(KYN `2) ^2 is V11() real ext-real Element of REAL
K37((KYN `2),(KYN `2)) is V11() real ext-real set
(0 ^2) + ((KYN `2) ^2) is V11() real ext-real Element of REAL
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
x2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
x2 `1 is V11() real ext-real Element of REAL
x2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
x2 `1 is V11() real ext-real Element of REAL
KYP is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p1 . KYP is V11() real ext-real Element of the carrier of R^1
proj2 . KYP is V11() real ext-real Element of REAL
KYN is V11() real ext-real Element of REAL
KXP . KYN is set
KYP is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KYP `2 is V11() real ext-real Element of REAL
KYN is V11() real ext-real Element of REAL
KXP . KYN is set
KYP is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KYP `2 is V11() real ext-real Element of REAL
x2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
x2 `2 is V11() real ext-real Element of REAL
x2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
x2 `2 is V11() real ext-real Element of REAL
[#] ((TOP-REAL 2) | I) is non empty non proper closed Element of K6( the carrier of ((TOP-REAL 2) | I))
z3 is set
KXP . z3 is set
(p1 * KXP) . KYN is set
p1 . KYP is V11() real ext-real Element of the carrier of R^1
z2 is V11() real ext-real Element of REAL
(p1 * KXP) . z2 is set
p1 . x2 is V11() real ext-real Element of the carrier of R^1
[.z2,KYN.] is V142() V143() V144() V204() Element of K6(REAL)
f4 is non empty V142() V143() V144() Element of K6( the carrier of I[01])
g is V142() V143() V144() Element of K6( the carrier of I[01])
I[01] | g is strict TopSpace-like V196() SubSpace of I[01]
the carrier of (I[01] | g) is V142() V143() V144() set
K7( the carrier of (I[01] | g), the carrier of R^1) is set
K6(K7( the carrier of (I[01] | g), the carrier of R^1)) is set
KXN is non empty Relation-like the carrier of I[01] -defined the carrier of R^1 -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of R^1))
KXN | g is Relation-like the carrier of I[01] -defined the carrier of R^1 -valued Function-like Element of K6(K7( the carrier of I[01], the carrier of R^1))
(x2 `2) * (KYP `2) is V11() real ext-real Element of REAL
{ b1 where b1 is V11() real ext-real Element of REAL : ( z2 <= b1 & b1 <= KYN ) } is set
q is Relation-like the carrier of (I[01] | g) -defined the carrier of R^1 -valued Function-like V29( the carrier of (I[01] | g)) quasi_total Element of K6(K7( the carrier of (I[01] | g), the carrier of R^1))
q . KYN is set
q . z2 is set
Closed-Interval-TSpace (z2,KYN) is non empty strict TopSpace-like V196() SubSpace of R^1
I[01] | f4 is non empty strict TopSpace-like V196() SubSpace of I[01]
r1 is V11() real ext-real Element of REAL
q . r1 is set
KXP . r1 is set
q3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.q3.| is V11() real ext-real non negative Element of REAL
q3 `2 is V11() real ext-real Element of REAL
p1 . (KXP . r1) is set
(p1 * KXP) . r1 is set
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
q3 `1 is V11() real ext-real Element of REAL
(q3 `1) ^2 is V11() real ext-real Element of REAL
K37((q3 `1),(q3 `1)) is V11() real ext-real set
0 ^2 is V11() real ext-real Element of REAL
K37(0,0) is empty V11() real ext-real non positive non negative Function-like functional V142() V143() V144() V145() V146() V147() V148() V201() V204() set
((q3 `1) ^2) + (0 ^2) is V11() real ext-real Element of REAL
[.KYN,z2.] is V142() V143() V144() V204() Element of K6(REAL)
f4 is non empty V142() V143() V144() Element of K6( the carrier of I[01])
g is V142() V143() V144() Element of K6( the carrier of I[01])
I[01] | g is strict TopSpace-like V196() SubSpace of I[01]
the carrier of (I[01] | g) is V142() V143() V144() set
K7( the carrier of (I[01] | g), the carrier of R^1) is set
K6(K7( the carrier of (I[01] | g), the carrier of R^1)) is set
KXN is non empty Relation-like the carrier of I[01] -defined the carrier of R^1 -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of R^1))
KXN | g is Relation-like the carrier of I[01] -defined the carrier of R^1 -valued Function-like Element of K6(K7( the carrier of I[01], the carrier of R^1))
(x2 `2) * (KYP `2) is V11() real ext-real Element of REAL
{ b1 where b1 is V11() real ext-real Element of REAL : ( KYN <= b1 & b1 <= z2 ) } is set
q is Relation-like the carrier of (I[01] | g) -defined the carrier of R^1 -valued Function-like V29( the carrier of (I[01] | g)) quasi_total Element of K6(K7( the carrier of (I[01] | g), the carrier of R^1))
q . KYN is set
q . z2 is set
Closed-Interval-TSpace (KYN,z2) is non empty strict TopSpace-like V196() SubSpace of R^1
I[01] | f4 is non empty strict TopSpace-like V196() SubSpace of I[01]
r1 is V11() real ext-real Element of REAL
q . r1 is set
KXP . r1 is set
q3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.q3.| is V11() real ext-real non negative Element of REAL
q3 `2 is V11() real ext-real Element of REAL
p1 . (KXP . r1) is set
KXN . r1 is set
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
q3 `1 is V11() real ext-real Element of REAL
(q3 `1) ^2 is V11() real ext-real Element of REAL
K37((q3 `1),(q3 `1)) is V11() real ext-real set
0 ^2 is V11() real ext-real Element of REAL
K37(0,0) is empty V11() real ext-real non positive non negative Function-like functional V142() V143() V144() V145() V146() V147() V148() V201() V204() set
((q3 `1) ^2) + (0 ^2) is V11() real ext-real Element of REAL
x2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
x2 `2 is V11() real ext-real Element of REAL
KYP is non empty functional Element of K6( the carrier of (TOP-REAL 2))
(Upper_Arc p2) /\ KYP is functional Element of K6( the carrier of (TOP-REAL 2))
(Upper_Arc p2) \/ KYP is non empty functional Element of K6( the carrier of (TOP-REAL 2))
Last_Point (KYP,(E-max p2),(W-min p2),(Vertical_Line (((W-bound p2) + (E-bound p2)) / 2))) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(Last_Point (KYP,(E-max p2),(W-min p2),(Vertical_Line (((W-bound p2) + (E-bound p2)) / 2)))) `2 is V11() real ext-real Element of REAL
KYP is non empty functional Element of K6( the carrier of (TOP-REAL 2))
(Upper_Arc p2) /\ KYP is functional Element of K6( the carrier of (TOP-REAL 2))
(Upper_Arc p2) \/ KYP is non empty functional Element of K6( the carrier of (TOP-REAL 2))
Last_Point (KYP,(E-max p2),(W-min p2),(Vertical_Line (((W-bound p2) + (E-bound p2)) / 2))) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(Last_Point (KYP,(E-max p2),(W-min p2),(Vertical_Line (((W-bound p2) + (E-bound p2)) / 2)))) `2 is V11() real ext-real Element of REAL
KYP is set
KYN is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KYN `2 is V11() real ext-real Element of REAL
KYN `1 is V11() real ext-real Element of REAL
(KYN `1) ^2 is V11() real ext-real Element of REAL
K37((KYN `1),(KYN `1)) is V11() real ext-real set
(KYN `2) ^2 is V11() real ext-real Element of REAL
K37((KYN `2),(KYN `2)) is V11() real ext-real set
((KYN `1) ^2) + ((KYN `2) ^2) is V11() real ext-real Element of REAL
sqrt (((KYN `1) ^2) + ((KYN `2) ^2)) is V11() real ext-real Element of REAL
abs (KYN `1) is V11() real ext-real Element of REAL
x2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.x2.| is V11() real ext-real non negative Element of REAL
|[(KYN `1),(KYN `2)]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
[#] ((TOP-REAL 2) | I) is non empty non proper closed Element of K6( the carrier of ((TOP-REAL 2) | I))
x2 is set
KXP . x2 is set
z3 is V11() real ext-real Element of REAL
|[0,(- 1)]| `2 is V11() real ext-real Element of REAL
|[0,(- 1)]| `1 is V11() real ext-real Element of REAL
|.|[0,(- 1)]|.| is V11() real ext-real non negative Element of REAL
0 ^2 is V11() real ext-real Element of REAL
K37(0,0) is empty V11() real ext-real non positive non negative Function-like functional V142() V143() V144() V145() V146() V147() V148() V201() V204() set
(- 1) ^2 is V11() real ext-real Element of REAL
K37((- 1),(- 1)) is V11() real ext-real non negative set
(0 ^2) + ((- 1) ^2) is V11() real ext-real Element of REAL
sqrt ((0 ^2) + ((- 1) ^2)) is V11() real ext-real Element of REAL
KYP is set
KYN is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KYN `2 is V11() real ext-real Element of REAL
Vertical_Line 0 is functional Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : b1 `1 = 0 } is set
p3 is non empty functional closed compact Element of K6( the carrier of (TOP-REAL 2))
Lower_Arc p3 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : ( b1 in p3 & b1 `2 <= 0 ) } is set
Upper_Arc p3 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
W-min p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
E-max p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
First_Point ((Upper_Arc p3),(W-min p3),(E-max p3),(Vertical_Line 0)) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
Last_Point ((Lower_Arc p3),(E-max p3),(W-min p3),(Vertical_Line 0)) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
LSeg (|[0,(- 1)]|,|[0,1]|) is functional Element of K6( the carrier of (TOP-REAL 2))
{ (((1 - b1) * |[0,(- 1)]|) + (b1 * |[0,1]|)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
p2 is functional Element of K6( the carrier of (TOP-REAL 2))
h is set
f2 is V11() real ext-real Element of REAL
1 - f2 is V11() real ext-real Element of REAL
(1 - f2) * |[0,(- 1)]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
f2 * |[0,1]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
((1 - f2) * |[0,(- 1)]|) + (f2 * |[0,1]|) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(((1 - f2) * |[0,(- 1)]|) + (f2 * |[0,1]|)) `1 is V11() real ext-real Element of REAL
((1 - f2) * |[0,(- 1)]|) `1 is V11() real ext-real Element of REAL
(f2 * |[0,1]|) `1 is V11() real ext-real Element of REAL
(((1 - f2) * |[0,(- 1)]|) `1) + ((f2 * |[0,1]|) `1) is V11() real ext-real Element of REAL
|[0,(- 1)]| `1 is V11() real ext-real Element of REAL
(1 - f2) * (|[0,(- 1)]| `1) is V11() real ext-real Element of REAL
((1 - f2) * (|[0,(- 1)]| `1)) + ((f2 * |[0,1]|) `1) is V11() real ext-real Element of REAL
|[0,1]| `1 is V11() real ext-real Element of REAL
f2 * (|[0,1]| `1) is V11() real ext-real Element of REAL
((1 - f2) * (|[0,(- 1)]| `1)) + (f2 * (|[0,1]| `1)) is V11() real ext-real Element of REAL
(1 - f2) * 0 is V11() real ext-real Element of REAL
((1 - f2) * 0) + (f2 * (|[0,1]| `1)) is V11() real ext-real Element of REAL
f2 * 0 is V11() real ext-real Element of REAL
((1 - f2) * 0) + (f2 * 0) is V11() real ext-real Element of REAL
(Upper_Arc p3) \/ (Lower_Arc p3) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
C0 is functional Element of K6( the carrier of (TOP-REAL 2))
C0 /\ p2 is functional Element of K6( the carrier of (TOP-REAL 2))
{|[0,(- 1)]|,|[0,1]|} is non empty functional set
h is set
f2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.f2.| is V11() real ext-real non negative Element of REAL
0 ^2 is V11() real ext-real Element of REAL
K37(0,0) is empty V11() real ext-real non positive non negative Function-like functional V142() V143() V144() V145() V146() V147() V148() V201() V204() set
f2 `2 is V11() real ext-real Element of REAL
(f2 `2) ^2 is V11() real ext-real Element of REAL
K37((f2 `2),(f2 `2)) is V11() real ext-real set
(0 ^2) + ((f2 `2) ^2) is V11() real ext-real Element of REAL
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
g2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g2 `1 is V11() real ext-real Element of REAL
g2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g2 `1 is V11() real ext-real Element of REAL
p1 is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of R^1))
h is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p1 . h is V11() real ext-real Element of the carrier of R^1
proj2 . h is V11() real ext-real Element of REAL
f2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p1 . f2 is V11() real ext-real Element of the carrier of R^1
proj2 . f2 is V11() real ext-real Element of REAL
S-bound p3 is V11() real ext-real Element of REAL
N-bound p3 is V11() real ext-real Element of REAL
W-bound p3 is V11() real ext-real Element of REAL
E-bound p3 is V11() real ext-real Element of REAL
P is functional Element of K6( the carrier of (TOP-REAL 2))
(Upper_Arc p3) /\ (Lower_Arc p3) is functional Element of K6( the carrier of (TOP-REAL 2))
{(W-min p3),(E-max p3)} is non empty functional set
h is non empty functional Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | h is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | h) is non empty set
K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | h)) is set
K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | h))) is set
f2 is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | h) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | h)))
f2 . 0 is set
f2 . 1 is set
dom f2 is V142() V143() V144() Element of K6( the carrier of I[01])
dom p1 is functional Element of K6( the carrier of (TOP-REAL 2))
rng f2 is Element of K6( the carrier of ((TOP-REAL 2) | h))
K6( the carrier of ((TOP-REAL 2) | h)) is set
[#] ((TOP-REAL 2) | h) is non empty non proper closed Element of K6( the carrier of ((TOP-REAL 2) | h))
p1 * f2 is Relation-like the carrier of I[01] -defined the carrier of R^1 -valued Function-like Element of K6(K7( the carrier of I[01], the carrier of R^1))
K7( the carrier of I[01], the carrier of R^1) is set
K6(K7( the carrier of I[01], the carrier of R^1)) is set
rng (p1 * f2) is V142() V143() V144() Element of K6( the carrier of R^1)
dom (p1 * f2) is V142() V143() V144() Element of K6( the carrier of I[01])
O is V11() real ext-real Element of REAL
f2 . O is set
h1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
h1 `2 is V11() real ext-real Element of REAL
O is V11() real ext-real Element of REAL
f2 . O is set
h1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
h1 `2 is V11() real ext-real Element of REAL
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
I `2 is V11() real ext-real Element of REAL
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
I `2 is V11() real ext-real Element of REAL
KXP is set
f2 . KXP is set
{ b1 where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
(p1 * f2) . O is set
p1 . h1 is V11() real ext-real Element of the carrier of R^1
KXN is V11() real ext-real Element of REAL
(p1 * f2) . KXN is set
p1 . I is V11() real ext-real Element of the carrier of R^1
[.KXN,O.] is V142() V143() V144() V204() Element of K6(REAL)
KYP is non empty V142() V143() V144() Element of K6( the carrier of I[01])
KYN is V142() V143() V144() Element of K6( the carrier of I[01])
I[01] | KYN is strict TopSpace-like V196() SubSpace of I[01]
the carrier of (I[01] | KYN) is V142() V143() V144() set
K7( the carrier of (I[01] | KYN), the carrier of R^1) is set
K6(K7( the carrier of (I[01] | KYN), the carrier of R^1)) is set
g2 is non empty Relation-like the carrier of I[01] -defined the carrier of R^1 -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of R^1))
g2 | KYN is Relation-like the carrier of I[01] -defined the carrier of R^1 -valued Function-like Element of K6(K7( the carrier of I[01], the carrier of R^1))
(I `2) * (h1 `2) is V11() real ext-real Element of REAL
{ b1 where b1 is V11() real ext-real Element of REAL : ( KXN <= b1 & b1 <= O ) } is set
x2 is Relation-like the carrier of (I[01] | KYN) -defined the carrier of R^1 -valued Function-like V29( the carrier of (I[01] | KYN)) quasi_total Element of K6(K7( the carrier of (I[01] | KYN), the carrier of R^1))
x2 . O is set
x2 . KXN is set
Closed-Interval-TSpace (KXN,O) is non empty strict TopSpace-like V196() SubSpace of R^1
I[01] | KYP is non empty strict TopSpace-like V196() SubSpace of I[01]
z3 is V11() real ext-real Element of REAL
x2 . z3 is set
f2 . z3 is set
z2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.z2.| is V11() real ext-real non negative Element of REAL
z2 `2 is V11() real ext-real Element of REAL
p1 . (f2 . z3) is set
(p1 * f2) . z3 is set
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
z2 `1 is V11() real ext-real Element of REAL
(z2 `1) ^2 is V11() real ext-real Element of REAL
K37((z2 `1),(z2 `1)) is V11() real ext-real set
0 ^2 is V11() real ext-real Element of REAL
K37(0,0) is empty V11() real ext-real non positive non negative Function-like functional V142() V143() V144() V145() V146() V147() V148() V201() V204() set
((z2 `1) ^2) + (0 ^2) is V11() real ext-real Element of REAL
[.O,KXN.] is V142() V143() V144() V204() Element of K6(REAL)
KYP is non empty V142() V143() V144() Element of K6( the carrier of I[01])
KYN is V142() V143() V144() Element of K6( the carrier of I[01])
I[01] | KYN is strict TopSpace-like V196() SubSpace of I[01]
the carrier of (I[01] | KYN) is V142() V143() V144() set
K7( the carrier of (I[01] | KYN), the carrier of R^1) is set
K6(K7( the carrier of (I[01] | KYN), the carrier of R^1)) is set
g2 is non empty Relation-like the carrier of I[01] -defined the carrier of R^1 -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of R^1))
g2 | KYN is Relation-like the carrier of I[01] -defined the carrier of R^1 -valued Function-like Element of K6(K7( the carrier of I[01], the carrier of R^1))
(I `2) * (h1 `2) is V11() real ext-real Element of REAL
{ b1 where b1 is V11() real ext-real Element of REAL : ( O <= b1 & b1 <= KXN ) } is set
x2 is Relation-like the carrier of (I[01] | KYN) -defined the carrier of R^1 -valued Function-like V29( the carrier of (I[01] | KYN)) quasi_total Element of K6(K7( the carrier of (I[01] | KYN), the carrier of R^1))
x2 . O is set
x2 . KXN is set
Closed-Interval-TSpace (O,KXN) is non empty strict TopSpace-like V196() SubSpace of R^1
I[01] | KYP is non empty strict TopSpace-like V196() SubSpace of I[01]
z3 is V11() real ext-real Element of REAL
x2 . z3 is set
f2 . z3 is set
z2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.z2.| is V11() real ext-real non negative Element of REAL
z2 `2 is V11() real ext-real Element of REAL
p1 . (f2 . z3) is set
(p1 * f2) . z3 is set
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
z2 `1 is V11() real ext-real Element of REAL
(z2 `1) ^2 is V11() real ext-real Element of REAL
K37((z2 `1),(z2 `1)) is V11() real ext-real set
0 ^2 is V11() real ext-real Element of REAL
K37(0,0) is empty V11() real ext-real non positive non negative Function-like functional V142() V143() V144() V145() V146() V147() V148() V201() V204() set
((z2 `1) ^2) + (0 ^2) is V11() real ext-real Element of REAL
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
I `2 is V11() real ext-real Element of REAL
h1 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | h1 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | h1) is non empty set
K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | h1)) is set
K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | h1))) is set
O is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | h1) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | h1)))
O . 0 is set
O . 1 is set
dom O is V142() V143() V144() Element of K6( the carrier of I[01])
p1 * O is Relation-like the carrier of I[01] -defined the carrier of R^1 -valued Function-like Element of K6(K7( the carrier of I[01], the carrier of R^1))
rng (p1 * O) is V142() V143() V144() Element of K6( the carrier of R^1)
rng O is Element of K6( the carrier of ((TOP-REAL 2) | h1))
K6( the carrier of ((TOP-REAL 2) | h1)) is set
dom (p1 * O) is V142() V143() V144() Element of K6( the carrier of I[01])
KXN is V11() real ext-real Element of REAL
O . KXN is set
KXP is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KXP `2 is V11() real ext-real Element of REAL
KXN is V11() real ext-real Element of REAL
O . KXN is set
KXP is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KXP `2 is V11() real ext-real Element of REAL
KYP is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KYP `2 is V11() real ext-real Element of REAL
KYP is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KYP `2 is V11() real ext-real Element of REAL
[#] ((TOP-REAL 2) | h1) is non empty non proper closed Element of K6( the carrier of ((TOP-REAL 2) | h1))
KYN is set
O . KYN is set
{ b1 where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
(p1 * O) . KXN is set
p1 . KXP is V11() real ext-real Element of the carrier of R^1
x2 is V11() real ext-real Element of REAL
(p1 * O) . x2 is set
p1 . KYP is V11() real ext-real Element of the carrier of R^1
[.x2,KXN.] is V142() V143() V144() V204() Element of K6(REAL)
z3 is non empty V142() V143() V144() Element of K6( the carrier of I[01])
z2 is V142() V143() V144() Element of K6( the carrier of I[01])
I[01] | z2 is strict TopSpace-like V196() SubSpace of I[01]
the carrier of (I[01] | z2) is V142() V143() V144() set
K7( the carrier of (I[01] | z2), the carrier of R^1) is set
K6(K7( the carrier of (I[01] | z2), the carrier of R^1)) is set
I is non empty Relation-like the carrier of I[01] -defined the carrier of R^1 -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of R^1))
I | z2 is Relation-like the carrier of I[01] -defined the carrier of R^1 -valued Function-like Element of K6(K7( the carrier of I[01], the carrier of R^1))
(KYP `2) * (KXP `2) is V11() real ext-real Element of REAL
{ b1 where b1 is V11() real ext-real Element of REAL : ( x2 <= b1 & b1 <= KXN ) } is set
f4 is Relation-like the carrier of (I[01] | z2) -defined the carrier of R^1 -valued Function-like V29( the carrier of (I[01] | z2)) quasi_total Element of K6(K7( the carrier of (I[01] | z2), the carrier of R^1))
f4 . KXN is set
f4 . x2 is set
Closed-Interval-TSpace (x2,KXN) is non empty strict TopSpace-like V196() SubSpace of R^1
I[01] | z3 is non empty strict TopSpace-like V196() SubSpace of I[01]
g is V11() real ext-real Element of REAL
f4 . g is set
O . g is set
q is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.q.| is V11() real ext-real non negative Element of REAL
q `2 is V11() real ext-real Element of REAL
p1 . (O . g) is set
(p1 * O) . g is set
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
q `1 is V11() real ext-real Element of REAL
(q `1) ^2 is V11() real ext-real Element of REAL
K37((q `1),(q `1)) is V11() real ext-real set
0 ^2 is V11() real ext-real Element of REAL
K37(0,0) is empty V11() real ext-real non positive non negative Function-like functional V142() V143() V144() V145() V146() V147() V148() V201() V204() set
((q `1) ^2) + (0 ^2) is V11() real ext-real Element of REAL
[.KXN,x2.] is V142() V143() V144() V204() Element of K6(REAL)
z3 is non empty V142() V143() V144() Element of K6( the carrier of I[01])
z2 is V142() V143() V144() Element of K6( the carrier of I[01])
I[01] | z2 is strict TopSpace-like V196() SubSpace of I[01]
the carrier of (I[01] | z2) is V142() V143() V144() set
K7( the carrier of (I[01] | z2), the carrier of R^1) is set
K6(K7( the carrier of (I[01] | z2), the carrier of R^1)) is set
I is non empty Relation-like the carrier of I[01] -defined the carrier of R^1 -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of R^1))
I | z2 is Relation-like the carrier of I[01] -defined the carrier of R^1 -valued Function-like Element of K6(K7( the carrier of I[01], the carrier of R^1))
(KYP `2) * (KXP `2) is V11() real ext-real Element of REAL
{ b1 where b1 is V11() real ext-real Element of REAL : ( KXN <= b1 & b1 <= x2 ) } is set
f4 is Relation-like the carrier of (I[01] | z2) -defined the carrier of R^1 -valued Function-like V29( the carrier of (I[01] | z2)) quasi_total Element of K6(K7( the carrier of (I[01] | z2), the carrier of R^1))
f4 . KXN is set
f4 . x2 is set
Closed-Interval-TSpace (KXN,x2) is non empty strict TopSpace-like V196() SubSpace of R^1
I[01] | z3 is non empty strict TopSpace-like V196() SubSpace of I[01]
g is V11() real ext-real Element of REAL
f4 . g is set
O . g is set
q is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.q.| is V11() real ext-real non negative Element of REAL
q `2 is V11() real ext-real Element of REAL
p1 . (O . g) is set
(p1 * O) . g is set
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
q `1 is V11() real ext-real Element of REAL
(q `1) ^2 is V11() real ext-real Element of REAL
K37((q `1),(q `1)) is V11() real ext-real set
0 ^2 is V11() real ext-real Element of REAL
K37(0,0) is empty V11() real ext-real non positive non negative Function-like functional V142() V143() V144() V145() V146() V147() V148() V201() V204() set
((q `1) ^2) + (0 ^2) is V11() real ext-real Element of REAL
KYP is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KYP `2 is V11() real ext-real Element of REAL
P /\ p2 is functional Element of K6( the carrier of (TOP-REAL 2))
KXP is set
f2 . KXP is set
{ b1 where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
KXN is V11() real ext-real Element of REAL
KYP is set
KYN is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.KYN.| is V11() real ext-real non negative Element of REAL
0 ^2 is V11() real ext-real Element of REAL
K37(0,0) is empty V11() real ext-real non positive non negative Function-like functional V142() V143() V144() V145() V146() V147() V148() V201() V204() set
KYN `2 is V11() real ext-real Element of REAL
(KYN `2) ^2 is V11() real ext-real Element of REAL
K37((KYN `2),(KYN `2)) is V11() real ext-real set
(0 ^2) + ((KYN `2) ^2) is V11() real ext-real Element of REAL
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
x2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
x2 `1 is V11() real ext-real Element of REAL
x2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
x2 `1 is V11() real ext-real Element of REAL
(Last_Point ((Lower_Arc p3),(E-max p3),(W-min p3),(Vertical_Line 0))) `2 is V11() real ext-real Element of REAL
(W-bound p3) + (E-bound p3) is V11() real ext-real Element of REAL
((W-bound p3) + (E-bound p3)) / 2 is V11() real ext-real Element of REAL
Vertical_Line (((W-bound p3) + (E-bound p3)) / 2) is functional Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : b1 `1 = ((W-bound p3) + (E-bound p3)) / 2 } is set
First_Point ((Upper_Arc p3),(W-min p3),(E-max p3),(Vertical_Line (((W-bound p3) + (E-bound p3)) / 2))) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(First_Point ((Upper_Arc p3),(W-min p3),(E-max p3),(Vertical_Line (((W-bound p3) + (E-bound p3)) / 2)))) `2 is V11() real ext-real Element of REAL
Last_Point ((Lower_Arc p3),(E-max p3),(W-min p3),(Vertical_Line (((W-bound p3) + (E-bound p3)) / 2))) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(Last_Point ((Lower_Arc p3),(E-max p3),(W-min p3),(Vertical_Line (((W-bound p3) + (E-bound p3)) / 2)))) `2 is V11() real ext-real Element of REAL
KYP is set
KYN is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KYN `2 is V11() real ext-real Element of REAL
KYN `1 is V11() real ext-real Element of REAL
(KYN `1) ^2 is V11() real ext-real Element of REAL
K37((KYN `1),(KYN `1)) is V11() real ext-real set
(KYN `2) ^2 is V11() real ext-real Element of REAL
K37((KYN `2),(KYN `2)) is V11() real ext-real set
((KYN `1) ^2) + ((KYN `2) ^2) is V11() real ext-real Element of REAL
sqrt (((KYN `1) ^2) + ((KYN `2) ^2)) is V11() real ext-real Element of REAL
abs (KYN `1) is V11() real ext-real Element of REAL
x2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.x2.| is V11() real ext-real non negative Element of REAL
|[(KYN `1),(KYN `2)]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
[#] ((TOP-REAL 2) | h1) is non empty non proper closed Element of K6( the carrier of ((TOP-REAL 2) | h1))
x2 is set
O . x2 is set
z3 is V11() real ext-real Element of REAL
|[0,1]| `2 is V11() real ext-real Element of REAL
|[0,1]| `1 is V11() real ext-real Element of REAL
|.|[0,1]|.| is V11() real ext-real non negative Element of REAL
0 ^2 is V11() real ext-real Element of REAL
K37(0,0) is empty V11() real ext-real non positive non negative Function-like functional V142() V143() V144() V145() V146() V147() V148() V201() V204() set
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
(0 ^2) + (1 ^2) is V11() real ext-real Element of REAL
sqrt ((0 ^2) + (1 ^2)) is V11() real ext-real Element of REAL
KYP is set
KYN is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KYN `2 is V11() real ext-real Element of REAL
p1 is V11() real ext-real Element of REAL
p2 is V11() real ext-real Element of REAL
p4 is V11() real ext-real Element of REAL
Closed-Interval-TSpace (p1,p2) is non empty strict TopSpace-like V196() SubSpace of R^1
the carrier of (Closed-Interval-TSpace (p1,p2)) is non empty V142() V143() V144() set
p4 * p1 is V11() real ext-real Element of REAL
p3 is V11() real ext-real Element of REAL
(p4 * p1) + p3 is V11() real ext-real Element of REAL
p4 * p2 is V11() real ext-real Element of REAL
(p4 * p2) + p3 is V11() real ext-real Element of REAL
Closed-Interval-TSpace (((p4 * p1) + p3),((p4 * p2) + p3)) is non empty strict TopSpace-like V196() SubSpace of R^1
the carrier of (Closed-Interval-TSpace (((p4 * p1) + p3),((p4 * p2) + p3))) is non empty V142() V143() V144() set
K7( the carrier of (Closed-Interval-TSpace (p1,p2)), the carrier of (Closed-Interval-TSpace (((p4 * p1) + p3),((p4 * p2) + p3)))) is set
K6(K7( the carrier of (Closed-Interval-TSpace (p1,p2)), the carrier of (Closed-Interval-TSpace (((p4 * p1) + p3),((p4 * p2) + p3))))) is set
[.p1,p2.] is V142() V143() V144() V204() Element of K6(REAL)
f is V142() V143() V144() Element of K6( the carrier of R^1)
R^1 | f is strict TopSpace-like V196() SubSpace of R^1
[.((p4 * p1) + p3),((p4 * p2) + p3).] is V142() V143() V144() V204() Element of K6(REAL)
Closed-Interval-MSpace (((p4 * p1) + p3),((p4 * p2) + p3)) is non empty strict Reflexive discerning V91() triangle Discerning SubSpace of RealSpace
TopSpaceMetr (Closed-Interval-MSpace (((p4 * p1) + p3),((p4 * p2) + p3))) is TopStruct
g2 is set
h1 is V11() real ext-real Element of REAL
p4 * h1 is V11() real ext-real Element of REAL
(p4 * h1) + p3 is V11() real ext-real Element of REAL
I is V11() real ext-real Element of REAL
p4 * I is V11() real ext-real Element of REAL
(p4 * I) + p3 is V11() real ext-real Element of REAL
g2 is non empty Relation-like the carrier of (Closed-Interval-TSpace (p1,p2)) -defined the carrier of (Closed-Interval-TSpace (((p4 * p1) + p3),((p4 * p2) + p3))) -valued Function-like V29( the carrier of (Closed-Interval-TSpace (p1,p2))) quasi_total Element of K6(K7( the carrier of (Closed-Interval-TSpace (p1,p2)), the carrier of (Closed-Interval-TSpace (((p4 * p1) + p3),((p4 * p2) + p3)))))
g2 is non empty Relation-like the carrier of (Closed-Interval-TSpace (p1,p2)) -defined the carrier of (Closed-Interval-TSpace (((p4 * p1) + p3),((p4 * p2) + p3))) -valued Function-like V29( the carrier of (Closed-Interval-TSpace (p1,p2))) quasi_total Element of K6(K7( the carrier of (Closed-Interval-TSpace (p1,p2)), the carrier of (Closed-Interval-TSpace (((p4 * p1) + p3),((p4 * p2) + p3)))))
h1 is non empty Relation-like the carrier of (Closed-Interval-TSpace (p1,p2)) -defined the carrier of (Closed-Interval-TSpace (((p4 * p1) + p3),((p4 * p2) + p3))) -valued Function-like V29( the carrier of (Closed-Interval-TSpace (p1,p2))) quasi_total Element of K6(K7( the carrier of (Closed-Interval-TSpace (p1,p2)), the carrier of (Closed-Interval-TSpace (((p4 * p1) + p3),((p4 * p2) + p3)))))
O is V11() real ext-real Element of REAL
h1 . O is set
p4 * O is V11() real ext-real Element of REAL
(p4 * O) + p3 is V11() real ext-real Element of REAL
dom h1 is V142() V143() V144() Element of K6( the carrier of (Closed-Interval-TSpace (p1,p2)))
K6( the carrier of (Closed-Interval-TSpace (p1,p2))) is set
[#] (Closed-Interval-TSpace (((p4 * p1) + p3),((p4 * p2) + p3))) is non empty non proper closed V142() V143() V144() Element of K6( the carrier of (Closed-Interval-TSpace (((p4 * p1) + p3),((p4 * p2) + p3))))
K6( the carrier of (Closed-Interval-TSpace (((p4 * p1) + p3),((p4 * p2) + p3)))) is set
rng h1 is V142() V143() V144() Element of K6( the carrier of (Closed-Interval-TSpace (((p4 * p1) + p3),((p4 * p2) + p3))))
O is set
I is V11() real ext-real Element of REAL
I - p3 is V11() real ext-real Element of REAL
((p4 * p2) + p3) - p3 is V11() real ext-real Element of REAL
(I - p3) / p4 is V11() real ext-real Element of REAL
p2 * p4 is V11() real ext-real Element of REAL
(p2 * p4) / p4 is V11() real ext-real Element of REAL
((p4 * p1) + p3) - p3 is V11() real ext-real Element of REAL
p1 * p4 is V11() real ext-real Element of REAL
(p1 * p4) / p4 is V11() real ext-real Element of REAL
h1 . ((I - p3) / p4) is set
p4 * ((I - p3) / p4) is V11() real ext-real Element of REAL
(p4 * ((I - p3) / p4)) + p3 is V11() real ext-real Element of REAL
(I - p3) + p3 is V11() real ext-real Element of REAL
K7( the carrier of (Closed-Interval-TSpace (p1,p2)), the carrier of R^1) is set
K6(K7( the carrier of (Closed-Interval-TSpace (p1,p2)), the carrier of R^1)) is set
I is set
KXP is set
h1 . I is set
h1 . KXP is set
KYP is V11() real ext-real Element of REAL
p4 * KYP is V11() real ext-real Element of REAL
(p4 * KYP) + p3 is V11() real ext-real Element of REAL
((p4 * KYP) + p3) - p3 is V11() real ext-real Element of REAL
KXN is V11() real ext-real Element of REAL
p4 * KXN is V11() real ext-real Element of REAL
(p4 * KXN) + p3 is V11() real ext-real Element of REAL
((p4 * KXN) + p3) - p3 is V11() real ext-real Element of REAL
KYP * p4 is V11() real ext-real Element of REAL
(KYP * p4) / p4 is V11() real ext-real Element of REAL
[#] (Closed-Interval-TSpace (p1,p2)) is non empty non proper closed V142() V143() V144() Element of K6( the carrier of (Closed-Interval-TSpace (p1,p2)))
I is set
KXP is V11() real ext-real Element of REAL
p4 * KXP is V11() real ext-real Element of REAL
(p4 * KXP) + p3 is V11() real ext-real Element of REAL
KXN is V11() real ext-real Element of REAL
KYP is V11() real ext-real Element of REAL
p4 * KYP is V11() real ext-real Element of REAL
(p4 * KYP) + p3 is V11() real ext-real Element of REAL
I is non empty Relation-like the carrier of R^1 -defined the carrier of R^1 -valued Function-like V29( the carrier of R^1) quasi_total Element of K6(K7( the carrier of R^1, the carrier of R^1))
I is non empty Relation-like the carrier of R^1 -defined the carrier of R^1 -valued Function-like V29( the carrier of R^1) quasi_total Element of K6(K7( the carrier of R^1, the carrier of R^1))
KXP is non empty Relation-like the carrier of R^1 -defined the carrier of R^1 -valued Function-like V29( the carrier of R^1) quasi_total Element of K6(K7( the carrier of R^1, the carrier of R^1))
KXN is V11() real ext-real Element of REAL
KXP . KXN is set
p4 * KXN is V11() real ext-real Element of REAL
(p4 * KXN) + p3 is V11() real ext-real Element of REAL
dom KXP is V142() V143() V144() Element of K6( the carrier of R^1)
(dom KXP) /\ f is V142() V143() V144() Element of K6( the carrier of R^1)
REAL /\ f is V142() V143() V144() Element of K6( the carrier of R^1)
O is non empty Relation-like the carrier of (Closed-Interval-TSpace (p1,p2)) -defined the carrier of R^1 -valued Function-like V29( the carrier of (Closed-Interval-TSpace (p1,p2))) quasi_total Element of K6(K7( the carrier of (Closed-Interval-TSpace (p1,p2)), the carrier of R^1))
dom O is V142() V143() V144() Element of K6( the carrier of (Closed-Interval-TSpace (p1,p2)))
KXN is set
O . KXN is set
KXP . KXN is set
I . KXN is set
KYP is V11() real ext-real Element of REAL
p4 * KYP is V11() real ext-real Element of REAL
(p4 * KYP) + p3 is V11() real ext-real Element of REAL
KXP | f is Relation-like the carrier of R^1 -defined the carrier of R^1 -valued Function-like Element of K6(K7( the carrier of R^1, the carrier of R^1))
f2 is V142() V143() V144() Element of K6( the carrier of R^1)
R^1 | f2 is strict TopSpace-like V196() SubSpace of R^1
p1 is V11() real ext-real Element of REAL
p2 is V11() real ext-real Element of REAL
p4 is V11() real ext-real Element of REAL
Closed-Interval-TSpace (p1,p2) is non empty strict TopSpace-like V196() SubSpace of R^1
the carrier of (Closed-Interval-TSpace (p1,p2)) is non empty V142() V143() V144() set
p4 * p2 is V11() real ext-real Element of REAL
p3 is V11() real ext-real Element of REAL
(p4 * p2) + p3 is V11() real ext-real Element of REAL
p4 * p1 is V11() real ext-real Element of REAL
(p4 * p1) + p3 is V11() real ext-real Element of REAL
Closed-Interval-TSpace (((p4 * p2) + p3),((p4 * p1) + p3)) is non empty strict TopSpace-like V196() SubSpace of R^1
the carrier of (Closed-Interval-TSpace (((p4 * p2) + p3),((p4 * p1) + p3))) is non empty V142() V143() V144() set
K7( the carrier of (Closed-Interval-TSpace (p1,p2)), the carrier of (Closed-Interval-TSpace (((p4 * p2) + p3),((p4 * p1) + p3)))) is set
K6(K7( the carrier of (Closed-Interval-TSpace (p1,p2)), the carrier of (Closed-Interval-TSpace (((p4 * p2) + p3),((p4 * p1) + p3))))) is set
[.p1,p2.] is V142() V143() V144() V204() Element of K6(REAL)
f is V142() V143() V144() Element of K6( the carrier of R^1)
R^1 | f is strict TopSpace-like V196() SubSpace of R^1
[.((p4 * p2) + p3),((p4 * p1) + p3).] is V142() V143() V144() V204() Element of K6(REAL)
Closed-Interval-MSpace (((p4 * p2) + p3),((p4 * p1) + p3)) is non empty strict Reflexive discerning V91() triangle Discerning SubSpace of RealSpace
TopSpaceMetr (Closed-Interval-MSpace (((p4 * p2) + p3),((p4 * p1) + p3))) is TopStruct
g2 is set
h1 is V11() real ext-real Element of REAL
p4 * h1 is V11() real ext-real Element of REAL
(p4 * h1) + p3 is V11() real ext-real Element of REAL
I is V11() real ext-real Element of REAL
p4 * I is V11() real ext-real Element of REAL
(p4 * I) + p3 is V11() real ext-real Element of REAL
g2 is non empty Relation-like the carrier of (Closed-Interval-TSpace (p1,p2)) -defined the carrier of (Closed-Interval-TSpace (((p4 * p2) + p3),((p4 * p1) + p3))) -valued Function-like V29( the carrier of (Closed-Interval-TSpace (p1,p2))) quasi_total Element of K6(K7( the carrier of (Closed-Interval-TSpace (p1,p2)), the carrier of (Closed-Interval-TSpace (((p4 * p2) + p3),((p4 * p1) + p3)))))
g2 is non empty Relation-like the carrier of (Closed-Interval-TSpace (p1,p2)) -defined the carrier of (Closed-Interval-TSpace (((p4 * p2) + p3),((p4 * p1) + p3))) -valued Function-like V29( the carrier of (Closed-Interval-TSpace (p1,p2))) quasi_total Element of K6(K7( the carrier of (Closed-Interval-TSpace (p1,p2)), the carrier of (Closed-Interval-TSpace (((p4 * p2) + p3),((p4 * p1) + p3)))))
h1 is non empty Relation-like the carrier of (Closed-Interval-TSpace (p1,p2)) -defined the carrier of (Closed-Interval-TSpace (((p4 * p2) + p3),((p4 * p1) + p3))) -valued Function-like V29( the carrier of (Closed-Interval-TSpace (p1,p2))) quasi_total Element of K6(K7( the carrier of (Closed-Interval-TSpace (p1,p2)), the carrier of (Closed-Interval-TSpace (((p4 * p2) + p3),((p4 * p1) + p3)))))
O is V11() real ext-real Element of REAL
h1 . O is set
p4 * O is V11() real ext-real Element of REAL
(p4 * O) + p3 is V11() real ext-real Element of REAL
dom h1 is V142() V143() V144() Element of K6( the carrier of (Closed-Interval-TSpace (p1,p2)))
K6( the carrier of (Closed-Interval-TSpace (p1,p2))) is set
[#] (Closed-Interval-TSpace (((p4 * p2) + p3),((p4 * p1) + p3))) is non empty non proper closed V142() V143() V144() Element of K6( the carrier of (Closed-Interval-TSpace (((p4 * p2) + p3),((p4 * p1) + p3))))
K6( the carrier of (Closed-Interval-TSpace (((p4 * p2) + p3),((p4 * p1) + p3)))) is set
rng h1 is V142() V143() V144() Element of K6( the carrier of (Closed-Interval-TSpace (((p4 * p2) + p3),((p4 * p1) + p3))))
O is set
I is V11() real ext-real Element of REAL
I - p3 is V11() real ext-real Element of REAL
((p4 * p1) + p3) - p3 is V11() real ext-real Element of REAL
p1 * p4 is V11() real ext-real Element of REAL
(p1 * p4) / p4 is V11() real ext-real Element of REAL
(I - p3) / p4 is V11() real ext-real Element of REAL
((p4 * p2) + p3) - p3 is V11() real ext-real Element of REAL
p2 * p4 is V11() real ext-real Element of REAL
(p2 * p4) / p4 is V11() real ext-real Element of REAL
h1 . ((I - p3) / p4) is set
p4 * ((I - p3) / p4) is V11() real ext-real Element of REAL
(p4 * ((I - p3) / p4)) + p3 is V11() real ext-real Element of REAL
(I - p3) + p3 is V11() real ext-real Element of REAL
K7( the carrier of (Closed-Interval-TSpace (p1,p2)), the carrier of R^1) is set
K6(K7( the carrier of (Closed-Interval-TSpace (p1,p2)), the carrier of R^1)) is set
I is set
KXP is set
h1 . I is set
h1 . KXP is set
KYP is V11() real ext-real Element of REAL
p4 * KYP is V11() real ext-real Element of REAL
(p4 * KYP) + p3 is V11() real ext-real Element of REAL
((p4 * KYP) + p3) - p3 is V11() real ext-real Element of REAL
KXN is V11() real ext-real Element of REAL
p4 * KXN is V11() real ext-real Element of REAL
(p4 * KXN) + p3 is V11() real ext-real Element of REAL
((p4 * KXN) + p3) - p3 is V11() real ext-real Element of REAL
KYP * p4 is V11() real ext-real Element of REAL
(KYP * p4) / p4 is V11() real ext-real Element of REAL
[#] (Closed-Interval-TSpace (p1,p2)) is non empty non proper closed V142() V143() V144() Element of K6( the carrier of (Closed-Interval-TSpace (p1,p2)))
I is set
KXP is V11() real ext-real Element of REAL
p4 * KXP is V11() real ext-real Element of REAL
(p4 * KXP) + p3 is V11() real ext-real Element of REAL
KXN is V11() real ext-real Element of REAL
KYP is V11() real ext-real Element of REAL
p4 * KYP is V11() real ext-real Element of REAL
(p4 * KYP) + p3 is V11() real ext-real Element of REAL
I is non empty Relation-like the carrier of R^1 -defined the carrier of R^1 -valued Function-like V29( the carrier of R^1) quasi_total Element of K6(K7( the carrier of R^1, the carrier of R^1))
I is non empty Relation-like the carrier of R^1 -defined the carrier of R^1 -valued Function-like V29( the carrier of R^1) quasi_total Element of K6(K7( the carrier of R^1, the carrier of R^1))
KXP is non empty Relation-like the carrier of R^1 -defined the carrier of R^1 -valued Function-like V29( the carrier of R^1) quasi_total Element of K6(K7( the carrier of R^1, the carrier of R^1))
KXN is V11() real ext-real Element of REAL
KXP . KXN is set
p4 * KXN is V11() real ext-real Element of REAL
(p4 * KXN) + p3 is V11() real ext-real Element of REAL
dom KXP is V142() V143() V144() Element of K6( the carrier of R^1)
(dom KXP) /\ f is V142() V143() V144() Element of K6( the carrier of R^1)
REAL /\ f is V142() V143() V144() Element of K6( the carrier of R^1)
O is non empty Relation-like the carrier of (Closed-Interval-TSpace (p1,p2)) -defined the carrier of R^1 -valued Function-like V29( the carrier of (Closed-Interval-TSpace (p1,p2))) quasi_total Element of K6(K7( the carrier of (Closed-Interval-TSpace (p1,p2)), the carrier of R^1))
dom O is V142() V143() V144() Element of K6( the carrier of (Closed-Interval-TSpace (p1,p2)))
KXN is set
O . KXN is set
KXP . KXN is set
I . KXN is set
KYP is V11() real ext-real Element of REAL
p4 * KYP is V11() real ext-real Element of REAL
(p4 * KYP) + p3 is V11() real ext-real Element of REAL
KXP | f is Relation-like the carrier of R^1 -defined the carrier of R^1 -valued Function-like Element of K6(K7( the carrier of R^1, the carrier of R^1))
f2 is V142() V143() V144() Element of K6( the carrier of R^1)
R^1 | f2 is strict TopSpace-like V196() SubSpace of R^1
Closed-Interval-TSpace ((- 1),1) is non empty strict TopSpace-like V196() SubSpace of R^1
the carrier of (Closed-Interval-TSpace ((- 1),1)) is non empty V142() V143() V144() set
K7( the carrier of I[01], the carrier of (Closed-Interval-TSpace ((- 1),1))) is set
K6(K7( the carrier of I[01], the carrier of (Closed-Interval-TSpace ((- 1),1)))) is set
- 2 is V11() real ext-real non positive Element of REAL
(- 2) * 1 is V11() real ext-real non positive Element of REAL
((- 2) * 1) + 1 is V11() real ext-real Element of REAL
(- 2) * 0 is empty V11() real ext-real non positive non negative Function-like functional V142() V143() V144() V145() V146() V147() V148() V201() V204() Element of REAL
((- 2) * 0) + 1 is non empty V11() real ext-real positive non negative Element of REAL
Closed-Interval-TSpace ((((- 2) * 1) + 1),(((- 2) * 0) + 1)) is non empty strict TopSpace-like V196() SubSpace of R^1
the carrier of (Closed-Interval-TSpace ((((- 2) * 1) + 1),(((- 2) * 0) + 1))) is non empty V142() V143() V144() set
K7( the carrier of I[01], the carrier of (Closed-Interval-TSpace ((((- 2) * 1) + 1),(((- 2) * 0) + 1)))) is set
K6(K7( the carrier of I[01], the carrier of (Closed-Interval-TSpace ((((- 2) * 1) + 1),(((- 2) * 0) + 1))))) is set
p1 is non empty Relation-like the carrier of I[01] -defined the carrier of (Closed-Interval-TSpace ((((- 2) * 1) + 1),(((- 2) * 0) + 1))) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (Closed-Interval-TSpace ((((- 2) * 1) + 1),(((- 2) * 0) + 1)))))
p1 . 1 is set
p1 . 0 is set
2 * 0 is empty V11() real ext-real non positive non negative Function-like functional V142() V143() V144() V145() V146() V147() V148() V201() V204() Element of REAL
(2 * 0) + (- 1) is V11() real ext-real non positive Element of REAL
2 * 1 is V11() real ext-real non negative Element of REAL
(2 * 1) + (- 1) is V11() real ext-real Element of REAL
Closed-Interval-TSpace (((2 * 0) + (- 1)),((2 * 1) + (- 1))) is non empty strict TopSpace-like V196() SubSpace of R^1
the carrier of (Closed-Interval-TSpace (((2 * 0) + (- 1)),((2 * 1) + (- 1)))) is non empty V142() V143() V144() set
K7( the carrier of I[01], the carrier of (Closed-Interval-TSpace (((2 * 0) + (- 1)),((2 * 1) + (- 1))))) is set
K6(K7( the carrier of I[01], the carrier of (Closed-Interval-TSpace (((2 * 0) + (- 1)),((2 * 1) + (- 1)))))) is set
p1 is non empty Relation-like the carrier of I[01] -defined the carrier of (Closed-Interval-TSpace (((2 * 0) + (- 1)),((2 * 1) + (- 1)))) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (Closed-Interval-TSpace (((2 * 0) + (- 1)),((2 * 1) + (- 1))))))
p2 is V11() real ext-real Element of REAL
p1 . p2 is set
2 * p2 is V11() real ext-real Element of REAL
(2 * p2) - 1 is V11() real ext-real Element of REAL
(2 * p2) + (- 1) is V11() real ext-real Element of REAL
p1 . 1 is set
(2 * 1) - 1 is V11() real ext-real Element of REAL
p1 . 0 is set
(2 * 0) - 1 is non empty V11() real ext-real non positive negative Element of REAL
p3 is non empty functional closed compact Element of K6( the carrier of (TOP-REAL 2))
Lower_Arc p3 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (Lower_Arc p3) is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (Lower_Arc p3)) is non empty set
K7( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)), the carrier of R^1) is set
K6(K7( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)), the carrier of R^1)) is set
p2 is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of R^1))
p2 | (Lower_Arc p3) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of R^1))
P is non empty Relation-like the carrier of ((TOP-REAL 2) | (Lower_Arc p3)) -defined the carrier of R^1 -valued Function-like V29( the carrier of ((TOP-REAL 2) | (Lower_Arc p3))) quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)), the carrier of R^1))
C0 is Element of the carrier of ((TOP-REAL 2) | (Lower_Arc p3))
P . C0 is V11() real ext-real Element of the carrier of R^1
proj1 . C0 is set
dom P is Element of K6( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)))
K6( the carrier of ((TOP-REAL 2) | (Lower_Arc p3))) is set
rng P is V142() V143() V144() Element of K6( the carrier of R^1)
C0 is set
f is set
P . f is set
g is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.g.| is V11() real ext-real non negative Element of REAL
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
g `1 is V11() real ext-real Element of REAL
(g `1) ^2 is V11() real ext-real Element of REAL
K37((g `1),(g `1)) is V11() real ext-real set
g `2 is V11() real ext-real Element of REAL
(g `2) ^2 is V11() real ext-real Element of REAL
K37((g `2),(g `2)) is V11() real ext-real set
((g `1) ^2) + ((g `2) ^2) is V11() real ext-real Element of REAL
1 - ((g `1) ^2) is V11() real ext-real Element of REAL
- (1 - ((g `1) ^2)) is V11() real ext-real Element of REAL
((g `1) ^2) - 1 is V11() real ext-real Element of REAL
proj1 . g is V11() real ext-real Element of REAL
K7( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)), the carrier of (Closed-Interval-TSpace ((- 1),1))) is set
K6(K7( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)), the carrier of (Closed-Interval-TSpace ((- 1),1)))) is set
C0 is non empty Relation-like the carrier of ((TOP-REAL 2) | (Lower_Arc p3)) -defined the carrier of (Closed-Interval-TSpace ((- 1),1)) -valued Function-like V29( the carrier of ((TOP-REAL 2) | (Lower_Arc p3))) quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)), the carrier of (Closed-Interval-TSpace ((- 1),1))))
dom C0 is Element of K6( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)))
[#] ((TOP-REAL 2) | (Lower_Arc p3)) is non empty non proper closed Element of K6( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)))
f is set
g is set
C0 . f is set
C0 . g is set
h is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
proj1 . h is V11() real ext-real Element of REAL
h `1 is V11() real ext-real Element of REAL
f2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
proj1 . f2 is V11() real ext-real Element of REAL
f2 `1 is V11() real ext-real Element of REAL
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
(h `1) ^2 is V11() real ext-real Element of REAL
K37((h `1),(h `1)) is V11() real ext-real set
h `2 is V11() real ext-real Element of REAL
(h `2) ^2 is V11() real ext-real Element of REAL
K37((h `2),(h `2)) is V11() real ext-real set
((h `1) ^2) + ((h `2) ^2) is V11() real ext-real Element of REAL
g2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.g2.| is V11() real ext-real non negative Element of REAL
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : ( b1 in p3 & b1 `2 <= 0 ) } is set
(f2 `1) ^2 is V11() real ext-real Element of REAL
K37((f2 `1),(f2 `1)) is V11() real ext-real set
f2 `2 is V11() real ext-real Element of REAL
(f2 `2) ^2 is V11() real ext-real Element of REAL
K37((f2 `2),(f2 `2)) is V11() real ext-real set
((f2 `1) ^2) + ((f2 `2) ^2) is V11() real ext-real Element of REAL
g2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.g2.| is V11() real ext-real non negative Element of REAL
- (f2 `2) is V11() real ext-real Element of REAL
(- (f2 `2)) ^2 is V11() real ext-real Element of REAL
K37((- (f2 `2)),(- (f2 `2))) is V11() real ext-real set
- (h `2) is V11() real ext-real Element of REAL
(- (h `2)) ^2 is V11() real ext-real Element of REAL
K37((- (h `2)),(- (h `2))) is V11() real ext-real set
sqrt ((- (h `2)) ^2) is V11() real ext-real Element of REAL
g2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g2 `2 is V11() real ext-real Element of REAL
g2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g2 `2 is V11() real ext-real Element of REAL
|[(h `1),(h `2)]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
[#] (Closed-Interval-TSpace ((- 1),1)) is non empty non proper closed V142() V143() V144() Element of K6( the carrier of (Closed-Interval-TSpace ((- 1),1)))
K6( the carrier of (Closed-Interval-TSpace ((- 1),1))) is set
rng C0 is V142() V143() V144() Element of K6( the carrier of (Closed-Interval-TSpace ((- 1),1)))
f is set
g is V11() real ext-real Element of REAL
g ^2 is V11() real ext-real Element of REAL
K37(g,g) is V11() real ext-real set
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
1 - (g ^2) is V11() real ext-real Element of REAL
sqrt (1 - (g ^2)) is V11() real ext-real Element of REAL
- (sqrt (1 - (g ^2))) is V11() real ext-real Element of REAL
|[g,(- (sqrt (1 - (g ^2))))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|[g,(- (sqrt (1 - (g ^2))))]| `2 is V11() real ext-real Element of REAL
|.|[g,(- (sqrt (1 - (g ^2))))]|.| is V11() real ext-real non negative Element of REAL
|[g,(- (sqrt (1 - (g ^2))))]| `1 is V11() real ext-real Element of REAL
(|[g,(- (sqrt (1 - (g ^2))))]| `1) ^2 is V11() real ext-real Element of REAL
K37((|[g,(- (sqrt (1 - (g ^2))))]| `1),(|[g,(- (sqrt (1 - (g ^2))))]| `1)) is V11() real ext-real set
(|[g,(- (sqrt (1 - (g ^2))))]| `2) ^2 is V11() real ext-real Element of REAL
K37((|[g,(- (sqrt (1 - (g ^2))))]| `2),(|[g,(- (sqrt (1 - (g ^2))))]| `2)) is V11() real ext-real set
((|[g,(- (sqrt (1 - (g ^2))))]| `1) ^2) + ((|[g,(- (sqrt (1 - (g ^2))))]| `2) ^2) is V11() real ext-real Element of REAL
sqrt (((|[g,(- (sqrt (1 - (g ^2))))]| `1) ^2) + ((|[g,(- (sqrt (1 - (g ^2))))]| `2) ^2)) is V11() real ext-real Element of REAL
(g ^2) + ((|[g,(- (sqrt (1 - (g ^2))))]| `2) ^2) is V11() real ext-real Element of REAL
sqrt ((g ^2) + ((|[g,(- (sqrt (1 - (g ^2))))]| `2) ^2)) is V11() real ext-real Element of REAL
(- (sqrt (1 - (g ^2)))) ^2 is V11() real ext-real Element of REAL
K37((- (sqrt (1 - (g ^2)))),(- (sqrt (1 - (g ^2))))) is V11() real ext-real set
(g ^2) + ((- (sqrt (1 - (g ^2)))) ^2) is V11() real ext-real Element of REAL
sqrt ((g ^2) + ((- (sqrt (1 - (g ^2)))) ^2)) is V11() real ext-real Element of REAL
(sqrt (1 - (g ^2))) ^2 is V11() real ext-real Element of REAL
K37((sqrt (1 - (g ^2))),(sqrt (1 - (g ^2)))) is V11() real ext-real set
(g ^2) + ((sqrt (1 - (g ^2))) ^2) is V11() real ext-real Element of REAL
sqrt ((g ^2) + ((sqrt (1 - (g ^2))) ^2)) is V11() real ext-real Element of REAL
(g ^2) + (1 - (g ^2)) is V11() real ext-real Element of REAL
sqrt ((g ^2) + (1 - (g ^2))) is V11() real ext-real Element of REAL
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : ( b1 in p3 & b1 `2 <= 0 ) } is set
C0 . |[g,(- (sqrt (1 - (g ^2))))]| is set
proj1 . |[g,(- (sqrt (1 - (g ^2))))]| is V11() real ext-real Element of REAL
p1 is non empty V142() V143() V144() Element of K6( the carrier of R^1)
R^1 | p1 is non empty strict TopSpace-like V196() SubSpace of R^1
proj1 | (Lower_Arc p3) is Relation-like the carrier of ((TOP-REAL 2) | (Lower_Arc p3)) -defined REAL -valued Function-like quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)),REAL))
K7( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)),REAL)) is set
rng (proj1 | (Lower_Arc p3)) is V142() V143() V144() Element of K6(REAL)
p3 is non empty functional closed compact Element of K6( the carrier of (TOP-REAL 2))
Upper_Arc p3 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (Upper_Arc p3) is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (Upper_Arc p3)) is non empty set
K7( the carrier of ((TOP-REAL 2) | (Upper_Arc p3)), the carrier of R^1) is set
K6(K7( the carrier of ((TOP-REAL 2) | (Upper_Arc p3)), the carrier of R^1)) is set
p2 is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of R^1))
p2 | (Upper_Arc p3) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of R^1))
P is non empty Relation-like the carrier of ((TOP-REAL 2) | (Upper_Arc p3)) -defined the carrier of R^1 -valued Function-like V29( the carrier of ((TOP-REAL 2) | (Upper_Arc p3))) quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (Upper_Arc p3)), the carrier of R^1))
C0 is Element of the carrier of ((TOP-REAL 2) | (Upper_Arc p3))
P . C0 is V11() real ext-real Element of the carrier of R^1
proj1 . C0 is set
dom P is Element of K6( the carrier of ((TOP-REAL 2) | (Upper_Arc p3)))
K6( the carrier of ((TOP-REAL 2) | (Upper_Arc p3))) is set
rng P is V142() V143() V144() Element of K6( the carrier of R^1)
C0 is set
f is set
P . f is set
g is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.g.| is V11() real ext-real non negative Element of REAL
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
g `1 is V11() real ext-real Element of REAL
(g `1) ^2 is V11() real ext-real Element of REAL
K37((g `1),(g `1)) is V11() real ext-real set
g `2 is V11() real ext-real Element of REAL
(g `2) ^2 is V11() real ext-real Element of REAL
K37((g `2),(g `2)) is V11() real ext-real set
((g `1) ^2) + ((g `2) ^2) is V11() real ext-real Element of REAL
1 - ((g `1) ^2) is V11() real ext-real Element of REAL
- (1 - ((g `1) ^2)) is V11() real ext-real Element of REAL
((g `1) ^2) - 1 is V11() real ext-real Element of REAL
proj1 . g is V11() real ext-real Element of REAL
K7( the carrier of ((TOP-REAL 2) | (Upper_Arc p3)), the carrier of (Closed-Interval-TSpace ((- 1),1))) is set
K6(K7( the carrier of ((TOP-REAL 2) | (Upper_Arc p3)), the carrier of (Closed-Interval-TSpace ((- 1),1)))) is set
C0 is non empty Relation-like the carrier of ((TOP-REAL 2) | (Upper_Arc p3)) -defined the carrier of (Closed-Interval-TSpace ((- 1),1)) -valued Function-like V29( the carrier of ((TOP-REAL 2) | (Upper_Arc p3))) quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (Upper_Arc p3)), the carrier of (Closed-Interval-TSpace ((- 1),1))))
dom C0 is Element of K6( the carrier of ((TOP-REAL 2) | (Upper_Arc p3)))
[#] ((TOP-REAL 2) | (Upper_Arc p3)) is non empty non proper closed Element of K6( the carrier of ((TOP-REAL 2) | (Upper_Arc p3)))
f is set
g is set
C0 . f is set
C0 . g is set
h is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
proj1 . h is V11() real ext-real Element of REAL
h `1 is V11() real ext-real Element of REAL
f2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
proj1 . f2 is V11() real ext-real Element of REAL
f2 `1 is V11() real ext-real Element of REAL
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
(h `1) ^2 is V11() real ext-real Element of REAL
K37((h `1),(h `1)) is V11() real ext-real set
h `2 is V11() real ext-real Element of REAL
(h `2) ^2 is V11() real ext-real Element of REAL
K37((h `2),(h `2)) is V11() real ext-real set
((h `1) ^2) + ((h `2) ^2) is V11() real ext-real Element of REAL
g2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.g2.| is V11() real ext-real non negative Element of REAL
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : ( b1 in p3 & 0 <= b1 `2 ) } is set
(f2 `1) ^2 is V11() real ext-real Element of REAL
K37((f2 `1),(f2 `1)) is V11() real ext-real set
f2 `2 is V11() real ext-real Element of REAL
(f2 `2) ^2 is V11() real ext-real Element of REAL
K37((f2 `2),(f2 `2)) is V11() real ext-real set
((f2 `1) ^2) + ((f2 `2) ^2) is V11() real ext-real Element of REAL
g2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.g2.| is V11() real ext-real non negative Element of REAL
sqrt ((h `2) ^2) is V11() real ext-real Element of REAL
g2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g2 `2 is V11() real ext-real Element of REAL
g2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g2 `2 is V11() real ext-real Element of REAL
|[(h `1),(h `2)]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
rng C0 is V142() V143() V144() Element of K6( the carrier of (Closed-Interval-TSpace ((- 1),1)))
f is set
g is V11() real ext-real Element of REAL
g ^2 is V11() real ext-real Element of REAL
K37(g,g) is V11() real ext-real set
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
1 - (g ^2) is V11() real ext-real Element of REAL
sqrt (1 - (g ^2)) is V11() real ext-real Element of REAL
|[g,(sqrt (1 - (g ^2)))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|[g,(sqrt (1 - (g ^2)))]| `2 is V11() real ext-real Element of REAL
|.|[g,(sqrt (1 - (g ^2)))]|.| is V11() real ext-real non negative Element of REAL
|[g,(sqrt (1 - (g ^2)))]| `1 is V11() real ext-real Element of REAL
(|[g,(sqrt (1 - (g ^2)))]| `1) ^2 is V11() real ext-real Element of REAL
K37((|[g,(sqrt (1 - (g ^2)))]| `1),(|[g,(sqrt (1 - (g ^2)))]| `1)) is V11() real ext-real set
(|[g,(sqrt (1 - (g ^2)))]| `2) ^2 is V11() real ext-real Element of REAL
K37((|[g,(sqrt (1 - (g ^2)))]| `2),(|[g,(sqrt (1 - (g ^2)))]| `2)) is V11() real ext-real set
((|[g,(sqrt (1 - (g ^2)))]| `1) ^2) + ((|[g,(sqrt (1 - (g ^2)))]| `2) ^2) is V11() real ext-real Element of REAL
sqrt (((|[g,(sqrt (1 - (g ^2)))]| `1) ^2) + ((|[g,(sqrt (1 - (g ^2)))]| `2) ^2)) is V11() real ext-real Element of REAL
(g ^2) + ((|[g,(sqrt (1 - (g ^2)))]| `2) ^2) is V11() real ext-real Element of REAL
sqrt ((g ^2) + ((|[g,(sqrt (1 - (g ^2)))]| `2) ^2)) is V11() real ext-real Element of REAL
(sqrt (1 - (g ^2))) ^2 is V11() real ext-real Element of REAL
K37((sqrt (1 - (g ^2))),(sqrt (1 - (g ^2)))) is V11() real ext-real set
(g ^2) + ((sqrt (1 - (g ^2))) ^2) is V11() real ext-real Element of REAL
sqrt ((g ^2) + ((sqrt (1 - (g ^2))) ^2)) is V11() real ext-real Element of REAL
(g ^2) + (1 - (g ^2)) is V11() real ext-real Element of REAL
sqrt ((g ^2) + (1 - (g ^2))) is V11() real ext-real Element of REAL
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : ( b1 in p3 & 0 <= b1 `2 ) } is set
C0 . |[g,(sqrt (1 - (g ^2)))]| is set
proj1 . |[g,(sqrt (1 - (g ^2)))]| is V11() real ext-real Element of REAL
p1 is non empty V142() V143() V144() Element of K6( the carrier of R^1)
R^1 | p1 is non empty strict TopSpace-like V196() SubSpace of R^1
proj1 | (Upper_Arc p3) is Relation-like the carrier of ((TOP-REAL 2) | (Upper_Arc p3)) -defined REAL -valued Function-like quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (Upper_Arc p3)),REAL))
K7( the carrier of ((TOP-REAL 2) | (Upper_Arc p3)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (Upper_Arc p3)),REAL)) is set
rng (proj1 | (Upper_Arc p3)) is V142() V143() V144() Element of K6(REAL)
p2 is non empty functional closed compact Element of K6( the carrier of (TOP-REAL 2))
Lower_Arc p2 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (Lower_Arc p2) is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (Lower_Arc p2)) is non empty set
K7( the carrier of (Closed-Interval-TSpace ((- 1),1)), the carrier of ((TOP-REAL 2) | (Lower_Arc p2))) is set
K6(K7( the carrier of (Closed-Interval-TSpace ((- 1),1)), the carrier of ((TOP-REAL 2) | (Lower_Arc p2)))) is set
W-min p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
E-max p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
K7( the carrier of ((TOP-REAL 2) | (Lower_Arc p2)), the carrier of R^1) is set
K6(K7( the carrier of ((TOP-REAL 2) | (Lower_Arc p2)), the carrier of R^1)) is set
p1 is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of R^1))
p1 | (Lower_Arc p2) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of R^1))
P is non empty Relation-like the carrier of ((TOP-REAL 2) | (Lower_Arc p2)) -defined the carrier of R^1 -valued Function-like V29( the carrier of ((TOP-REAL 2) | (Lower_Arc p2))) quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (Lower_Arc p2)), the carrier of R^1))
C0 is Element of the carrier of ((TOP-REAL 2) | (Lower_Arc p2))
P . C0 is V11() real ext-real Element of the carrier of R^1
proj1 . C0 is set
K7( the carrier of ((TOP-REAL 2) | (Lower_Arc p2)), the carrier of (Closed-Interval-TSpace ((- 1),1))) is set
K6(K7( the carrier of ((TOP-REAL 2) | (Lower_Arc p2)), the carrier of (Closed-Interval-TSpace ((- 1),1)))) is set
C0 is non empty Relation-like the carrier of ((TOP-REAL 2) | (Lower_Arc p2)) -defined the carrier of (Closed-Interval-TSpace ((- 1),1)) -valued Function-like V29( the carrier of ((TOP-REAL 2) | (Lower_Arc p2))) quasi_total continuous Element of K6(K7( the carrier of ((TOP-REAL 2) | (Lower_Arc p2)), the carrier of (Closed-Interval-TSpace ((- 1),1))))
rng C0 is V142() V143() V144() Element of K6( the carrier of (Closed-Interval-TSpace ((- 1),1)))
Upper_Arc p2 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
(Upper_Arc p2) /\ (Lower_Arc p2) is functional Element of K6( the carrier of (TOP-REAL 2))
{(W-min p2),(E-max p2)} is non empty functional set
Closed-Interval-MSpace ((- 1),1) is non empty strict Reflexive discerning V91() triangle Discerning SubSpace of RealSpace
TopSpaceMetr (Closed-Interval-MSpace ((- 1),1)) is TopStruct
dom C0 is Element of K6( the carrier of ((TOP-REAL 2) | (Lower_Arc p2)))
K6( the carrier of ((TOP-REAL 2) | (Lower_Arc p2))) is set
[#] ((TOP-REAL 2) | (Lower_Arc p2)) is non empty non proper closed Element of K6( the carrier of ((TOP-REAL 2) | (Lower_Arc p2)))
C0 /" is non empty Relation-like the carrier of (Closed-Interval-TSpace ((- 1),1)) -defined the carrier of ((TOP-REAL 2) | (Lower_Arc p2)) -valued Function-like V29( the carrier of (Closed-Interval-TSpace ((- 1),1))) quasi_total Element of K6(K7( the carrier of (Closed-Interval-TSpace ((- 1),1)), the carrier of ((TOP-REAL 2) | (Lower_Arc p2))))
g is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g `1 is V11() real ext-real Element of REAL
(C0 /") . (g `1) is set
f is Relation-like Function-like set
dom f is set
f " is Relation-like Function-like set
f . g is set
(f ") . (f . g) is set
f (#) (f ") is Relation-like Function-like set
(f (#) (f ")) . g is set
C0 . g is set
proj1 . g is V11() real ext-real Element of REAL
(C0 /") . 1 is set
|[1,0]| `1 is V11() real ext-real Element of REAL
(C0 /") . (|[1,0]| `1) is set
(C0 /") . (- 1) is set
|[(- 1),0]| `1 is V11() real ext-real Element of REAL
(C0 /") . (|[(- 1),0]| `1) is set
p2 is non empty functional closed compact Element of K6( the carrier of (TOP-REAL 2))
Upper_Arc p2 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (Upper_Arc p2) is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (Upper_Arc p2)) is non empty set
K7( the carrier of (Closed-Interval-TSpace ((- 1),1)), the carrier of ((TOP-REAL 2) | (Upper_Arc p2))) is set
K6(K7( the carrier of (Closed-Interval-TSpace ((- 1),1)), the carrier of ((TOP-REAL 2) | (Upper_Arc p2)))) is set
W-min p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
E-max p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
Lower_Arc p2 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
K7( the carrier of ((TOP-REAL 2) | (Upper_Arc p2)), the carrier of R^1) is set
K6(K7( the carrier of ((TOP-REAL 2) | (Upper_Arc p2)), the carrier of R^1)) is set
p1 is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of R^1))
p1 | (Upper_Arc p2) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of R^1))
P is non empty Relation-like the carrier of ((TOP-REAL 2) | (Upper_Arc p2)) -defined the carrier of R^1 -valued Function-like V29( the carrier of ((TOP-REAL 2) | (Upper_Arc p2))) quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (Upper_Arc p2)), the carrier of R^1))
C0 is Element of the carrier of ((TOP-REAL 2) | (Upper_Arc p2))
P . C0 is V11() real ext-real Element of the carrier of R^1
proj1 . C0 is set
K7( the carrier of ((TOP-REAL 2) | (Upper_Arc p2)), the carrier of (Closed-Interval-TSpace ((- 1),1))) is set
K6(K7( the carrier of ((TOP-REAL 2) | (Upper_Arc p2)), the carrier of (Closed-Interval-TSpace ((- 1),1)))) is set
C0 is non empty Relation-like the carrier of ((TOP-REAL 2) | (Upper_Arc p2)) -defined the carrier of (Closed-Interval-TSpace ((- 1),1)) -valued Function-like V29( the carrier of ((TOP-REAL 2) | (Upper_Arc p2))) quasi_total continuous Element of K6(K7( the carrier of ((TOP-REAL 2) | (Upper_Arc p2)), the carrier of (Closed-Interval-TSpace ((- 1),1))))
rng C0 is V142() V143() V144() Element of K6( the carrier of (Closed-Interval-TSpace ((- 1),1)))
(Upper_Arc p2) /\ (Lower_Arc p2) is functional Element of K6( the carrier of (TOP-REAL 2))
{(W-min p2),(E-max p2)} is non empty functional set
Closed-Interval-MSpace ((- 1),1) is non empty strict Reflexive discerning V91() triangle Discerning SubSpace of RealSpace
TopSpaceMetr (Closed-Interval-MSpace ((- 1),1)) is TopStruct
dom C0 is Element of K6( the carrier of ((TOP-REAL 2) | (Upper_Arc p2)))
K6( the carrier of ((TOP-REAL 2) | (Upper_Arc p2))) is set
[#] ((TOP-REAL 2) | (Upper_Arc p2)) is non empty non proper closed Element of K6( the carrier of ((TOP-REAL 2) | (Upper_Arc p2)))
C0 /" is non empty Relation-like the carrier of (Closed-Interval-TSpace ((- 1),1)) -defined the carrier of ((TOP-REAL 2) | (Upper_Arc p2)) -valued Function-like V29( the carrier of (Closed-Interval-TSpace ((- 1),1))) quasi_total Element of K6(K7( the carrier of (Closed-Interval-TSpace ((- 1),1)), the carrier of ((TOP-REAL 2) | (Upper_Arc p2))))
g is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g `1 is V11() real ext-real Element of REAL
(C0 /") . (g `1) is set
f is Relation-like Function-like set
dom f is set
f " is Relation-like Function-like set
f . g is set
(f ") . (f . g) is set
f (#) (f ") is Relation-like Function-like set
(f (#) (f ")) . g is set
C0 . g is set
proj1 . g is V11() real ext-real Element of REAL
(C0 /") . 1 is set
|[1,0]| `1 is V11() real ext-real Element of REAL
(C0 /") . (|[1,0]| `1) is set
(C0 /") . (- 1) is set
|[(- 1),0]| `1 is V11() real ext-real Element of REAL
(C0 /") . (|[(- 1),0]| `1) is set
p1 is non empty functional closed compact Element of K6( the carrier of (TOP-REAL 2))
Lower_Arc p1 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (Lower_Arc p1) is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (Lower_Arc p1)) is non empty set
K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | (Lower_Arc p1))) is set
K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | (Lower_Arc p1)))) is set
E-max p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
W-min p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 is non empty Relation-like the carrier of I[01] -defined the carrier of (Closed-Interval-TSpace ((- 1),1)) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (Closed-Interval-TSpace ((- 1),1))))
p3 . 0 is set
p3 . 1 is set
p3 is non empty Relation-like the carrier of I[01] -defined the carrier of (Closed-Interval-TSpace ((- 1),1)) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (Closed-Interval-TSpace ((- 1),1))))
p3 . 0 is set
p3 . 1 is set
K7( the carrier of (Closed-Interval-TSpace ((- 1),1)), the carrier of ((TOP-REAL 2) | (Lower_Arc p1))) is set
K6(K7( the carrier of (Closed-Interval-TSpace ((- 1),1)), the carrier of ((TOP-REAL 2) | (Lower_Arc p1)))) is set
p4 is non empty Relation-like the carrier of (Closed-Interval-TSpace ((- 1),1)) -defined the carrier of ((TOP-REAL 2) | (Lower_Arc p1)) -valued Function-like V29( the carrier of (Closed-Interval-TSpace ((- 1),1))) quasi_total Element of K6(K7( the carrier of (Closed-Interval-TSpace ((- 1),1)), the carrier of ((TOP-REAL 2) | (Lower_Arc p1))))
p4 . (- 1) is set
p4 . 1 is set
p4 * p3 is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | (Lower_Arc p1)) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | (Lower_Arc p1))))
P is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | (Lower_Arc p1)) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | (Lower_Arc p1))))
dom P is V142() V143() V144() Element of K6( the carrier of I[01])
P . 0 is set
C0 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
f is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
C0 `1 is V11() real ext-real Element of REAL
f `1 is V11() real ext-real Element of REAL
g is V11() real ext-real Element of REAL
P . g is set
h is V11() real ext-real Element of REAL
P . h is set
(- 2) * h is V11() real ext-real Element of REAL
((- 2) * h) + 1 is V11() real ext-real Element of REAL
(- 2) * g is V11() real ext-real Element of REAL
((- 2) * g) + 1 is V11() real ext-real Element of REAL
(((- 2) * h) + 1) ^2 is V11() real ext-real Element of REAL
K37((((- 2) * h) + 1),(((- 2) * h) + 1)) is V11() real ext-real set
1 - ((((- 2) * h) + 1) ^2) is V11() real ext-real Element of REAL
sqrt (1 - ((((- 2) * h) + 1) ^2)) is V11() real ext-real Element of REAL
- (sqrt (1 - ((((- 2) * h) + 1) ^2))) is V11() real ext-real Element of REAL
|[(((- 2) * h) + 1),(- (sqrt (1 - ((((- 2) * h) + 1) ^2))))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(((- 2) * g) + 1) ^2 is V11() real ext-real Element of REAL
K37((((- 2) * g) + 1),(((- 2) * g) + 1)) is V11() real ext-real set
1 - ((((- 2) * g) + 1) ^2) is V11() real ext-real Element of REAL
sqrt (1 - ((((- 2) * g) + 1) ^2)) is V11() real ext-real Element of REAL
- (sqrt (1 - ((((- 2) * g) + 1) ^2))) is V11() real ext-real Element of REAL
|[(((- 2) * g) + 1),(- (sqrt (1 - ((((- 2) * g) + 1) ^2))))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|[(((- 2) * h) + 1),(- (sqrt (1 - ((((- 2) * h) + 1) ^2))))]| `2 is V11() real ext-real Element of REAL
(- 2) * 1 is V11() real ext-real non positive Element of REAL
((- 2) * 1) + 1 is V11() real ext-real Element of REAL
(- 2) * 0 is empty V11() real ext-real non positive non negative Function-like functional V142() V143() V144() V145() V146() V147() V148() V201() V204() Element of REAL
((- 2) * 0) + 1 is non empty V11() real ext-real positive non negative Element of REAL
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
|.|[(((- 2) * h) + 1),(- (sqrt (1 - ((((- 2) * h) + 1) ^2))))]|.| is V11() real ext-real non negative Element of REAL
|[(((- 2) * h) + 1),(- (sqrt (1 - ((((- 2) * h) + 1) ^2))))]| `1 is V11() real ext-real Element of REAL
(|[(((- 2) * h) + 1),(- (sqrt (1 - ((((- 2) * h) + 1) ^2))))]| `1) ^2 is V11() real ext-real Element of REAL
K37((|[(((- 2) * h) + 1),(- (sqrt (1 - ((((- 2) * h) + 1) ^2))))]| `1),(|[(((- 2) * h) + 1),(- (sqrt (1 - ((((- 2) * h) + 1) ^2))))]| `1)) is V11() real ext-real set
(|[(((- 2) * h) + 1),(- (sqrt (1 - ((((- 2) * h) + 1) ^2))))]| `2) ^2 is V11() real ext-real Element of REAL
K37((|[(((- 2) * h) + 1),(- (sqrt (1 - ((((- 2) * h) + 1) ^2))))]| `2),(|[(((- 2) * h) + 1),(- (sqrt (1 - ((((- 2) * h) + 1) ^2))))]| `2)) is V11() real ext-real set
((|[(((- 2) * h) + 1),(- (sqrt (1 - ((((- 2) * h) + 1) ^2))))]| `1) ^2) + ((|[(((- 2) * h) + 1),(- (sqrt (1 - ((((- 2) * h) + 1) ^2))))]| `2) ^2) is V11() real ext-real Element of REAL
sqrt (((|[(((- 2) * h) + 1),(- (sqrt (1 - ((((- 2) * h) + 1) ^2))))]| `1) ^2) + ((|[(((- 2) * h) + 1),(- (sqrt (1 - ((((- 2) * h) + 1) ^2))))]| `2) ^2)) is V11() real ext-real Element of REAL
(sqrt (1 - ((((- 2) * h) + 1) ^2))) ^2 is V11() real ext-real Element of REAL
K37((sqrt (1 - ((((- 2) * h) + 1) ^2))),(sqrt (1 - ((((- 2) * h) + 1) ^2)))) is V11() real ext-real set
((((- 2) * h) + 1) ^2) + ((sqrt (1 - ((((- 2) * h) + 1) ^2))) ^2) is V11() real ext-real Element of REAL
sqrt (((((- 2) * h) + 1) ^2) + ((sqrt (1 - ((((- 2) * h) + 1) ^2))) ^2)) is V11() real ext-real Element of REAL
((((- 2) * h) + 1) ^2) + (1 - ((((- 2) * h) + 1) ^2)) is V11() real ext-real Element of REAL
sqrt (((((- 2) * h) + 1) ^2) + (1 - ((((- 2) * h) + 1) ^2))) is V11() real ext-real Element of REAL
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : ( b1 in p1 & b1 `2 <= 0 ) } is set
p3 . h is set
p4 . (((- 2) * h) + 1) is set
|[(((- 2) * g) + 1),(- (sqrt (1 - ((((- 2) * g) + 1) ^2))))]| `1 is V11() real ext-real Element of REAL
|[(((- 2) * g) + 1),(- (sqrt (1 - ((((- 2) * g) + 1) ^2))))]| `2 is V11() real ext-real Element of REAL
|.|[(((- 2) * g) + 1),(- (sqrt (1 - ((((- 2) * g) + 1) ^2))))]|.| is V11() real ext-real non negative Element of REAL
(|[(((- 2) * g) + 1),(- (sqrt (1 - ((((- 2) * g) + 1) ^2))))]| `1) ^2 is V11() real ext-real Element of REAL
K37((|[(((- 2) * g) + 1),(- (sqrt (1 - ((((- 2) * g) + 1) ^2))))]| `1),(|[(((- 2) * g) + 1),(- (sqrt (1 - ((((- 2) * g) + 1) ^2))))]| `1)) is V11() real ext-real set
(|[(((- 2) * g) + 1),(- (sqrt (1 - ((((- 2) * g) + 1) ^2))))]| `2) ^2 is V11() real ext-real Element of REAL
K37((|[(((- 2) * g) + 1),(- (sqrt (1 - ((((- 2) * g) + 1) ^2))))]| `2),(|[(((- 2) * g) + 1),(- (sqrt (1 - ((((- 2) * g) + 1) ^2))))]| `2)) is V11() real ext-real set
((|[(((- 2) * g) + 1),(- (sqrt (1 - ((((- 2) * g) + 1) ^2))))]| `1) ^2) + ((|[(((- 2) * g) + 1),(- (sqrt (1 - ((((- 2) * g) + 1) ^2))))]| `2) ^2) is V11() real ext-real Element of REAL
sqrt (((|[(((- 2) * g) + 1),(- (sqrt (1 - ((((- 2) * g) + 1) ^2))))]| `1) ^2) + ((|[(((- 2) * g) + 1),(- (sqrt (1 - ((((- 2) * g) + 1) ^2))))]| `2) ^2)) is V11() real ext-real Element of REAL
(sqrt (1 - ((((- 2) * g) + 1) ^2))) ^2 is V11() real ext-real Element of REAL
K37((sqrt (1 - ((((- 2) * g) + 1) ^2))),(sqrt (1 - ((((- 2) * g) + 1) ^2)))) is V11() real ext-real set
((((- 2) * g) + 1) ^2) + ((sqrt (1 - ((((- 2) * g) + 1) ^2))) ^2) is V11() real ext-real Element of REAL
sqrt (((((- 2) * g) + 1) ^2) + ((sqrt (1 - ((((- 2) * g) + 1) ^2))) ^2)) is V11() real ext-real Element of REAL
((((- 2) * g) + 1) ^2) + (1 - ((((- 2) * g) + 1) ^2)) is V11() real ext-real Element of REAL
sqrt (((((- 2) * g) + 1) ^2) + (1 - ((((- 2) * g) + 1) ^2))) is V11() real ext-real Element of REAL
p3 . g is set
p4 . (((- 2) * g) + 1) is set
P . 1 is set
p2 is non empty TopSpace-like TopStruct
the carrier of p2 is non empty set
K7( the carrier of (Closed-Interval-TSpace ((- 1),1)), the carrier of p2) is set
K6(K7( the carrier of (Closed-Interval-TSpace ((- 1),1)), the carrier of p2)) is set
C0 is non empty Relation-like the carrier of (Closed-Interval-TSpace ((- 1),1)) -defined the carrier of p2 -valued Function-like V29( the carrier of (Closed-Interval-TSpace ((- 1),1))) quasi_total Element of K6(K7( the carrier of (Closed-Interval-TSpace ((- 1),1)), the carrier of p2))
C0 * p3 is non empty Relation-like the carrier of I[01] -defined the carrier of p2 -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of p2))
K7( the carrier of I[01], the carrier of p2) is set
K6(K7( the carrier of I[01], the carrier of p2)) is set
p1 is non empty functional closed compact Element of K6( the carrier of (TOP-REAL 2))
Upper_Arc p1 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (Upper_Arc p1) is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (Upper_Arc p1)) is non empty set
K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | (Upper_Arc p1))) is set
K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | (Upper_Arc p1)))) is set
W-min p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
E-max p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 is non empty Relation-like the carrier of I[01] -defined the carrier of (Closed-Interval-TSpace ((- 1),1)) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (Closed-Interval-TSpace ((- 1),1))))
p3 . 0 is set
p3 . 1 is set
p3 is non empty Relation-like the carrier of I[01] -defined the carrier of (Closed-Interval-TSpace ((- 1),1)) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (Closed-Interval-TSpace ((- 1),1))))
p3 . 0 is set
p3 . 1 is set
K7( the carrier of (Closed-Interval-TSpace ((- 1),1)), the carrier of ((TOP-REAL 2) | (Upper_Arc p1))) is set
K6(K7( the carrier of (Closed-Interval-TSpace ((- 1),1)), the carrier of ((TOP-REAL 2) | (Upper_Arc p1)))) is set
p4 is non empty Relation-like the carrier of (Closed-Interval-TSpace ((- 1),1)) -defined the carrier of ((TOP-REAL 2) | (Upper_Arc p1)) -valued Function-like V29( the carrier of (Closed-Interval-TSpace ((- 1),1))) quasi_total Element of K6(K7( the carrier of (Closed-Interval-TSpace ((- 1),1)), the carrier of ((TOP-REAL 2) | (Upper_Arc p1))))
p4 . (- 1) is set
p4 . 1 is set
p4 * p3 is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | (Upper_Arc p1)) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | (Upper_Arc p1))))
P is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | (Upper_Arc p1)) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | (Upper_Arc p1))))
dom P is V142() V143() V144() Element of K6( the carrier of I[01])
P . 0 is set
C0 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
f is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
f `1 is V11() real ext-real Element of REAL
C0 `1 is V11() real ext-real Element of REAL
g is V11() real ext-real Element of REAL
P . g is set
h is V11() real ext-real Element of REAL
P . h is set
2 * h is V11() real ext-real Element of REAL
2 * 1 is V11() real ext-real non negative Element of REAL
(2 * h) - 1 is V11() real ext-real Element of REAL
(2 * 1) - 1 is V11() real ext-real Element of REAL
2 * 0 is empty V11() real ext-real non positive non negative Function-like functional V142() V143() V144() V145() V146() V147() V148() V201() V204() Element of REAL
(2 * 0) - 1 is non empty V11() real ext-real non positive negative Element of REAL
2 * g is V11() real ext-real Element of REAL
(2 * g) - 1 is V11() real ext-real Element of REAL
((2 * g) - 1) ^2 is V11() real ext-real Element of REAL
K37(((2 * g) - 1),((2 * g) - 1)) is V11() real ext-real set
1 - (((2 * g) - 1) ^2) is V11() real ext-real Element of REAL
sqrt (1 - (((2 * g) - 1) ^2)) is V11() real ext-real Element of REAL
|[((2 * g) - 1),(sqrt (1 - (((2 * g) - 1) ^2)))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
((2 * h) - 1) ^2 is V11() real ext-real Element of REAL
K37(((2 * h) - 1),((2 * h) - 1)) is V11() real ext-real set
1 - (((2 * h) - 1) ^2) is V11() real ext-real Element of REAL
sqrt (1 - (((2 * h) - 1) ^2)) is V11() real ext-real Element of REAL
|[((2 * h) - 1),(sqrt (1 - (((2 * h) - 1) ^2)))]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|[((2 * g) - 1),(sqrt (1 - (((2 * g) - 1) ^2)))]| `1 is V11() real ext-real Element of REAL
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
|[((2 * g) - 1),(sqrt (1 - (((2 * g) - 1) ^2)))]| `2 is V11() real ext-real Element of REAL
|.|[((2 * g) - 1),(sqrt (1 - (((2 * g) - 1) ^2)))]|.| is V11() real ext-real non negative Element of REAL
(sqrt (1 - (((2 * g) - 1) ^2))) ^2 is V11() real ext-real Element of REAL
K37((sqrt (1 - (((2 * g) - 1) ^2))),(sqrt (1 - (((2 * g) - 1) ^2)))) is V11() real ext-real set
(((2 * g) - 1) ^2) + ((sqrt (1 - (((2 * g) - 1) ^2))) ^2) is V11() real ext-real Element of REAL
sqrt ((((2 * g) - 1) ^2) + ((sqrt (1 - (((2 * g) - 1) ^2))) ^2)) is V11() real ext-real Element of REAL
(((2 * g) - 1) ^2) + (1 - (((2 * g) - 1) ^2)) is V11() real ext-real Element of REAL
sqrt ((((2 * g) - 1) ^2) + (1 - (((2 * g) - 1) ^2))) is V11() real ext-real Element of REAL
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : ( b1 in p1 & 0 <= b1 `2 ) } is set
p3 . g is set
p4 . ((2 * g) - 1) is set
|[((2 * h) - 1),(sqrt (1 - (((2 * h) - 1) ^2)))]| `1 is V11() real ext-real Element of REAL
|[((2 * h) - 1),(sqrt (1 - (((2 * h) - 1) ^2)))]| `2 is V11() real ext-real Element of REAL
|.|[((2 * h) - 1),(sqrt (1 - (((2 * h) - 1) ^2)))]|.| is V11() real ext-real non negative Element of REAL
(sqrt (1 - (((2 * h) - 1) ^2))) ^2 is V11() real ext-real Element of REAL
K37((sqrt (1 - (((2 * h) - 1) ^2))),(sqrt (1 - (((2 * h) - 1) ^2)))) is V11() real ext-real set
(((2 * h) - 1) ^2) + ((sqrt (1 - (((2 * h) - 1) ^2))) ^2) is V11() real ext-real Element of REAL
sqrt ((((2 * h) - 1) ^2) + ((sqrt (1 - (((2 * h) - 1) ^2))) ^2)) is V11() real ext-real Element of REAL
(((2 * h) - 1) ^2) + (1 - (((2 * h) - 1) ^2)) is V11() real ext-real Element of REAL
sqrt ((((2 * h) - 1) ^2) + (1 - (((2 * h) - 1) ^2))) is V11() real ext-real Element of REAL
p3 . h is set
p4 . ((2 * h) - 1) is set
P . 1 is set
p2 is non empty TopSpace-like TopStruct
the carrier of p2 is non empty set
K7( the carrier of (Closed-Interval-TSpace ((- 1),1)), the carrier of p2) is set
K6(K7( the carrier of (Closed-Interval-TSpace ((- 1),1)), the carrier of p2)) is set
C0 is non empty Relation-like the carrier of (Closed-Interval-TSpace ((- 1),1)) -defined the carrier of p2 -valued Function-like V29( the carrier of (Closed-Interval-TSpace ((- 1),1))) quasi_total Element of K6(K7( the carrier of (Closed-Interval-TSpace ((- 1),1)), the carrier of p2))
C0 * p3 is non empty Relation-like the carrier of I[01] -defined the carrier of p2 -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of p2))
K7( the carrier of I[01], the carrier of p2) is set
K6(K7( the carrier of I[01], the carrier of p2)) is set
p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 is non empty functional closed compact Element of K6( the carrier of (TOP-REAL 2))
Upper_Arc p3 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
Lower_Arc p3 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
W-min p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
E-max p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(Upper_Arc p3) /\ (Lower_Arc p3) is functional Element of K6( the carrier of (TOP-REAL 2))
{(W-min p3),(E-max p3)} is non empty functional set
p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p3 is non empty functional closed compact Element of K6( the carrier of (TOP-REAL 2))
Lower_Arc p3 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (Lower_Arc p3) is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (Lower_Arc p3)) is non empty set
K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | (Lower_Arc p3))) is set
K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | (Lower_Arc p3)))) is set
E-max p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
W-min p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p4 is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | (Lower_Arc p3)) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | (Lower_Arc p3))))
p4 . 0 is set
p4 . 1 is set
rng p4 is Element of K6( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)))
K6( the carrier of ((TOP-REAL 2) | (Lower_Arc p3))) is set
[#] ((TOP-REAL 2) | (Lower_Arc p3)) is non empty non proper closed Element of K6( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)))
Upper_Arc p3 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : ( b1 in p3 & 0 <= b1 `2 ) } is set
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P `2 is V11() real ext-real Element of REAL
dom p4 is V142() V143() V144() Element of K6( the carrier of I[01])
P is set
p4 . P is set
[#] I[01] is non empty non proper closed V142() V143() V144() Element of K6( the carrier of I[01])
C0 is V11() real ext-real Element of REAL
f is set
p4 . f is set
g is V11() real ext-real Element of REAL
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
(p1 `1) ^2 is V11() real ext-real Element of REAL
K37((p1 `1),(p1 `1)) is V11() real ext-real set
(p1 `2) ^2 is V11() real ext-real Element of REAL
K37((p1 `2),(p1 `2)) is V11() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V11() real ext-real Element of REAL
h is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.h.| is V11() real ext-real non negative Element of REAL
(1 ^2) - ((p1 `1) ^2) is V11() real ext-real Element of REAL
- (p1 `2) is V11() real ext-real Element of REAL
(- (p1 `2)) ^2 is V11() real ext-real Element of REAL
K37((- (p1 `2)),(- (p1 `2))) is V11() real ext-real set
- (p1 `1) is V11() real ext-real Element of REAL
(- (p1 `1)) ^2 is V11() real ext-real Element of REAL
K37((- (p1 `1)),(- (p1 `1))) is V11() real ext-real set
(1 ^2) - ((- (p1 `1)) ^2) is V11() real ext-real Element of REAL
sqrt ((1 ^2) - ((- (p1 `1)) ^2)) is V11() real ext-real Element of REAL
- (sqrt ((1 ^2) - ((- (p1 `1)) ^2))) is V11() real ext-real Element of REAL
(p2 `1) ^2 is V11() real ext-real Element of REAL
K37((p2 `1),(p2 `1)) is V11() real ext-real set
(p2 `2) ^2 is V11() real ext-real Element of REAL
K37((p2 `2),(p2 `2)) is V11() real ext-real set
((p2 `1) ^2) + ((p2 `2) ^2) is V11() real ext-real Element of REAL
h is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.h.| is V11() real ext-real non negative Element of REAL
(1 ^2) - ((p2 `1) ^2) is V11() real ext-real Element of REAL
- (p2 `2) is V11() real ext-real Element of REAL
(- (p2 `2)) ^2 is V11() real ext-real Element of REAL
K37((- (p2 `2)),(- (p2 `2))) is V11() real ext-real set
- (p2 `1) is V11() real ext-real Element of REAL
(- (p2 `1)) ^2 is V11() real ext-real Element of REAL
K37((- (p2 `1)),(- (p2 `1))) is V11() real ext-real set
(1 ^2) - ((- (p2 `1)) ^2) is V11() real ext-real Element of REAL
sqrt ((1 ^2) - ((- (p2 `1)) ^2)) is V11() real ext-real Element of REAL
- (sqrt ((1 ^2) - ((- (p2 `1)) ^2))) is V11() real ext-real Element of REAL
p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p1 `1 is V11() real ext-real Element of REAL
p3 is non empty functional closed compact Element of K6( the carrier of (TOP-REAL 2))
Lower_Arc p3 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
Upper_Arc p3 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
(Upper_Arc p3) /\ (Lower_Arc p3) is functional Element of K6( the carrier of (TOP-REAL 2))
W-min p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
E-max p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
{(W-min p3),(E-max p3)} is non empty functional set
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
(p2 `1) ^2 is V11() real ext-real Element of REAL
K37((p2 `1),(p2 `1)) is V11() real ext-real set
(p2 `2) ^2 is V11() real ext-real Element of REAL
K37((p2 `2),(p2 `2)) is V11() real ext-real set
((p2 `1) ^2) + ((p2 `2) ^2) is V11() real ext-real Element of REAL
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.P.| is V11() real ext-real non negative Element of REAL
- (p2 `1) is V11() real ext-real Element of REAL
(- (p2 `1)) ^2 is V11() real ext-real Element of REAL
K37((- (p2 `1)),(- (p2 `1))) is V11() real ext-real set
(1 ^2) - ((- (p2 `1)) ^2) is V11() real ext-real Element of REAL
sqrt ((1 ^2) - ((- (p2 `1)) ^2)) is V11() real ext-real Element of REAL
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : ( b1 in p3 & 0 <= b1 `2 ) } is set
(p1 `1) ^2 is V11() real ext-real Element of REAL
K37((p1 `1),(p1 `1)) is V11() real ext-real set
(p1 `2) ^2 is V11() real ext-real Element of REAL
K37((p1 `2),(p1 `2)) is V11() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V11() real ext-real Element of REAL
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.P.| is V11() real ext-real non negative Element of REAL
- (p1 `1) is V11() real ext-real Element of REAL
(- (p1 `1)) ^2 is V11() real ext-real Element of REAL
K37((- (p1 `1)),(- (p1 `1))) is V11() real ext-real set
(1 ^2) - ((- (p1 `1)) ^2) is V11() real ext-real Element of REAL
sqrt ((1 ^2) - ((- (p1 `1)) ^2)) is V11() real ext-real Element of REAL
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.P.| is V11() real ext-real non negative Element of REAL
(TOP-REAL 2) | (Upper_Arc p3) is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (Upper_Arc p3)) is non empty set
K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | (Upper_Arc p3))) is set
K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | (Upper_Arc p3)))) is set
P is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | (Upper_Arc p3)) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | (Upper_Arc p3))))
P . 0 is set
P . 1 is set
rng P is Element of K6( the carrier of ((TOP-REAL 2) | (Upper_Arc p3)))
K6( the carrier of ((TOP-REAL 2) | (Upper_Arc p3))) is set
[#] ((TOP-REAL 2) | (Upper_Arc p3)) is non empty non proper closed Element of K6( the carrier of ((TOP-REAL 2) | (Upper_Arc p3)))
dom P is V142() V143() V144() Element of K6( the carrier of I[01])
C0 is set
P . C0 is set
[#] I[01] is non empty non proper closed V142() V143() V144() Element of K6( the carrier of I[01])
f is V11() real ext-real Element of REAL
g is set
P . g is set
h is V11() real ext-real Element of REAL
p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p1 `1 is V11() real ext-real Element of REAL
p3 is non empty functional closed compact Element of K6( the carrier of (TOP-REAL 2))
Lower_Arc p3 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
Upper_Arc p3 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : ( b1 in p3 & 0 <= b1 `2 ) } is set
(Upper_Arc p3) /\ (Lower_Arc p3) is functional Element of K6( the carrier of (TOP-REAL 2))
W-min p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
E-max p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
{(W-min p3),(E-max p3)} is non empty functional set
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
(p1 `1) ^2 is V11() real ext-real Element of REAL
K37((p1 `1),(p1 `1)) is V11() real ext-real set
p1 `2 is V11() real ext-real Element of REAL
(p1 `2) ^2 is V11() real ext-real Element of REAL
K37((p1 `2),(p1 `2)) is V11() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V11() real ext-real Element of REAL
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.P.| is V11() real ext-real non negative Element of REAL
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.P.| is V11() real ext-real non negative Element of REAL
(TOP-REAL 2) | (Upper_Arc p3) is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (Upper_Arc p3)) is non empty set
K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | (Upper_Arc p3))) is set
K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | (Upper_Arc p3)))) is set
P is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | (Upper_Arc p3)) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | (Upper_Arc p3))))
P . 0 is set
P . 1 is set
rng P is Element of K6( the carrier of ((TOP-REAL 2) | (Upper_Arc p3)))
K6( the carrier of ((TOP-REAL 2) | (Upper_Arc p3))) is set
[#] ((TOP-REAL 2) | (Upper_Arc p3)) is non empty non proper closed Element of K6( the carrier of ((TOP-REAL 2) | (Upper_Arc p3)))
dom P is V142() V143() V144() Element of K6( the carrier of I[01])
C0 is set
P . C0 is set
f is set
P . f is set
[#] I[01] is non empty non proper closed V142() V143() V144() Element of K6( the carrier of I[01])
g is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p1 `2 is V11() real ext-real Element of REAL
p1 `1 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p3 is non empty functional closed compact Element of K6( the carrier of (TOP-REAL 2))
W-min p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
Lower_Arc p3 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : ( b1 in p3 & b1 `2 <= 0 ) } is set
Upper_Arc p3 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
(Upper_Arc p3) /\ (Lower_Arc p3) is functional Element of K6( the carrier of (TOP-REAL 2))
E-max p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
{(W-min p3),(E-max p3)} is non empty functional set
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
(p2 `1) ^2 is V11() real ext-real Element of REAL
K37((p2 `1),(p2 `1)) is V11() real ext-real set
p2 `2 is V11() real ext-real Element of REAL
(p2 `2) ^2 is V11() real ext-real Element of REAL
K37((p2 `2),(p2 `2)) is V11() real ext-real set
((p2 `1) ^2) + ((p2 `2) ^2) is V11() real ext-real Element of REAL
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.P.| is V11() real ext-real non negative Element of REAL
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.P.| is V11() real ext-real non negative Element of REAL
(TOP-REAL 2) | (Lower_Arc p3) is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (Lower_Arc p3)) is non empty set
K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | (Lower_Arc p3))) is set
K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | (Lower_Arc p3)))) is set
P is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | (Lower_Arc p3)) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | (Lower_Arc p3))))
P . 0 is set
P . 1 is set
rng P is Element of K6( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)))
K6( the carrier of ((TOP-REAL 2) | (Lower_Arc p3))) is set
[#] ((TOP-REAL 2) | (Lower_Arc p3)) is non empty non proper closed Element of K6( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)))
dom P is V142() V143() V144() Element of K6( the carrier of I[01])
C0 is set
P . C0 is set
f is set
P . f is set
[#] I[01] is non empty non proper closed V142() V143() V144() Element of K6( the carrier of I[01])
g is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p1 `2 is V11() real ext-real Element of REAL
p1 `1 is V11() real ext-real Element of REAL
p3 is non empty functional closed compact Element of K6( the carrier of (TOP-REAL 2))
Upper_Arc p3 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : ( b1 in p3 & 0 <= b1 `2 ) } is set
E-max p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
W-min p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
Lower_Arc p3 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p3 is non empty functional closed compact Element of K6( the carrier of (TOP-REAL 2))
Upper_Arc p3 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : ( b1 in p3 & 0 <= b1 `2 ) } is set
W-min p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(W-min p3) `2 is V11() real ext-real Element of REAL
Lower_Arc p3 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : ( b1 in p3 & b1 `2 <= 0 ) } is set
(p2 `1) ^2 is V11() real ext-real Element of REAL
K37((p2 `1),(p2 `1)) is V11() real ext-real set
(p1 `1) ^2 is V11() real ext-real Element of REAL
K37((p1 `1),(p1 `1)) is V11() real ext-real set
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
(1 ^2) - ((p1 `1) ^2) is V11() real ext-real Element of REAL
(1 ^2) - ((p2 `1) ^2) is V11() real ext-real Element of REAL
(p1 `2) ^2 is V11() real ext-real Element of REAL
K37((p1 `2),(p1 `2)) is V11() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V11() real ext-real Element of REAL
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.p4.| is V11() real ext-real non negative Element of REAL
sqrt ((1 ^2) - ((p1 `1) ^2)) is V11() real ext-real Element of REAL
(p2 `2) ^2 is V11() real ext-real Element of REAL
K37((p2 `2),(p2 `2)) is V11() real ext-real set
((p2 `1) ^2) + ((p2 `2) ^2) is V11() real ext-real Element of REAL
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.p4.| is V11() real ext-real non negative Element of REAL
sqrt ((1 ^2) - ((p2 `1) ^2)) is V11() real ext-real Element of REAL
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
(p1 `1) ^2 is V11() real ext-real Element of REAL
K37((p1 `1),(p1 `1)) is V11() real ext-real set
(p1 `2) ^2 is V11() real ext-real Element of REAL
K37((p1 `2),(p1 `2)) is V11() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V11() real ext-real Element of REAL
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.p4.| is V11() real ext-real non negative Element of REAL
(1 ^2) - ((p1 `1) ^2) is V11() real ext-real Element of REAL
- (p1 `2) is V11() real ext-real Element of REAL
(- (p1 `2)) ^2 is V11() real ext-real Element of REAL
K37((- (p1 `2)),(- (p1 `2))) is V11() real ext-real set
sqrt ((1 ^2) - ((p1 `1) ^2)) is V11() real ext-real Element of REAL
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
E-max p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(p2 `1) ^2 is V11() real ext-real Element of REAL
K37((p2 `1),(p2 `1)) is V11() real ext-real set
(p2 `2) ^2 is V11() real ext-real Element of REAL
K37((p2 `2),(p2 `2)) is V11() real ext-real set
((p2 `1) ^2) + ((p2 `2) ^2) is V11() real ext-real Element of REAL
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.p4.| is V11() real ext-real non negative Element of REAL
(1 ^2) - ((p2 `1) ^2) is V11() real ext-real Element of REAL
- (p2 `2) is V11() real ext-real Element of REAL
(- (p2 `2)) ^2 is V11() real ext-real Element of REAL
K37((- (p2 `2)),(- (p2 `2))) is V11() real ext-real set
sqrt ((1 ^2) - ((p2 `1) ^2)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (Lower_Arc p3) is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (Lower_Arc p3)) is non empty set
K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | (Lower_Arc p3))) is set
K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | (Lower_Arc p3)))) is set
p4 is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | (Lower_Arc p3)) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | (Lower_Arc p3))))
p4 . 0 is set
p4 . 1 is set
rng p4 is Element of K6( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)))
K6( the carrier of ((TOP-REAL 2) | (Lower_Arc p3))) is set
[#] ((TOP-REAL 2) | (Lower_Arc p3)) is non empty non proper closed Element of K6( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)))
dom p4 is V142() V143() V144() Element of K6( the carrier of I[01])
P is set
p4 . P is set
[#] I[01] is non empty non proper closed V142() V143() V144() Element of K6( the carrier of I[01])
C0 is V11() real ext-real Element of REAL
f is set
p4 . f is set
g is V11() real ext-real Element of REAL
p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p3 is non empty functional closed compact Element of K6( the carrier of (TOP-REAL 2))
Lower_Arc p3 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
Upper_Arc p3 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
(Upper_Arc p3) \/ (Lower_Arc p3) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : ( b1 in p3 & 0 <= b1 `2 ) } is set
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P `2 is V11() real ext-real Element of REAL
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P `2 is V11() real ext-real Element of REAL
- (p2 `2) is V11() real ext-real Element of REAL
- (p1 `2) is V11() real ext-real Element of REAL
(- (p2 `2)) ^2 is V11() real ext-real Element of REAL
K37((- (p2 `2)),(- (p2 `2))) is V11() real ext-real set
(- (p1 `2)) ^2 is V11() real ext-real Element of REAL
K37((- (p1 `2)),(- (p1 `2))) is V11() real ext-real set
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
(1 ^2) - ((- (p1 `2)) ^2) is V11() real ext-real Element of REAL
(1 ^2) - ((- (p2 `2)) ^2) is V11() real ext-real Element of REAL
(p1 `1) ^2 is V11() real ext-real Element of REAL
K37((p1 `1),(p1 `1)) is V11() real ext-real set
(p1 `2) ^2 is V11() real ext-real Element of REAL
K37((p1 `2),(p1 `2)) is V11() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V11() real ext-real Element of REAL
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.P.| is V11() real ext-real non negative Element of REAL
sqrt ((1 ^2) - ((- (p1 `2)) ^2)) is V11() real ext-real Element of REAL
sqrt ((1 ^2) - ((- (p2 `2)) ^2)) is V11() real ext-real Element of REAL
(p2 `1) ^2 is V11() real ext-real Element of REAL
K37((p2 `1),(p2 `1)) is V11() real ext-real set
(p2 `2) ^2 is V11() real ext-real Element of REAL
K37((p2 `2),(p2 `2)) is V11() real ext-real set
((p2 `1) ^2) + ((p2 `2) ^2) is V11() real ext-real Element of REAL
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.P.| is V11() real ext-real non negative Element of REAL
- (p2 `1) is V11() real ext-real Element of REAL
(- (p2 `1)) ^2 is V11() real ext-real Element of REAL
K37((- (p2 `1)),(- (p2 `1))) is V11() real ext-real set
- (p1 `1) is V11() real ext-real Element of REAL
(- (p1 `1)) ^2 is V11() real ext-real Element of REAL
K37((- (p1 `1)),(- (p1 `1))) is V11() real ext-real set
(Upper_Arc p3) /\ (Lower_Arc p3) is functional Element of K6( the carrier of (TOP-REAL 2))
W-min p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
E-max p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
{(W-min p3),(E-max p3)} is non empty functional set
(TOP-REAL 2) | (Lower_Arc p3) is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (Lower_Arc p3)) is non empty set
K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | (Lower_Arc p3))) is set
K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | (Lower_Arc p3)))) is set
K7( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)), the carrier of R^1) is set
K6(K7( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)), the carrier of R^1)) is set
C0 is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of R^1))
C0 | (Lower_Arc p3) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of R^1))
Closed-Interval-MSpace ((- 1),1) is non empty strict Reflexive discerning V91() triangle Discerning SubSpace of RealSpace
TopSpaceMetr (Closed-Interval-MSpace ((- 1),1)) is TopStruct
K7( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)), the carrier of (Closed-Interval-TSpace ((- 1),1))) is set
K6(K7( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)), the carrier of (Closed-Interval-TSpace ((- 1),1)))) is set
f is non empty Relation-like the carrier of ((TOP-REAL 2) | (Lower_Arc p3)) -defined the carrier of R^1 -valued Function-like V29( the carrier of ((TOP-REAL 2) | (Lower_Arc p3))) quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)), the carrier of R^1))
h is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | (Lower_Arc p3)) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | (Lower_Arc p3))))
h . 0 is set
h . 1 is set
f2 is V11() real ext-real Element of REAL
h . f2 is set
g2 is V11() real ext-real Element of REAL
h . g2 is set
the carrier of (Closed-Interval-TSpace (0,1)) is non empty V142() V143() V144() set
K7( the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((- 1),1))) is set
K6(K7( the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((- 1),1)))) is set
g is non empty Relation-like the carrier of ((TOP-REAL 2) | (Lower_Arc p3)) -defined the carrier of (Closed-Interval-TSpace ((- 1),1)) -valued Function-like V29( the carrier of ((TOP-REAL 2) | (Lower_Arc p3))) quasi_total continuous Element of K6(K7( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)), the carrier of (Closed-Interval-TSpace ((- 1),1))))
g * h is non empty Relation-like the carrier of I[01] -defined the carrier of (Closed-Interval-TSpace ((- 1),1)) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (Closed-Interval-TSpace ((- 1),1))))
dom g is Element of K6( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)))
K6( the carrier of ((TOP-REAL 2) | (Lower_Arc p3))) is set
[#] ((TOP-REAL 2) | (Lower_Arc p3)) is non empty non proper closed Element of K6( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)))
rng g is V142() V143() V144() Element of K6( the carrier of (Closed-Interval-TSpace ((- 1),1)))
h1 is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace ((- 1),1)) -valued Function-like V29( the carrier of (Closed-Interval-TSpace (0,1))) quasi_total Element of K6(K7( the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((- 1),1))))
dom h is V142() V143() V144() Element of K6( the carrier of I[01])
[#] I[01] is non empty non proper closed V142() V143() V144() Element of K6( the carrier of I[01])
|[(- 1),0]| `1 is V11() real ext-real Element of REAL
proj1 . |[(- 1),0]| is V11() real ext-real Element of REAL
g . (h . 1) is set
h1 . 1 is set
proj1 . p2 is V11() real ext-real Element of REAL
g . (h . g2) is set
h1 . g2 is set
C0 . p1 is V11() real ext-real Element of the carrier of R^1
g . (h . f2) is set
h1 . f2 is set
p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p3 is non empty functional closed compact Element of K6( the carrier of (TOP-REAL 2))
Lower_Arc p3 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
Upper_Arc p3 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
(Upper_Arc p3) \/ (Lower_Arc p3) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : ( b1 in p3 & 0 <= b1 `2 ) } is set
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P `2 is V11() real ext-real Element of REAL
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P `2 is V11() real ext-real Element of REAL
- (p1 `2) is V11() real ext-real Element of REAL
- (p2 `2) is V11() real ext-real Element of REAL
(- (p1 `2)) ^2 is V11() real ext-real Element of REAL
K37((- (p1 `2)),(- (p1 `2))) is V11() real ext-real set
(- (p2 `2)) ^2 is V11() real ext-real Element of REAL
K37((- (p2 `2)),(- (p2 `2))) is V11() real ext-real set
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
(1 ^2) - ((- (p2 `2)) ^2) is V11() real ext-real Element of REAL
(1 ^2) - ((- (p1 `2)) ^2) is V11() real ext-real Element of REAL
(p2 `1) ^2 is V11() real ext-real Element of REAL
K37((p2 `1),(p2 `1)) is V11() real ext-real set
(p2 `2) ^2 is V11() real ext-real Element of REAL
K37((p2 `2),(p2 `2)) is V11() real ext-real set
((p2 `1) ^2) + ((p2 `2) ^2) is V11() real ext-real Element of REAL
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.P.| is V11() real ext-real non negative Element of REAL
sqrt ((1 ^2) - ((- (p2 `2)) ^2)) is V11() real ext-real Element of REAL
(p1 `1) ^2 is V11() real ext-real Element of REAL
K37((p1 `1),(p1 `1)) is V11() real ext-real set
(p1 `2) ^2 is V11() real ext-real Element of REAL
K37((p1 `2),(p1 `2)) is V11() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V11() real ext-real Element of REAL
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.P.| is V11() real ext-real non negative Element of REAL
sqrt ((1 ^2) - ((- (p1 `2)) ^2)) is V11() real ext-real Element of REAL
(Upper_Arc p3) /\ (Lower_Arc p3) is functional Element of K6( the carrier of (TOP-REAL 2))
W-min p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
E-max p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
{(W-min p3),(E-max p3)} is non empty functional set
(TOP-REAL 2) | (Lower_Arc p3) is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (Lower_Arc p3)) is non empty set
K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | (Lower_Arc p3))) is set
K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | (Lower_Arc p3)))) is set
K7( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)), the carrier of R^1) is set
K6(K7( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)), the carrier of R^1)) is set
C0 is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of R^1))
C0 | (Lower_Arc p3) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of R^1))
Closed-Interval-MSpace ((- 1),1) is non empty strict Reflexive discerning V91() triangle Discerning SubSpace of RealSpace
TopSpaceMetr (Closed-Interval-MSpace ((- 1),1)) is TopStruct
K7( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)), the carrier of (Closed-Interval-TSpace ((- 1),1))) is set
K6(K7( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)), the carrier of (Closed-Interval-TSpace ((- 1),1)))) is set
f is non empty Relation-like the carrier of ((TOP-REAL 2) | (Lower_Arc p3)) -defined the carrier of R^1 -valued Function-like V29( the carrier of ((TOP-REAL 2) | (Lower_Arc p3))) quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)), the carrier of R^1))
h is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | (Lower_Arc p3)) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | (Lower_Arc p3))))
h . 0 is set
h . 1 is set
f2 is V11() real ext-real Element of REAL
h . f2 is set
g2 is V11() real ext-real Element of REAL
h . g2 is set
the carrier of (Closed-Interval-TSpace (0,1)) is non empty V142() V143() V144() set
K7( the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((- 1),1))) is set
K6(K7( the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((- 1),1)))) is set
g is non empty Relation-like the carrier of ((TOP-REAL 2) | (Lower_Arc p3)) -defined the carrier of (Closed-Interval-TSpace ((- 1),1)) -valued Function-like V29( the carrier of ((TOP-REAL 2) | (Lower_Arc p3))) quasi_total continuous Element of K6(K7( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)), the carrier of (Closed-Interval-TSpace ((- 1),1))))
g * h is non empty Relation-like the carrier of I[01] -defined the carrier of (Closed-Interval-TSpace ((- 1),1)) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (Closed-Interval-TSpace ((- 1),1))))
dom g is Element of K6( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)))
K6( the carrier of ((TOP-REAL 2) | (Lower_Arc p3))) is set
[#] ((TOP-REAL 2) | (Lower_Arc p3)) is non empty non proper closed Element of K6( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)))
rng g is V142() V143() V144() Element of K6( the carrier of (Closed-Interval-TSpace ((- 1),1)))
h1 is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace ((- 1),1)) -valued Function-like V29( the carrier of (Closed-Interval-TSpace (0,1))) quasi_total Element of K6(K7( the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((- 1),1))))
dom h is V142() V143() V144() Element of K6( the carrier of I[01])
[#] I[01] is non empty non proper closed V142() V143() V144() Element of K6( the carrier of I[01])
|[(- 1),0]| `1 is V11() real ext-real Element of REAL
proj1 . |[(- 1),0]| is V11() real ext-real Element of REAL
g . (h . 1) is set
h1 . 1 is set
proj1 . p2 is V11() real ext-real Element of REAL
g . p2 is set
h1 . g2 is set
C0 . p1 is V11() real ext-real Element of the carrier of R^1
g . (h . f2) is set
h1 . f2 is set
p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p3 is non empty functional closed compact Element of K6( the carrier of (TOP-REAL 2))
Upper_Arc p3 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
Lower_Arc p3 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
(Upper_Arc p3) /\ (Lower_Arc p3) is functional Element of K6( the carrier of (TOP-REAL 2))
W-min p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
E-max p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
{(W-min p3),(E-max p3)} is non empty functional set
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : ( b1 in p3 & 0 <= b1 `2 ) } is set
(p1 `2) ^2 is V11() real ext-real Element of REAL
K37((p1 `2),(p1 `2)) is V11() real ext-real set
(p2 `2) ^2 is V11() real ext-real Element of REAL
K37((p2 `2),(p2 `2)) is V11() real ext-real set
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
(1 ^2) - ((p2 `2) ^2) is V11() real ext-real Element of REAL
(1 ^2) - ((p1 `2) ^2) is V11() real ext-real Element of REAL
(p2 `1) ^2 is V11() real ext-real Element of REAL
K37((p2 `1),(p2 `1)) is V11() real ext-real set
((p2 `1) ^2) + ((p2 `2) ^2) is V11() real ext-real Element of REAL
C0 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.C0.| is V11() real ext-real non negative Element of REAL
sqrt ((1 ^2) - ((p2 `2) ^2)) is V11() real ext-real Element of REAL
sqrt ((1 ^2) - ((p1 `2) ^2)) is V11() real ext-real Element of REAL
(p1 `1) ^2 is V11() real ext-real Element of REAL
K37((p1 `1),(p1 `1)) is V11() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V11() real ext-real Element of REAL
C0 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.C0.| is V11() real ext-real non negative Element of REAL
- (p1 `1) is V11() real ext-real Element of REAL
(- (p1 `1)) ^2 is V11() real ext-real Element of REAL
K37((- (p1 `1)),(- (p1 `1))) is V11() real ext-real set
- (p2 `1) is V11() real ext-real Element of REAL
(- (p2 `1)) ^2 is V11() real ext-real Element of REAL
K37((- (p2 `1)),(- (p2 `1))) is V11() real ext-real set
(TOP-REAL 2) | (Upper_Arc p3) is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (Upper_Arc p3)) is non empty set
K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | (Upper_Arc p3))) is set
K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | (Upper_Arc p3)))) is set
K7( the carrier of ((TOP-REAL 2) | (Upper_Arc p3)), the carrier of R^1) is set
K6(K7( the carrier of ((TOP-REAL 2) | (Upper_Arc p3)), the carrier of R^1)) is set
f is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of R^1))
f | (Upper_Arc p3) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of R^1))
Closed-Interval-MSpace ((- 1),1) is non empty strict Reflexive discerning V91() triangle Discerning SubSpace of RealSpace
TopSpaceMetr (Closed-Interval-MSpace ((- 1),1)) is TopStruct
K7( the carrier of ((TOP-REAL 2) | (Upper_Arc p3)), the carrier of (Closed-Interval-TSpace ((- 1),1))) is set
K6(K7( the carrier of ((TOP-REAL 2) | (Upper_Arc p3)), the carrier of (Closed-Interval-TSpace ((- 1),1)))) is set
g is non empty Relation-like the carrier of ((TOP-REAL 2) | (Upper_Arc p3)) -defined the carrier of R^1 -valued Function-like V29( the carrier of ((TOP-REAL 2) | (Upper_Arc p3))) quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (Upper_Arc p3)), the carrier of R^1))
f2 is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | (Upper_Arc p3)) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | (Upper_Arc p3))))
f2 . 0 is set
f2 . 1 is set
g2 is V11() real ext-real Element of REAL
f2 . g2 is set
h1 is V11() real ext-real Element of REAL
f2 . h1 is set
the carrier of (Closed-Interval-TSpace (0,1)) is non empty V142() V143() V144() set
K7( the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((- 1),1))) is set
K6(K7( the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((- 1),1)))) is set
h is non empty Relation-like the carrier of ((TOP-REAL 2) | (Upper_Arc p3)) -defined the carrier of (Closed-Interval-TSpace ((- 1),1)) -valued Function-like V29( the carrier of ((TOP-REAL 2) | (Upper_Arc p3))) quasi_total continuous Element of K6(K7( the carrier of ((TOP-REAL 2) | (Upper_Arc p3)), the carrier of (Closed-Interval-TSpace ((- 1),1))))
h * f2 is non empty Relation-like the carrier of I[01] -defined the carrier of (Closed-Interval-TSpace ((- 1),1)) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (Closed-Interval-TSpace ((- 1),1))))
dom h is Element of K6( the carrier of ((TOP-REAL 2) | (Upper_Arc p3)))
K6( the carrier of ((TOP-REAL 2) | (Upper_Arc p3))) is set
[#] ((TOP-REAL 2) | (Upper_Arc p3)) is non empty non proper closed Element of K6( the carrier of ((TOP-REAL 2) | (Upper_Arc p3)))
rng h is V142() V143() V144() Element of K6( the carrier of (Closed-Interval-TSpace ((- 1),1)))
O is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace ((- 1),1)) -valued Function-like V29( the carrier of (Closed-Interval-TSpace (0,1))) quasi_total Element of K6(K7( the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((- 1),1))))
dom f2 is V142() V143() V144() Element of K6( the carrier of I[01])
[#] I[01] is non empty non proper closed V142() V143() V144() Element of K6( the carrier of I[01])
|[1,0]| `1 is V11() real ext-real Element of REAL
f . |[1,0]| is V11() real ext-real Element of the carrier of R^1
h . |[1,0]| is set
O . 1 is set
f . p2 is V11() real ext-real Element of the carrier of R^1
h . p2 is set
O . h1 is set
f . p1 is V11() real ext-real Element of the carrier of R^1
h . (f2 . g2) is set
O . g2 is set
p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p1 `1 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p3 is non empty functional closed compact Element of K6( the carrier of (TOP-REAL 2))
Upper_Arc p3 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : ( b1 in p3 & 0 <= b1 `2 ) } is set
Lower_Arc p3 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
(Upper_Arc p3) /\ (Lower_Arc p3) is functional Element of K6( the carrier of (TOP-REAL 2))
W-min p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
E-max p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
{(W-min p3),(E-max p3)} is non empty functional set
(TOP-REAL 2) | (Upper_Arc p3) is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (Upper_Arc p3)) is non empty set
K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | (Upper_Arc p3))) is set
K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | (Upper_Arc p3)))) is set
K7( the carrier of ((TOP-REAL 2) | (Upper_Arc p3)), the carrier of R^1) is set
K6(K7( the carrier of ((TOP-REAL 2) | (Upper_Arc p3)), the carrier of R^1)) is set
f is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of R^1))
f | (Upper_Arc p3) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of R^1))
Closed-Interval-MSpace ((- 1),1) is non empty strict Reflexive discerning V91() triangle Discerning SubSpace of RealSpace
TopSpaceMetr (Closed-Interval-MSpace ((- 1),1)) is TopStruct
K7( the carrier of ((TOP-REAL 2) | (Upper_Arc p3)), the carrier of (Closed-Interval-TSpace ((- 1),1))) is set
K6(K7( the carrier of ((TOP-REAL 2) | (Upper_Arc p3)), the carrier of (Closed-Interval-TSpace ((- 1),1)))) is set
g is non empty Relation-like the carrier of ((TOP-REAL 2) | (Upper_Arc p3)) -defined the carrier of R^1 -valued Function-like V29( the carrier of ((TOP-REAL 2) | (Upper_Arc p3))) quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (Upper_Arc p3)), the carrier of R^1))
f2 is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | (Upper_Arc p3)) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | (Upper_Arc p3))))
f2 . 0 is set
f2 . 1 is set
g2 is V11() real ext-real Element of REAL
f2 . g2 is set
h1 is V11() real ext-real Element of REAL
f2 . h1 is set
the carrier of (Closed-Interval-TSpace (0,1)) is non empty V142() V143() V144() set
K7( the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((- 1),1))) is set
K6(K7( the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((- 1),1)))) is set
h is non empty Relation-like the carrier of ((TOP-REAL 2) | (Upper_Arc p3)) -defined the carrier of (Closed-Interval-TSpace ((- 1),1)) -valued Function-like V29( the carrier of ((TOP-REAL 2) | (Upper_Arc p3))) quasi_total continuous Element of K6(K7( the carrier of ((TOP-REAL 2) | (Upper_Arc p3)), the carrier of (Closed-Interval-TSpace ((- 1),1))))
h * f2 is non empty Relation-like the carrier of I[01] -defined the carrier of (Closed-Interval-TSpace ((- 1),1)) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (Closed-Interval-TSpace ((- 1),1))))
dom h is Element of K6( the carrier of ((TOP-REAL 2) | (Upper_Arc p3)))
K6( the carrier of ((TOP-REAL 2) | (Upper_Arc p3))) is set
[#] ((TOP-REAL 2) | (Upper_Arc p3)) is non empty non proper closed Element of K6( the carrier of ((TOP-REAL 2) | (Upper_Arc p3)))
rng h is V142() V143() V144() Element of K6( the carrier of (Closed-Interval-TSpace ((- 1),1)))
O is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace ((- 1),1)) -valued Function-like V29( the carrier of (Closed-Interval-TSpace (0,1))) quasi_total Element of K6(K7( the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((- 1),1))))
dom f2 is V142() V143() V144() Element of K6( the carrier of I[01])
[#] I[01] is non empty non proper closed V142() V143() V144() Element of K6( the carrier of I[01])
|[1,0]| `1 is V11() real ext-real Element of REAL
f . |[1,0]| is V11() real ext-real Element of the carrier of R^1
h . |[1,0]| is set
O . 1 is set
f . p2 is V11() real ext-real Element of the carrier of R^1
h . p2 is set
O . h1 is set
f . p1 is V11() real ext-real Element of the carrier of R^1
h . p1 is set
O . g2 is set
p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p3 is non empty functional closed compact Element of K6( the carrier of (TOP-REAL 2))
W-min p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
Upper_Arc p3 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : ( b1 in p3 & 0 <= b1 `2 ) } is set
Lower_Arc p3 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
(Upper_Arc p3) /\ (Lower_Arc p3) is functional Element of K6( the carrier of (TOP-REAL 2))
E-max p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
{(W-min p3),(E-max p3)} is non empty functional set
(Upper_Arc p3) \/ (Lower_Arc p3) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
(p1 `1) ^2 is V11() real ext-real Element of REAL
K37((p1 `1),(p1 `1)) is V11() real ext-real set
(p1 `2) ^2 is V11() real ext-real Element of REAL
K37((p1 `2),(p1 `2)) is V11() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V11() real ext-real Element of REAL
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.P.| is V11() real ext-real non negative Element of REAL
(1 ^2) - ((p1 `2) ^2) is V11() real ext-real Element of REAL
sqrt ((1 ^2) - ((p1 `2) ^2)) is V11() real ext-real Element of REAL
(p2 `1) ^2 is V11() real ext-real Element of REAL
K37((p2 `1),(p2 `1)) is V11() real ext-real set
(p2 `2) ^2 is V11() real ext-real Element of REAL
K37((p2 `2),(p2 `2)) is V11() real ext-real set
((p2 `1) ^2) + ((p2 `2) ^2) is V11() real ext-real Element of REAL
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.P.| is V11() real ext-real non negative Element of REAL
(1 ^2) - ((p2 `2) ^2) is V11() real ext-real Element of REAL
sqrt ((1 ^2) - ((p2 `2) ^2)) is V11() real ext-real Element of REAL
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P `2 is V11() real ext-real Element of REAL
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P `2 is V11() real ext-real Element of REAL
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P `2 is V11() real ext-real Element of REAL
- (p1 `2) is V11() real ext-real Element of REAL
- (p2 `2) is V11() real ext-real Element of REAL
(- (p1 `2)) ^2 is V11() real ext-real Element of REAL
K37((- (p1 `2)),(- (p1 `2))) is V11() real ext-real set
(- (p2 `2)) ^2 is V11() real ext-real Element of REAL
K37((- (p2 `2)),(- (p2 `2))) is V11() real ext-real set
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
(1 ^2) - ((- (p2 `2)) ^2) is V11() real ext-real Element of REAL
(1 ^2) - ((- (p1 `2)) ^2) is V11() real ext-real Element of REAL
(p2 `1) ^2 is V11() real ext-real Element of REAL
K37((p2 `1),(p2 `1)) is V11() real ext-real set
(p2 `2) ^2 is V11() real ext-real Element of REAL
K37((p2 `2),(p2 `2)) is V11() real ext-real set
((p2 `1) ^2) + ((p2 `2) ^2) is V11() real ext-real Element of REAL
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.P.| is V11() real ext-real non negative Element of REAL
sqrt ((1 ^2) - ((- (p2 `2)) ^2)) is V11() real ext-real Element of REAL
(p1 `1) ^2 is V11() real ext-real Element of REAL
K37((p1 `1),(p1 `1)) is V11() real ext-real set
(p1 `2) ^2 is V11() real ext-real Element of REAL
K37((p1 `2),(p1 `2)) is V11() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V11() real ext-real Element of REAL
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.P.| is V11() real ext-real non negative Element of REAL
sqrt ((1 ^2) - ((- (p1 `2)) ^2)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (Lower_Arc p3) is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (Lower_Arc p3)) is non empty set
K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | (Lower_Arc p3))) is set
K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | (Lower_Arc p3)))) is set
K7( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)), the carrier of R^1) is set
K6(K7( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)), the carrier of R^1)) is set
C0 is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of R^1))
C0 | (Lower_Arc p3) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of R^1))
Closed-Interval-MSpace ((- 1),1) is non empty strict Reflexive discerning V91() triangle Discerning SubSpace of RealSpace
TopSpaceMetr (Closed-Interval-MSpace ((- 1),1)) is TopStruct
K7( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)), the carrier of (Closed-Interval-TSpace ((- 1),1))) is set
K6(K7( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)), the carrier of (Closed-Interval-TSpace ((- 1),1)))) is set
f is non empty Relation-like the carrier of ((TOP-REAL 2) | (Lower_Arc p3)) -defined the carrier of R^1 -valued Function-like V29( the carrier of ((TOP-REAL 2) | (Lower_Arc p3))) quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)), the carrier of R^1))
h is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | (Lower_Arc p3)) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | (Lower_Arc p3))))
h . 0 is set
h . 1 is set
f2 is V11() real ext-real Element of REAL
h . f2 is set
g2 is V11() real ext-real Element of REAL
h . g2 is set
the carrier of (Closed-Interval-TSpace (0,1)) is non empty V142() V143() V144() set
K7( the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((- 1),1))) is set
K6(K7( the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((- 1),1)))) is set
g is non empty Relation-like the carrier of ((TOP-REAL 2) | (Lower_Arc p3)) -defined the carrier of (Closed-Interval-TSpace ((- 1),1)) -valued Function-like V29( the carrier of ((TOP-REAL 2) | (Lower_Arc p3))) quasi_total continuous Element of K6(K7( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)), the carrier of (Closed-Interval-TSpace ((- 1),1))))
g * h is non empty Relation-like the carrier of I[01] -defined the carrier of (Closed-Interval-TSpace ((- 1),1)) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (Closed-Interval-TSpace ((- 1),1))))
dom g is Element of K6( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)))
K6( the carrier of ((TOP-REAL 2) | (Lower_Arc p3))) is set
[#] ((TOP-REAL 2) | (Lower_Arc p3)) is non empty non proper closed Element of K6( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)))
rng g is V142() V143() V144() Element of K6( the carrier of (Closed-Interval-TSpace ((- 1),1)))
h1 is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace ((- 1),1)) -valued Function-like V29( the carrier of (Closed-Interval-TSpace (0,1))) quasi_total Element of K6(K7( the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((- 1),1))))
dom h is V142() V143() V144() Element of K6( the carrier of I[01])
[#] I[01] is non empty non proper closed V142() V143() V144() Element of K6( the carrier of I[01])
|[(- 1),0]| `1 is V11() real ext-real Element of REAL
proj1 . |[(- 1),0]| is V11() real ext-real Element of REAL
g . |[(- 1),0]| is set
h1 . 1 is set
C0 . p2 is V11() real ext-real Element of the carrier of R^1
g . p2 is set
h1 . g2 is set
C0 . p1 is V11() real ext-real Element of the carrier of R^1
g . p1 is set
h1 . f2 is set
p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p1 `1 is V11() real ext-real Element of REAL
p3 is non empty functional closed compact Element of K6( the carrier of (TOP-REAL 2))
W-min p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
Lower_Arc p3 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : ( b1 in p3 & b1 `2 <= 0 ) } is set
Upper_Arc p3 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
(Upper_Arc p3) /\ (Lower_Arc p3) is functional Element of K6( the carrier of (TOP-REAL 2))
E-max p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
{(W-min p3),(E-max p3)} is non empty functional set
(TOP-REAL 2) | (Lower_Arc p3) is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (Lower_Arc p3)) is non empty set
K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | (Lower_Arc p3))) is set
K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | (Lower_Arc p3)))) is set
K7( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)), the carrier of R^1) is set
K6(K7( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)), the carrier of R^1)) is set
C0 is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of R^1))
C0 | (Lower_Arc p3) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of R^1))
Closed-Interval-MSpace ((- 1),1) is non empty strict Reflexive discerning V91() triangle Discerning SubSpace of RealSpace
TopSpaceMetr (Closed-Interval-MSpace ((- 1),1)) is TopStruct
K7( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)), the carrier of (Closed-Interval-TSpace ((- 1),1))) is set
K6(K7( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)), the carrier of (Closed-Interval-TSpace ((- 1),1)))) is set
f is non empty Relation-like the carrier of ((TOP-REAL 2) | (Lower_Arc p3)) -defined the carrier of R^1 -valued Function-like V29( the carrier of ((TOP-REAL 2) | (Lower_Arc p3))) quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)), the carrier of R^1))
h is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | (Lower_Arc p3)) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | (Lower_Arc p3))))
h . 0 is set
h . 1 is set
f2 is V11() real ext-real Element of REAL
h . f2 is set
g2 is V11() real ext-real Element of REAL
h . g2 is set
the carrier of (Closed-Interval-TSpace (0,1)) is non empty V142() V143() V144() set
K7( the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((- 1),1))) is set
K6(K7( the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((- 1),1)))) is set
g is non empty Relation-like the carrier of ((TOP-REAL 2) | (Lower_Arc p3)) -defined the carrier of (Closed-Interval-TSpace ((- 1),1)) -valued Function-like V29( the carrier of ((TOP-REAL 2) | (Lower_Arc p3))) quasi_total continuous Element of K6(K7( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)), the carrier of (Closed-Interval-TSpace ((- 1),1))))
g * h is non empty Relation-like the carrier of I[01] -defined the carrier of (Closed-Interval-TSpace ((- 1),1)) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (Closed-Interval-TSpace ((- 1),1))))
dom g is Element of K6( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)))
K6( the carrier of ((TOP-REAL 2) | (Lower_Arc p3))) is set
[#] ((TOP-REAL 2) | (Lower_Arc p3)) is non empty non proper closed Element of K6( the carrier of ((TOP-REAL 2) | (Lower_Arc p3)))
rng g is V142() V143() V144() Element of K6( the carrier of (Closed-Interval-TSpace ((- 1),1)))
h1 is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace ((- 1),1)) -valued Function-like V29( the carrier of (Closed-Interval-TSpace (0,1))) quasi_total Element of K6(K7( the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((- 1),1))))
dom h is V142() V143() V144() Element of K6( the carrier of I[01])
[#] I[01] is non empty non proper closed V142() V143() V144() Element of K6( the carrier of I[01])
|[(- 1),0]| `1 is V11() real ext-real Element of REAL
proj1 . |[(- 1),0]| is V11() real ext-real Element of REAL
g . |[(- 1),0]| is set
h1 . 1 is set
C0 . p2 is V11() real ext-real Element of the carrier of R^1
g . p2 is set
h1 . g2 is set
C0 . p1 is V11() real ext-real Element of the carrier of R^1
g . p1 is set
h1 . f2 is set
p1 is V11() real ext-real Element of REAL
p1 -FanMorphS is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
(p1 -FanMorphS) . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
|.p2.| is V11() real ext-real non negative Element of REAL
(p2 `1) / |.p2.| is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
|.p2.| is V11() real ext-real non negative Element of REAL
(p2 `1) / |.p2.| is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
|.p2.| is V11() real ext-real non negative Element of REAL
(p2 `1) / |.p2.| is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
|.p2.| is V11() real ext-real non negative Element of REAL
(p2 `1) / |.p2.| is V11() real ext-real Element of REAL
p1 is V11() real ext-real Element of REAL
p1 -FanMorphS is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(p1 -FanMorphS) . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(p1 -FanMorphS) . p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
C0 is non empty functional closed compact Element of K6( the carrier of (TOP-REAL 2))
W-min C0 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(W-min C0) `2 is V11() real ext-real Element of REAL
(p1 -FanMorphS) . (W-min C0) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
dom (p1 -FanMorphS) is functional Element of K6( the carrier of (TOP-REAL 2))
Lower_Arc C0 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
Upper_Arc C0 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
E-max C0 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : ( b1 in C0 & 0 <= b1 `2 ) } is set
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : ( b1 in C0 & b1 `2 <= 0 ) } is set
|.P.| is V11() real ext-real non negative Element of REAL
|.p3.| is V11() real ext-real non negative Element of REAL
f is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
f `2 is V11() real ext-real Element of REAL
f is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.f.| is V11() real ext-real non negative Element of REAL
P `2 is V11() real ext-real Element of REAL
f is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
f `2 is V11() real ext-real Element of REAL
f is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
f `2 is V11() real ext-real Element of REAL
f is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
f `2 is V11() real ext-real Element of REAL
f is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
f `2 is V11() real ext-real Element of REAL
f is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
f `2 is V11() real ext-real Element of REAL
f is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
f `2 is V11() real ext-real Element of REAL
P `2 is V11() real ext-real Element of REAL
f is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
f `2 is V11() real ext-real Element of REAL
|.P.| is V11() real ext-real non negative Element of REAL
|.p3.| is V11() real ext-real non negative Element of REAL
f is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.f.| is V11() real ext-real non negative Element of REAL
p4 `2 is V11() real ext-real Element of REAL
f is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
f `2 is V11() real ext-real Element of REAL
|.p4.| is V11() real ext-real non negative Element of REAL
|.p2.| is V11() real ext-real non negative Element of REAL
f is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.f.| is V11() real ext-real non negative Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
|[(p3 `1),(p3 `2)]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
- (p3 `2) is V11() real ext-real Element of REAL
f is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
f `2 is V11() real ext-real Element of REAL
g is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g `2 is V11() real ext-real Element of REAL
(p2 `1) ^2 is V11() real ext-real Element of REAL
K37((p2 `1),(p2 `1)) is V11() real ext-real set
(p2 `2) ^2 is V11() real ext-real Element of REAL
K37((p2 `2),(p2 `2)) is V11() real ext-real set
((p2 `1) ^2) + ((p2 `2) ^2) is V11() real ext-real Element of REAL
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
(p3 `2) ^2 is V11() real ext-real Element of REAL
K37((p3 `2),(p3 `2)) is V11() real ext-real set
((p2 `1) ^2) + ((p3 `2) ^2) is V11() real ext-real Element of REAL
f is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.f.| is V11() real ext-real non negative Element of REAL
f is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.f.| is V11() real ext-real non negative Element of REAL
|[(p2 `1),(p2 `2)]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
(p2 `1) / |.p2.| is V11() real ext-real Element of REAL
(p3 `1) / |.p3.| is V11() real ext-real Element of REAL
f is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.f.| is V11() real ext-real non negative Element of REAL
g is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.g.| is V11() real ext-real non negative Element of REAL
P `1 is V11() real ext-real Element of REAL
(P `1) / |.P.| is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
(p4 `1) / |.p4.| is V11() real ext-real Element of REAL
f is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
f `2 is V11() real ext-real Element of REAL
g is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g `2 is V11() real ext-real Element of REAL
h is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.h.| is V11() real ext-real non negative Element of REAL
f2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.f2.| is V11() real ext-real non negative Element of REAL
f is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.f.| is V11() real ext-real non negative Element of REAL
g is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.g.| is V11() real ext-real non negative Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
f is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
f `2 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
P is non empty functional closed compact Element of K6( the carrier of (TOP-REAL 2))
C0 is V11() real ext-real set
f is V11() real ext-real Element of REAL
f ^2 is V11() real ext-real Element of REAL
K37(f,f) is V11() real ext-real set
1 - (f ^2) is V11() real ext-real Element of REAL
sqrt (1 - (f ^2)) is V11() real ext-real Element of REAL
h is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.h.| is V11() real ext-real non negative Element of REAL
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
(sqrt (1 - (f ^2))) ^2 is V11() real ext-real Element of REAL
K37((sqrt (1 - (f ^2))),(sqrt (1 - (f ^2)))) is V11() real ext-real set
1 - ((sqrt (1 - (f ^2))) ^2) is V11() real ext-real Element of REAL
(1 - ((sqrt (1 - (f ^2))) ^2)) + ((sqrt (1 - (f ^2))) ^2) is V11() real ext-real Element of REAL
0 + ((sqrt (1 - (f ^2))) ^2) is V11() real ext-real Element of REAL
(sqrt (1 - (f ^2))) -FanMorphW is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
h is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
h . p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
h . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
h . p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
h . p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.p4.| is V11() real ext-real non negative Element of REAL
(p4 `2) / |.p4.| is V11() real ext-real Element of REAL
|.p3.| is V11() real ext-real non negative Element of REAL
(p3 `2) / |.p3.| is V11() real ext-real Element of REAL
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.I.| is V11() real ext-real non negative Element of REAL
KXP is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.KXP.| is V11() real ext-real non negative Element of REAL
(h . p4) `2 is V11() real ext-real Element of REAL
|.(h . p4).| is V11() real ext-real non negative Element of REAL
((h . p4) `2) / |.(h . p4).| is V11() real ext-real Element of REAL
(h . p3) `2 is V11() real ext-real Element of REAL
|.(h . p3).| is V11() real ext-real non negative Element of REAL
((h . p3) `2) / |.(h . p3).| is V11() real ext-real Element of REAL
(p4 `1) ^2 is V11() real ext-real Element of REAL
K37((p4 `1),(p4 `1)) is V11() real ext-real set
1 - ((p4 `1) ^2) is V11() real ext-real Element of REAL
- (p4 `1) is V11() real ext-real Element of REAL
- (p3 `1) is V11() real ext-real Element of REAL
(- (p4 `1)) ^2 is V11() real ext-real Element of REAL
K37((- (p4 `1)),(- (p4 `1))) is V11() real ext-real set
(- (p3 `1)) ^2 is V11() real ext-real Element of REAL
K37((- (p3 `1)),(- (p3 `1))) is V11() real ext-real set
(p3 `1) ^2 is V11() real ext-real Element of REAL
K37((p3 `1),(p3 `1)) is V11() real ext-real set
1 - ((p3 `1) ^2) is V11() real ext-real Element of REAL
- (p2 `1) is V11() real ext-real Element of REAL
(- (p2 `1)) ^2 is V11() real ext-real Element of REAL
K37((- (p2 `1)),(- (p2 `1))) is V11() real ext-real set
(p2 `1) ^2 is V11() real ext-real Element of REAL
K37((p2 `1),(p2 `1)) is V11() real ext-real set
1 - ((p2 `1) ^2) is V11() real ext-real Element of REAL
- (p1 `1) is V11() real ext-real Element of REAL
(- (p1 `1)) ^2 is V11() real ext-real Element of REAL
K37((- (p1 `1)),(- (p1 `1))) is V11() real ext-real set
(p1 `1) ^2 is V11() real ext-real Element of REAL
K37((p1 `1),(p1 `1)) is V11() real ext-real set
1 - ((p1 `1) ^2) is V11() real ext-real Element of REAL
(p3 `2) ^2 is V11() real ext-real Element of REAL
K37((p3 `2),(p3 `2)) is V11() real ext-real set
((p3 `1) ^2) + ((p3 `2) ^2) is V11() real ext-real Element of REAL
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.I.| is V11() real ext-real non negative Element of REAL
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.I.| is V11() real ext-real non negative Element of REAL
(h . p3) `1 is V11() real ext-real Element of REAL
|.(h . p2).| is V11() real ext-real non negative Element of REAL
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.I.| is V11() real ext-real non negative Element of REAL
|.p2.| is V11() real ext-real non negative Element of REAL
(p2 `2) / |.p2.| is V11() real ext-real Element of REAL
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.I.| is V11() real ext-real non negative Element of REAL
KXP is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.KXP.| is V11() real ext-real non negative Element of REAL
(h . p2) `2 is V11() real ext-real Element of REAL
((h . p2) `2) / |.(h . p2).| is V11() real ext-real Element of REAL
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.I.| is V11() real ext-real non negative Element of REAL
(p2 `2) ^2 is V11() real ext-real Element of REAL
K37((p2 `2),(p2 `2)) is V11() real ext-real set
((p2 `1) ^2) + ((p2 `2) ^2) is V11() real ext-real Element of REAL
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.I.| is V11() real ext-real non negative Element of REAL
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.I.| is V11() real ext-real non negative Element of REAL
(h . p2) `1 is V11() real ext-real Element of REAL
(p4 `2) ^2 is V11() real ext-real Element of REAL
K37((p4 `2),(p4 `2)) is V11() real ext-real set
((p4 `1) ^2) + ((p4 `2) ^2) is V11() real ext-real Element of REAL
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.I.| is V11() real ext-real non negative Element of REAL
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.I.| is V11() real ext-real non negative Element of REAL
(h . p4) `1 is V11() real ext-real Element of REAL
|.p1.| is V11() real ext-real non negative Element of REAL
(p1 `2) / |.p1.| is V11() real ext-real Element of REAL
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.I.| is V11() real ext-real non negative Element of REAL
KXP is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.KXP.| is V11() real ext-real non negative Element of REAL
(h . p1) `2 is V11() real ext-real Element of REAL
|.(h . p1).| is V11() real ext-real non negative Element of REAL
((h . p1) `2) / |.(h . p1).| is V11() real ext-real Element of REAL
(p1 `2) ^2 is V11() real ext-real Element of REAL
K37((p1 `2),(p1 `2)) is V11() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V11() real ext-real Element of REAL
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.I.| is V11() real ext-real non negative Element of REAL
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.I.| is V11() real ext-real non negative Element of REAL
(h . p1) `1 is V11() real ext-real Element of REAL
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.I.| is V11() real ext-real non negative Element of REAL
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
h . I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.(h . I).| is V11() real ext-real non negative Element of REAL
|.I.| is V11() real ext-real non negative Element of REAL
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.I.| is V11() real ext-real non negative Element of REAL
p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
P is non empty functional closed compact Element of K6( the carrier of (TOP-REAL 2))
p4 `1 is V11() real ext-real Element of REAL
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
(p4 `2) ^2 is V11() real ext-real Element of REAL
K37((p4 `2),(p4 `2)) is V11() real ext-real set
1 + ((p4 `2) ^2) is V11() real ext-real Element of REAL
C0 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.C0.| is V11() real ext-real non negative Element of REAL
C0 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.C0.| is V11() real ext-real non negative Element of REAL
C0 is V11() real ext-real set
g is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.g.| is V11() real ext-real non negative Element of REAL
f is V11() real ext-real Element of REAL
f -FanMorphN is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
g is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
g . p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g . p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g . p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g . O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.(g . O).| is V11() real ext-real non negative Element of REAL
|.O.| is V11() real ext-real non negative Element of REAL
p3 `1 is V11() real ext-real Element of REAL
|.p4.| is V11() real ext-real non negative Element of REAL
(p4 `1) / |.p4.| is V11() real ext-real Element of REAL
|.p3.| is V11() real ext-real non negative Element of REAL
(p3 `1) / |.p3.| is V11() real ext-real Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.I.| is V11() real ext-real non negative Element of REAL
(g . p4) `1 is V11() real ext-real Element of REAL
|.(g . p4).| is V11() real ext-real non negative Element of REAL
((g . p4) `1) / |.(g . p4).| is V11() real ext-real Element of REAL
(g . p3) `1 is V11() real ext-real Element of REAL
|.(g . p3).| is V11() real ext-real non negative Element of REAL
((g . p3) `1) / |.(g . p3).| is V11() real ext-real Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.I.| is V11() real ext-real non negative Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
(g . p3) `2 is V11() real ext-real Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p1 `1 is V11() real ext-real Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
(g . p4) `2 is V11() real ext-real Element of REAL
|.(g . p2).| is V11() real ext-real non negative Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
|.p2.| is V11() real ext-real non negative Element of REAL
(p2 `1) / |.p2.| is V11() real ext-real Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
(g . p2) `2 is V11() real ext-real Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
|.p1.| is V11() real ext-real non negative Element of REAL
(p1 `1) / |.p1.| is V11() real ext-real Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.I.| is V11() real ext-real non negative Element of REAL
(g . p2) `1 is V11() real ext-real Element of REAL
((g . p2) `1) / |.(g . p2).| is V11() real ext-real Element of REAL
(g . p1) `1 is V11() real ext-real Element of REAL
|.(g . p1).| is V11() real ext-real non negative Element of REAL
((g . p1) `1) / |.(g . p1).| is V11() real ext-real Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.I.| is V11() real ext-real non negative Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
(g . p1) `2 is V11() real ext-real Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.I.| is V11() real ext-real non negative Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.I.| is V11() real ext-real non negative Element of REAL
p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
P is non empty functional closed compact Element of K6( the carrier of (TOP-REAL 2))
C0 is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
f is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
C0 . p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
C0 . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
h is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
C0 . p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
f2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
C0 . p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
f `1 is V11() real ext-real Element of REAL
f `2 is V11() real ext-real Element of REAL
g `1 is V11() real ext-real Element of REAL
g `2 is V11() real ext-real Element of REAL
h `1 is V11() real ext-real Element of REAL
h `2 is V11() real ext-real Element of REAL
f2 `1 is V11() real ext-real Element of REAL
f2 `2 is V11() real ext-real Element of REAL
g2 is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
h1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g2 . f is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g2 . g is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g2 . h is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KXP is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g2 . f2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
h1 `1 is V11() real ext-real Element of REAL
h1 `2 is V11() real ext-real Element of REAL
O `1 is V11() real ext-real Element of REAL
O `2 is V11() real ext-real Element of REAL
I `1 is V11() real ext-real Element of REAL
I `2 is V11() real ext-real Element of REAL
KXP `1 is V11() real ext-real Element of REAL
KXP `2 is V11() real ext-real Element of REAL
g2 * C0 is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
KXN is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
dom C0 is functional Element of K6( the carrier of (TOP-REAL 2))
KXN . p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KXN . p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KYP is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KXN . KYP is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.(KXN . KYP).| is V11() real ext-real non negative Element of REAL
|.KYP.| is V11() real ext-real non negative Element of REAL
C0 . KYP is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g2 . (C0 . KYP) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.(C0 . KYP).| is V11() real ext-real non negative Element of REAL
KXN . p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KXN . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p1 `2 is V11() real ext-real Element of REAL
p1 `1 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
P is non empty functional closed compact Element of K6( the carrier of (TOP-REAL 2))
C0 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.C0.| is V11() real ext-real non negative Element of REAL
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
(p4 `1) ^2 is V11() real ext-real Element of REAL
K37((p4 `1),(p4 `1)) is V11() real ext-real set
(p4 `2) ^2 is V11() real ext-real Element of REAL
K37((p4 `2),(p4 `2)) is V11() real ext-real set
((p4 `1) ^2) + ((p4 `2) ^2) is V11() real ext-real Element of REAL
((p4 `1) ^2) + 1 is V11() real ext-real Element of REAL
C0 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.C0.| is V11() real ext-real non negative Element of REAL
C0 is V11() real ext-real set
g is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.g.| is V11() real ext-real non negative Element of REAL
f is V11() real ext-real Element of REAL
f -FanMorphE is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
g is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
g . p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g . p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g . p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.(g . p4).| is V11() real ext-real non negative Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
|.(g . p1).| is V11() real ext-real non negative Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
|.(g . p3).| is V11() real ext-real non negative Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
|.(g . p2).| is V11() real ext-real non negative Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
Upper_Arc P is non empty functional Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : ( b1 in P & 0 <= b1 `2 ) } is set
|.p4.| is V11() real ext-real non negative Element of REAL
(p4 `2) / |.p4.| is V11() real ext-real Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
(g . p4) `1 is V11() real ext-real Element of REAL
f ^2 is V11() real ext-real Element of REAL
K37(f,f) is V11() real ext-real set
1 - (f ^2) is V11() real ext-real Element of REAL
sqrt (1 - (f ^2)) is V11() real ext-real Element of REAL
|[(sqrt (1 - (f ^2))),f]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(g . p4) `2 is V11() real ext-real Element of REAL
((g . p4) `1) ^2 is V11() real ext-real Element of REAL
K37(((g . p4) `1),((g . p4) `1)) is V11() real ext-real set
((g . p4) `2) ^2 is V11() real ext-real Element of REAL
K37(((g . p4) `2),((g . p4) `2)) is V11() real ext-real set
(((g . p4) `1) ^2) + (((g . p4) `2) ^2) is V11() real ext-real Element of REAL
g . |[(sqrt (1 - (f ^2))),f]| is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|[(sqrt (1 - (f ^2))),f]| `1 is V11() real ext-real Element of REAL
|[(sqrt (1 - (f ^2))),f]| `2 is V11() real ext-real Element of REAL
|.|[(sqrt (1 - (f ^2))),f]|.| is V11() real ext-real non negative Element of REAL
(sqrt (1 - (f ^2))) ^2 is V11() real ext-real Element of REAL
K37((sqrt (1 - (f ^2))),(sqrt (1 - (f ^2)))) is V11() real ext-real set
((sqrt (1 - (f ^2))) ^2) + (f ^2) is V11() real ext-real Element of REAL
sqrt (((sqrt (1 - (f ^2))) ^2) + (f ^2)) is V11() real ext-real Element of REAL
(1 - (f ^2)) + (f ^2) is V11() real ext-real Element of REAL
sqrt ((1 - (f ^2)) + (f ^2)) is V11() real ext-real Element of REAL
(|[(sqrt (1 - (f ^2))),f]| `2) / |.|[(sqrt (1 - (f ^2))),f]|.| is V11() real ext-real Element of REAL
(g . |[(sqrt (1 - (f ^2))),f]|) `2 is V11() real ext-real Element of REAL
|.(g . |[(sqrt (1 - (f ^2))),f]|).| is V11() real ext-real non negative Element of REAL
(g . |[(sqrt (1 - (f ^2))),f]|) `1 is V11() real ext-real Element of REAL
((g . |[(sqrt (1 - (f ^2))),f]|) `1) ^2 is V11() real ext-real Element of REAL
K37(((g . |[(sqrt (1 - (f ^2))),f]|) `1),((g . |[(sqrt (1 - (f ^2))),f]|) `1)) is V11() real ext-real set
((g . |[(sqrt (1 - (f ^2))),f]|) `2) ^2 is V11() real ext-real Element of REAL
K37(((g . |[(sqrt (1 - (f ^2))),f]|) `2),((g . |[(sqrt (1 - (f ^2))),f]|) `2)) is V11() real ext-real set
(((g . |[(sqrt (1 - (f ^2))),f]|) `1) ^2) + (((g . |[(sqrt (1 - (f ^2))),f]|) `2) ^2) is V11() real ext-real Element of REAL
dom g is functional Element of K6( the carrier of (TOP-REAL 2))
Lower_Arc P is non empty functional Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : ( b1 in P & b1 `2 <= 0 ) } is set
(g . p3) `2 is V11() real ext-real Element of REAL
0 ^2 is V11() real ext-real Element of REAL
K37(0,0) is empty V11() real ext-real non positive non negative Function-like functional V142() V143() V144() V145() V146() V147() V148() V201() V204() set
((g . p3) `2) ^2 is V11() real ext-real Element of REAL
K37(((g . p3) `2),((g . p3) `2)) is V11() real ext-real set
(0 ^2) + (((g . p3) `2) ^2) is V11() real ext-real Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
(g . p3) `2 is V11() real ext-real Element of REAL
(g . p3) `2 is V11() real ext-real Element of REAL
(g . p3) `2 is V11() real ext-real Element of REAL
W-min P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(g . p1) `2 is V11() real ext-real Element of REAL
(g . p2) `2 is V11() real ext-real Element of REAL
(g . p1) `2 is V11() real ext-real Element of REAL
(g . p2) `2 is V11() real ext-real Element of REAL
(g . p1) `2 is V11() real ext-real Element of REAL
(g . p2) `2 is V11() real ext-real Element of REAL
(g . p1) `2 is V11() real ext-real Element of REAL
(g . p2) `2 is V11() real ext-real Element of REAL
W-min P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(g . p1) `2 is V11() real ext-real Element of REAL
(g . p2) `2 is V11() real ext-real Element of REAL
W-min P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(g . p1) `2 is V11() real ext-real Element of REAL
(g . p2) `2 is V11() real ext-real Element of REAL
W-min P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(g . p1) `2 is V11() real ext-real Element of REAL
(g . p2) `2 is V11() real ext-real Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
|.p3.| is V11() real ext-real non negative Element of REAL
(p3 `2) / |.p3.| is V11() real ext-real Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
(g . p3) `1 is V11() real ext-real Element of REAL
(g . p3) `2 is V11() real ext-real Element of REAL
0 ^2 is V11() real ext-real Element of REAL
K37(0,0) is empty V11() real ext-real non positive non negative Function-like functional V142() V143() V144() V145() V146() V147() V148() V201() V204() set
(p2 `2) ^2 is V11() real ext-real Element of REAL
K37((p2 `2),(p2 `2)) is V11() real ext-real set
(0 ^2) + ((p2 `2) ^2) is V11() real ext-real Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
(g . p2) `2 is V11() real ext-real Element of REAL
(g . p2) `1 is V11() real ext-real Element of REAL
(g . p2) `2 is V11() real ext-real Element of REAL
|.p2.| is V11() real ext-real non negative Element of REAL
(p2 `2) / |.p2.| is V11() real ext-real Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.I.| is V11() real ext-real non negative Element of REAL
(g . p2) `2 is V11() real ext-real Element of REAL
((g . p2) `2) / |.(g . p2).| is V11() real ext-real Element of REAL
((g . p3) `2) / |.(g . p3).| is V11() real ext-real Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.I.| is V11() real ext-real non negative Element of REAL
(g . p2) `2 is V11() real ext-real Element of REAL
(g . p2) `2 is V11() real ext-real Element of REAL
(g . p2) `2 is V11() real ext-real Element of REAL
(g . p2) `2 is V11() real ext-real Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.I.| is V11() real ext-real non negative Element of REAL
((g . p3) `2) / |.(g . p3).| is V11() real ext-real Element of REAL
((g . p4) `2) / |.(g . p4).| is V11() real ext-real Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.I.| is V11() real ext-real non negative Element of REAL
((g . p3) `2) ^2 is V11() real ext-real Element of REAL
K37(((g . p3) `2),((g . p3) `2)) is V11() real ext-real set
(1 ^2) - (((g . p4) `2) ^2) is V11() real ext-real Element of REAL
(1 ^2) - (((g . p3) `2) ^2) is V11() real ext-real Element of REAL
sqrt ((1 ^2) - (((g . p4) `2) ^2)) is V11() real ext-real Element of REAL
((g . p3) `1) ^2 is V11() real ext-real Element of REAL
K37(((g . p3) `1),((g . p3) `1)) is V11() real ext-real set
(((g . p3) `1) ^2) + (((g . p3) `2) ^2) is V11() real ext-real Element of REAL
sqrt ((1 ^2) - (((g . p3) `2) ^2)) is V11() real ext-real Element of REAL
0 ^2 is V11() real ext-real Element of REAL
K37(0,0) is empty V11() real ext-real non positive non negative Function-like functional V142() V143() V144() V145() V146() V147() V148() V201() V204() set
(p2 `2) ^2 is V11() real ext-real Element of REAL
K37((p2 `2),(p2 `2)) is V11() real ext-real set
(0 ^2) + ((p2 `2) ^2) is V11() real ext-real Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
|.p3.| is V11() real ext-real non negative Element of REAL
(p3 `2) / |.p3.| is V11() real ext-real Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
(g . p3) `1 is V11() real ext-real Element of REAL
(g . p3) `2 is V11() real ext-real Element of REAL
(g . p2) `2 is V11() real ext-real Element of REAL
(g . p2) `1 is V11() real ext-real Element of REAL
(g . p2) `2 is V11() real ext-real Element of REAL
|.p2.| is V11() real ext-real non negative Element of REAL
(p2 `2) / |.p2.| is V11() real ext-real Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.I.| is V11() real ext-real non negative Element of REAL
(g . p2) `2 is V11() real ext-real Element of REAL
((g . p2) `2) / |.(g . p2).| is V11() real ext-real Element of REAL
((g . p3) `2) / |.(g . p3).| is V11() real ext-real Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.I.| is V11() real ext-real non negative Element of REAL
(g . p2) `2 is V11() real ext-real Element of REAL
(g . p2) `2 is V11() real ext-real Element of REAL
(g . p2) `2 is V11() real ext-real Element of REAL
(g . p2) `2 is V11() real ext-real Element of REAL
(g . p2) `2 is V11() real ext-real Element of REAL
(g . p3) `2 is V11() real ext-real Element of REAL
(g . p2) `2 is V11() real ext-real Element of REAL
(g . p3) `2 is V11() real ext-real Element of REAL
0 ^2 is V11() real ext-real Element of REAL
K37(0,0) is empty V11() real ext-real non positive non negative Function-like functional V142() V143() V144() V145() V146() V147() V148() V201() V204() set
(p2 `2) ^2 is V11() real ext-real Element of REAL
K37((p2 `2),(p2 `2)) is V11() real ext-real set
(0 ^2) + ((p2 `2) ^2) is V11() real ext-real Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
(p1 `2) ^2 is V11() real ext-real Element of REAL
K37((p1 `2),(p1 `2)) is V11() real ext-real set
(0 ^2) + ((p1 `2) ^2) is V11() real ext-real Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
(g . p1) `2 is V11() real ext-real Element of REAL
(g . p2) `1 is V11() real ext-real Element of REAL
(g . p1) `1 is V11() real ext-real Element of REAL
(g . p1) `1 is V11() real ext-real Element of REAL
W-min P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(g . p1) `2 is V11() real ext-real Element of REAL
(g . p2) `1 is V11() real ext-real Element of REAL
(g . p1) `2 is V11() real ext-real Element of REAL
|.p1.| is V11() real ext-real non negative Element of REAL
(p1 `2) / |.p1.| is V11() real ext-real Element of REAL
|.p2.| is V11() real ext-real non negative Element of REAL
(p2 `2) / |.p2.| is V11() real ext-real Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.I.| is V11() real ext-real non negative Element of REAL
(g . p1) `2 is V11() real ext-real Element of REAL
((g . p1) `2) / |.(g . p1).| is V11() real ext-real Element of REAL
((g . p2) `2) / |.(g . p2).| is V11() real ext-real Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.I.| is V11() real ext-real non negative Element of REAL
(g . p1) `2 is V11() real ext-real Element of REAL
(g . p1) `2 is V11() real ext-real Element of REAL
(g . p1) `2 is V11() real ext-real Element of REAL
(g . p1) `2 is V11() real ext-real Element of REAL
(g . p1) `2 is V11() real ext-real Element of REAL
(g . p1) `2 is V11() real ext-real Element of REAL
(g . p1) `2 is V11() real ext-real Element of REAL
(g . p2) `2 is V11() real ext-real Element of REAL
(g . p3) `2 is V11() real ext-real Element of REAL
(g . p1) `2 is V11() real ext-real Element of REAL
(g . p2) `2 is V11() real ext-real Element of REAL
(g . p3) `2 is V11() real ext-real Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g . O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.(g . O).| is V11() real ext-real non negative Element of REAL
|.O.| is V11() real ext-real non negative Element of REAL
Lower_Arc P is non empty functional Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : ( b1 in P & b1 `2 <= 0 ) } is set
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
O `2 is V11() real ext-real Element of REAL
Upper_Arc P is non empty functional Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : ( b1 in P & 0 <= b1 `2 ) } is set
W-min P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
E-max P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
id (TOP-REAL 2) is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total being_homeomorphism Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
id the carrier of (TOP-REAL 2) is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like one-to-one V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(id (TOP-REAL 2)) . p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(id (TOP-REAL 2)) . p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(id (TOP-REAL 2)) . I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.((id (TOP-REAL 2)) . I).| is V11() real ext-real non negative Element of REAL
|.I.| is V11() real ext-real non negative Element of REAL
(id (TOP-REAL 2)) . p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(id (TOP-REAL 2)) . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
I `2 is V11() real ext-real Element of REAL
KXP is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KXP `2 is V11() real ext-real Element of REAL
KXN is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KXN `2 is V11() real ext-real Element of REAL
O is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
O . p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KXP is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
O . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KXN is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
O . p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KYP is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
O . p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
I `2 is V11() real ext-real Element of REAL
KXP `2 is V11() real ext-real Element of REAL
KXN `2 is V11() real ext-real Element of REAL
KYP `2 is V11() real ext-real Element of REAL
KYN is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
x2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KYN . p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
z3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KYN . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
z2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KYN . p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
f4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KYN . p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
x2 `2 is V11() real ext-real Element of REAL
z3 `2 is V11() real ext-real Element of REAL
z2 `2 is V11() real ext-real Element of REAL
f4 `2 is V11() real ext-real Element of REAL
p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p1 `2 is V11() real ext-real Element of REAL
p1 `1 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
P is non empty functional closed compact Element of K6( the carrier of (TOP-REAL 2))
C0 is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
f is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
C0 . p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
C0 . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
h is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
C0 . p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
f2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
C0 . p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
f `2 is V11() real ext-real Element of REAL
g `2 is V11() real ext-real Element of REAL
h `2 is V11() real ext-real Element of REAL
f2 `2 is V11() real ext-real Element of REAL
g2 is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
h1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g2 . f is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g2 . g is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g2 . h is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KXP is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g2 . f2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
h1 `1 is V11() real ext-real Element of REAL
h1 `2 is V11() real ext-real Element of REAL
O `1 is V11() real ext-real Element of REAL
O `2 is V11() real ext-real Element of REAL
I `1 is V11() real ext-real Element of REAL
I `2 is V11() real ext-real Element of REAL
KXP `1 is V11() real ext-real Element of REAL
KXP `2 is V11() real ext-real Element of REAL
g2 * C0 is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
KXN is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
dom C0 is functional Element of K6( the carrier of (TOP-REAL 2))
KXN . p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KXN . p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KYP is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KXN . KYP is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.(KXN . KYP).| is V11() real ext-real non negative Element of REAL
|.KYP.| is V11() real ext-real non negative Element of REAL
C0 . KYP is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g2 . (C0 . KYP) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.(C0 . KYP).| is V11() real ext-real non negative Element of REAL
KXN . p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KXN . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P is non empty functional closed compact Element of K6( the carrier of (TOP-REAL 2))
W-min P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
Upper_Arc P is non empty functional Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : ( b1 in P & 0 <= b1 `2 ) } is set
(W-min P) `2 is V11() real ext-real Element of REAL
E-max P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(W-min P) `1 is V11() real ext-real Element of REAL
p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P is non empty functional closed compact Element of K6( the carrier of (TOP-REAL 2))
Lower_Arc P is non empty functional Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : ( b1 in P & b1 `2 <= 0 ) } is set
W-min P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(W-min P) `2 is V11() real ext-real Element of REAL
E-max P is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
Upper_Arc P is non empty functional Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : ( b1 in P & 0 <= b1 `2 ) } is set
p4 `1 is V11() real ext-real Element of REAL
C0 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.C0.| is V11() real ext-real non negative Element of REAL
C0 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.C0.| is V11() real ext-real non negative Element of REAL
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
(p4 `1) ^2 is V11() real ext-real Element of REAL
K37((p4 `1),(p4 `1)) is V11() real ext-real set
p4 `2 is V11() real ext-real Element of REAL
(p4 `2) ^2 is V11() real ext-real Element of REAL
K37((p4 `2),(p4 `2)) is V11() real ext-real set
((p4 `1) ^2) + ((p4 `2) ^2) is V11() real ext-real Element of REAL
((p4 `2) ^2) + 1 is V11() real ext-real Element of REAL
C0 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.C0.| is V11() real ext-real non negative Element of REAL
p1 `2 is V11() real ext-real Element of REAL
C0 is V11() real ext-real set
f is V11() real ext-real Element of REAL
f -FanMorphS is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
g is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
g . p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g . p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g . p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
(p4 `1) ^2 is V11() real ext-real Element of REAL
K37((p4 `1),(p4 `1)) is V11() real ext-real set
(p4 `2) ^2 is V11() real ext-real Element of REAL
K37((p4 `2),(p4 `2)) is V11() real ext-real set
((p4 `1) ^2) + ((p4 `2) ^2) is V11() real ext-real Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p1 `1 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
|.p4.| is V11() real ext-real non negative Element of REAL
(p4 `1) / |.p4.| is V11() real ext-real Element of REAL
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.O.| is V11() real ext-real non negative Element of REAL
(g . p4) `1 is V11() real ext-real Element of REAL
(g . p3) `2 is V11() real ext-real Element of REAL
(g . p3) `1 is V11() real ext-real Element of REAL
(g . p3) `2 is V11() real ext-real Element of REAL
(g . p3) `1 is V11() real ext-real Element of REAL
(g . p3) `2 is V11() real ext-real Element of REAL
(g . p3) `1 is V11() real ext-real Element of REAL
(g . p3) `2 is V11() real ext-real Element of REAL
(g . p3) `1 is V11() real ext-real Element of REAL
(g . p2) `2 is V11() real ext-real Element of REAL
(g . p2) `1 is V11() real ext-real Element of REAL
(g . p2) `2 is V11() real ext-real Element of REAL
(g . p2) `1 is V11() real ext-real Element of REAL
(g . p2) `2 is V11() real ext-real Element of REAL
(g . p2) `1 is V11() real ext-real Element of REAL
(g . p2) `2 is V11() real ext-real Element of REAL
(g . p2) `1 is V11() real ext-real Element of REAL
(g . p1) `2 is V11() real ext-real Element of REAL
(g . p1) `1 is V11() real ext-real Element of REAL
(g . p1) `2 is V11() real ext-real Element of REAL
(g . p1) `1 is V11() real ext-real Element of REAL
(g . p1) `2 is V11() real ext-real Element of REAL
(g . p1) `1 is V11() real ext-real Element of REAL
(g . p1) `2 is V11() real ext-real Element of REAL
(g . p1) `1 is V11() real ext-real Element of REAL
O is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
O . (g . p1) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KXP is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
O . (g . p2) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KXN is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
O . (g . p3) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KYP is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
O . (g . p4) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
I `1 is V11() real ext-real Element of REAL
I `2 is V11() real ext-real Element of REAL
KXP `1 is V11() real ext-real Element of REAL
KXP `2 is V11() real ext-real Element of REAL
KXN `1 is V11() real ext-real Element of REAL
KXN `2 is V11() real ext-real Element of REAL
KYP `1 is V11() real ext-real Element of REAL
KYP `2 is V11() real ext-real Element of REAL
O * g is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
dom g is functional Element of K6( the carrier of (TOP-REAL 2))
KYN is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
KYN . p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KYN . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
x2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KYN . x2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.(KYN . x2).| is V11() real ext-real non negative Element of REAL
|.x2.| is V11() real ext-real non negative Element of REAL
g . x2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
O . (g . x2) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.(g . x2).| is V11() real ext-real non negative Element of REAL
KYN . p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KYN . p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
O is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
O . p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KXP is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
O . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KXN is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
O . p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KYP is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
O . p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
I `1 is V11() real ext-real Element of REAL
I `2 is V11() real ext-real Element of REAL
KXP `1 is V11() real ext-real Element of REAL
KXP `2 is V11() real ext-real Element of REAL
KXN `1 is V11() real ext-real Element of REAL
KXN `2 is V11() real ext-real Element of REAL
KYP `1 is V11() real ext-real Element of REAL
KYP `2 is V11() real ext-real Element of REAL
KYN is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
x2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KYN . p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
z3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KYN . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
z2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KYN . p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
f4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KYN . p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
x2 `1 is V11() real ext-real Element of REAL
x2 `2 is V11() real ext-real Element of REAL
z3 `1 is V11() real ext-real Element of REAL
z3 `2 is V11() real ext-real Element of REAL
z2 `1 is V11() real ext-real Element of REAL
z2 `2 is V11() real ext-real Element of REAL
f4 `1 is V11() real ext-real Element of REAL
f4 `2 is V11() real ext-real Element of REAL
C0 is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
f is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
C0 . p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
C0 . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
h is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
C0 . p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
f2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
C0 . p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
f `1 is V11() real ext-real Element of REAL
f `2 is V11() real ext-real Element of REAL
g `1 is V11() real ext-real Element of REAL
g `2 is V11() real ext-real Element of REAL
h `1 is V11() real ext-real Element of REAL
h `2 is V11() real ext-real Element of REAL
f2 `1 is V11() real ext-real Element of REAL
f2 `2 is V11() real ext-real Element of REAL
g2 is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
h1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g2 . p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g2 . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g2 . p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KXP is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g2 . p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
h1 `1 is V11() real ext-real Element of REAL
h1 `2 is V11() real ext-real Element of REAL
O `1 is V11() real ext-real Element of REAL
O `2 is V11() real ext-real Element of REAL
I `1 is V11() real ext-real Element of REAL
I `2 is V11() real ext-real Element of REAL
KXP `1 is V11() real ext-real Element of REAL
KXP `2 is V11() real ext-real Element of REAL
p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
P is non empty functional closed compact Element of K6( the carrier of (TOP-REAL 2))
(p1 `2) -FanMorphW is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
((p1 `2) -FanMorphW) . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
((p1 `2) -FanMorphW) . p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
((p1 `2) -FanMorphW) . p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.p1.| is V11() real ext-real non negative Element of REAL
(p1 `2) / |.p1.| is V11() real ext-real Element of REAL
h is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.h.| is V11() real ext-real non negative Element of REAL
(((p1 `2) -FanMorphW) . p1) `2 is V11() real ext-real Element of REAL
|.(((p1 `2) -FanMorphW) . p1).| is V11() real ext-real non negative Element of REAL
h is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.h.| is V11() real ext-real non negative Element of REAL
((((p1 `2) -FanMorphW) . p1) `2) / |.(((p1 `2) -FanMorphW) . p1).| is V11() real ext-real Element of REAL
|.p2.| is V11() real ext-real non negative Element of REAL
(p2 `2) / |.p2.| is V11() real ext-real Element of REAL
h is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.h.| is V11() real ext-real non negative Element of REAL
(((p1 `2) -FanMorphW) . p2) `1 is V11() real ext-real Element of REAL
|.(((p1 `2) -FanMorphW) . p2).| is V11() real ext-real non negative Element of REAL
h is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.h.| is V11() real ext-real non negative Element of REAL
(((p1 `2) -FanMorphW) . p2) `2 is V11() real ext-real Element of REAL
((((p1 `2) -FanMorphW) . p2) `2) / |.(((p1 `2) -FanMorphW) . p2).| is V11() real ext-real Element of REAL
|.(((p1 `2) -FanMorphW) . p3).| is V11() real ext-real non negative Element of REAL
h is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.h.| is V11() real ext-real non negative Element of REAL
(((p1 `2) -FanMorphW) . p3) `2 is V11() real ext-real Element of REAL
((((p1 `2) -FanMorphW) . p3) `2) / |.(((p1 `2) -FanMorphW) . p3).| is V11() real ext-real Element of REAL
((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p2) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(((p1 `2) -FanMorphW) . p3) `1 is V11() real ext-real Element of REAL
((((p1 `2) -FanMorphW) . p3) `1) / |.(((p1 `2) -FanMorphW) . p3).| is V11() real ext-real Element of REAL
|.p3.| is V11() real ext-real non negative Element of REAL
(p3 `2) / |.p3.| is V11() real ext-real Element of REAL
g2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.g2.| is V11() real ext-real non negative Element of REAL
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
((((p1 `2) -FanMorphW) . p3) `1) ^2 is V11() real ext-real Element of REAL
K37(((((p1 `2) -FanMorphW) . p3) `1),((((p1 `2) -FanMorphW) . p3) `1)) is V11() real ext-real set
((((p1 `2) -FanMorphW) . p3) `2) ^2 is V11() real ext-real Element of REAL
K37(((((p1 `2) -FanMorphW) . p3) `2),((((p1 `2) -FanMorphW) . p3) `2)) is V11() real ext-real set
(((((p1 `2) -FanMorphW) . p3) `1) ^2) + (((((p1 `2) -FanMorphW) . p3) `2) ^2) is V11() real ext-real Element of REAL
((((p1 `2) -FanMorphW) . p2) `1) ^2 is V11() real ext-real Element of REAL
K37(((((p1 `2) -FanMorphW) . p2) `1),((((p1 `2) -FanMorphW) . p2) `1)) is V11() real ext-real set
((((p1 `2) -FanMorphW) . p2) `2) ^2 is V11() real ext-real Element of REAL
K37(((((p1 `2) -FanMorphW) . p2) `2),((((p1 `2) -FanMorphW) . p2) `2)) is V11() real ext-real set
(((((p1 `2) -FanMorphW) . p2) `1) ^2) + (((((p1 `2) -FanMorphW) . p2) `2) ^2) is V11() real ext-real Element of REAL
g2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.g2.| is V11() real ext-real non negative Element of REAL
- ((((p1 `2) -FanMorphW) . p2) `1) is V11() real ext-real Element of REAL
(- ((((p1 `2) -FanMorphW) . p2) `1)) ^2 is V11() real ext-real Element of REAL
K37((- ((((p1 `2) -FanMorphW) . p2) `1)),(- ((((p1 `2) -FanMorphW) . p2) `1))) is V11() real ext-real set
- (- ((((p1 `2) -FanMorphW) . p2) `1)) is V11() real ext-real Element of REAL
((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2 is V11() real ext-real Element of REAL
|.((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)).| is V11() real ext-real non negative Element of REAL
((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `1 is V11() real ext-real Element of REAL
(((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `1) / |.((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)).| is V11() real ext-real Element of REAL
g2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.g2.| is V11() real ext-real non negative Element of REAL
g2 is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
h1 is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
((((p1 `2) -FanMorphW) . p2) `1) / |.(((p1 `2) -FanMorphW) . p2).| is V11() real ext-real Element of REAL
((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p2)) `1 is V11() real ext-real Element of REAL
|.((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p2)).| is V11() real ext-real non negative Element of REAL
(((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p2)) `1) / |.((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p2)).| is V11() real ext-real Element of REAL
((p1 `2) -FanMorphW) . p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.(((p1 `2) -FanMorphW) . p4).| is V11() real ext-real non negative Element of REAL
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.I.| is V11() real ext-real non negative Element of REAL
(((p1 `2) -FanMorphW) . p4) `2 is V11() real ext-real Element of REAL
((((p1 `2) -FanMorphW) . p4) `2) / |.(((p1 `2) -FanMorphW) . p4).| is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
|.p4.| is V11() real ext-real non negative Element of REAL
(p4 `2) / |.p4.| is V11() real ext-real Element of REAL
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.I.| is V11() real ext-real non negative Element of REAL
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.I.| is V11() real ext-real non negative Element of REAL
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.I.| is V11() real ext-real non negative Element of REAL
((((p1 `2) -FanMorphW) . p4) `2) ^2 is V11() real ext-real Element of REAL
K37(((((p1 `2) -FanMorphW) . p4) `2),((((p1 `2) -FanMorphW) . p4) `2)) is V11() real ext-real set
(((p1 `2) -FanMorphW) . p4) `1 is V11() real ext-real Element of REAL
((((p1 `2) -FanMorphW) . p4) `1) ^2 is V11() real ext-real Element of REAL
K37(((((p1 `2) -FanMorphW) . p4) `1),((((p1 `2) -FanMorphW) . p4) `1)) is V11() real ext-real set
(((((p1 `2) -FanMorphW) . p4) `1) ^2) + (((((p1 `2) -FanMorphW) . p4) `2) ^2) is V11() real ext-real Element of REAL
- ((((p1 `2) -FanMorphW) . p3) `1) is V11() real ext-real Element of REAL
(- ((((p1 `2) -FanMorphW) . p3) `1)) ^2 is V11() real ext-real Element of REAL
K37((- ((((p1 `2) -FanMorphW) . p3) `1)),(- ((((p1 `2) -FanMorphW) . p3) `1))) is V11() real ext-real set
- (- ((((p1 `2) -FanMorphW) . p3) `1)) is V11() real ext-real Element of REAL
((((p1 `2) -FanMorphW) . p4) `1) / |.(((p1 `2) -FanMorphW) . p4).| is V11() real ext-real Element of REAL
(((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `1) ^2 is V11() real ext-real Element of REAL
K37((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `1),(((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `1)) is V11() real ext-real set
(((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) ^2 is V11() real ext-real Element of REAL
K37((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2),(((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2)) is V11() real ext-real set
((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `1) ^2) + ((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) ^2) is V11() real ext-real Element of REAL
|.((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4)).| is V11() real ext-real non negative Element of REAL
((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4)) `1 is V11() real ext-real Element of REAL
(((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4)) `1) / |.((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4)).| is V11() real ext-real Element of REAL
(((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p1) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.(((p1 `2) -FanMorphW) . p1).| ^2 is V11() real ext-real Element of REAL
K37(|.(((p1 `2) -FanMorphW) . p1).|,|.(((p1 `2) -FanMorphW) . p1).|) is V11() real ext-real non negative set
(((p1 `2) -FanMorphW) . p1) `1 is V11() real ext-real Element of REAL
((((p1 `2) -FanMorphW) . p1) `1) ^2 is V11() real ext-real Element of REAL
K37(((((p1 `2) -FanMorphW) . p1) `1),((((p1 `2) -FanMorphW) . p1) `1)) is V11() real ext-real set
((((p1 `2) -FanMorphW) . p1) `2) ^2 is V11() real ext-real Element of REAL
K37(((((p1 `2) -FanMorphW) . p1) `2),((((p1 `2) -FanMorphW) . p1) `2)) is V11() real ext-real set
(((((p1 `2) -FanMorphW) . p1) `1) ^2) + (((((p1 `2) -FanMorphW) . p1) `2) ^2) is V11() real ext-real Element of REAL
((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p1)) `1 is V11() real ext-real Element of REAL
(((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4)) `1) ^2 is V11() real ext-real Element of REAL
K37((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4)) `1),(((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4)) `1)) is V11() real ext-real set
((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4)) `2 is V11() real ext-real Element of REAL
(((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4)) `2) ^2 is V11() real ext-real Element of REAL
K37((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4)) `2),(((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4)) `2)) is V11() real ext-real set
((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4)) `1) ^2) + ((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4)) `2) ^2) is V11() real ext-real Element of REAL
((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) ^2) - ((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4)) `2) ^2) is V11() real ext-real Element of REAL
(((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) ^2) - ((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4)) `2) ^2)) + ((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4)) `2) ^2) is V11() real ext-real Element of REAL
0 + ((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4)) `2) ^2) is V11() real ext-real Element of REAL
(((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4)) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p1)) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p1)) `2 is V11() real ext-real Element of REAL
(((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p1))) `2 is V11() real ext-real Element of REAL
(((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4))) `1 is V11() real ext-real Element of REAL
((((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4))) `1) -FanMorphS is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(((((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4))) `1) -FanMorphS) . (((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4))) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p2)) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.(((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3))).| is V11() real ext-real non negative Element of REAL
|.(((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3))).| ^2 is V11() real ext-real Element of REAL
K37(|.(((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3))).|,|.(((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3))).|) is V11() real ext-real non negative set
(((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3))) `1 is V11() real ext-real Element of REAL
((((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3))) `1) ^2 is V11() real ext-real Element of REAL
K37(((((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3))) `1),((((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3))) `1)) is V11() real ext-real set
(((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3))) `2 is V11() real ext-real Element of REAL
((((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3))) `2) ^2 is V11() real ext-real Element of REAL
K37(((((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3))) `2),((((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3))) `2)) is V11() real ext-real set
(((((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3))) `1) ^2) + (((((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3))) `2) ^2) is V11() real ext-real Element of REAL
(((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) / |.((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)).| is V11() real ext-real Element of REAL
|.((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p2)).| ^2 is V11() real ext-real Element of REAL
K37(|.((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p2)).|,|.((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p2)).|) is V11() real ext-real non negative set
(((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p2)) `1) ^2 is V11() real ext-real Element of REAL
K37((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p2)) `1),(((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p2)) `1)) is V11() real ext-real set
((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p2)) `2 is V11() real ext-real Element of REAL
(((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p2)) `2) ^2 is V11() real ext-real Element of REAL
K37((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p2)) `2),(((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p2)) `2)) is V11() real ext-real set
((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p2)) `1) ^2) + ((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p2)) `2) ^2) is V11() real ext-real Element of REAL
(((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p2))) `2 is V11() real ext-real Element of REAL
(((((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4))) `1) -FanMorphS) . (((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p2))) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
z2 is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
h1 * g2 is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
dom (h1 * g2) is functional Element of K6( the carrier of (TOP-REAL 2))
(((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4)) `2) / |.((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4)).| is V11() real ext-real Element of REAL
((((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3))) `2) / |.(((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3))).| is V11() real ext-real Element of REAL
(((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4))) `2 is V11() real ext-real Element of REAL
|.(((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4))).| is V11() real ext-real non negative Element of REAL
((((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4))) `2) / |.(((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4))).| is V11() real ext-real Element of REAL
((((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4))) `1) / |.(((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4))).| is V11() real ext-real Element of REAL
((((((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4))) `1) -FanMorphS) . (((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4)))) `1 is V11() real ext-real Element of REAL
f4 is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
z2 * (h1 * g2) is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
f4 * (z2 * (h1 * g2)) is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
dom (z2 * (h1 * g2)) is functional Element of K6( the carrier of (TOP-REAL 2))
g is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
dom g is functional Element of K6( the carrier of (TOP-REAL 2))
g . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(z2 * (h1 * g2)) . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
f4 . ((z2 * (h1 * g2)) . p2) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(h1 * g2) . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
z2 . ((h1 * g2) . p2) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
f4 . (z2 . ((h1 * g2) . p2)) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(((((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4))) `1) -FanMorphS) . (((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3))) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(((((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4))) `1) -FanMorphS) . (((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p1))) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.((((((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4))) `1) -FanMorphS) . (((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4)))).| is V11() real ext-real non negative Element of REAL
|.((((((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4))) `1) -FanMorphS) . (((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4)))).| ^2 is V11() real ext-real Element of REAL
K37(|.((((((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4))) `1) -FanMorphS) . (((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4)))).|,|.((((((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4))) `1) -FanMorphS) . (((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4)))).|) is V11() real ext-real non negative set
(((((((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4))) `1) -FanMorphS) . (((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4)))) `1) ^2 is V11() real ext-real Element of REAL
K37((((((((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4))) `1) -FanMorphS) . (((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4)))) `1),(((((((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4))) `1) -FanMorphS) . (((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4)))) `1)) is V11() real ext-real set
((((((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4))) `1) -FanMorphS) . (((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4)))) `2 is V11() real ext-real Element of REAL
(((((((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4))) `1) -FanMorphS) . (((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4)))) `2) ^2 is V11() real ext-real Element of REAL
K37((((((((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4))) `1) -FanMorphS) . (((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4)))) `2),(((((((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4))) `1) -FanMorphS) . (((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4)))) `2)) is V11() real ext-real set
((((((((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4))) `1) -FanMorphS) . (((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4)))) `1) ^2) + ((((((((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4))) `1) -FanMorphS) . (((((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p3)) `2) -FanMorphE) . ((((((p1 `2) -FanMorphW) . p2) `1) -FanMorphN) . (((p1 `2) -FanMorphW) . p4)))) `2) ^2) is V11() real ext-real Element of REAL
q is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g . q is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.(g . q).| is V11() real ext-real non negative Element of REAL
|.q.| is V11() real ext-real non negative Element of REAL
(h1 * g2) . q is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.((h1 * g2) . q).| is V11() real ext-real non negative Element of REAL
g2 . q is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
h1 . (g2 . q) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.(h1 . (g2 . q)).| is V11() real ext-real non negative Element of REAL
|.(g2 . q).| is V11() real ext-real non negative Element of REAL
(z2 * (h1 * g2)) . q is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.((z2 * (h1 * g2)) . q).| is V11() real ext-real non negative Element of REAL
z2 . ((h1 * g2) . q) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.(z2 . ((h1 * g2) . q)).| is V11() real ext-real non negative Element of REAL
f4 . ((z2 * (h1 * g2)) . q) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.(f4 . ((z2 * (h1 * g2)) . q)).| is V11() real ext-real non negative Element of REAL
g . p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(z2 * (h1 * g2)) . p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
f4 . ((z2 * (h1 * g2)) . p3) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(h1 * g2) . p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
z2 . ((h1 * g2) . p3) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
f4 . (z2 . ((h1 * g2) . p3)) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g . p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(z2 * (h1 * g2)) . p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
f4 . ((z2 * (h1 * g2)) . p4) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(h1 * g2) . p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
z2 . ((h1 * g2) . p4) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
f4 . (z2 . ((h1 * g2) . p4)) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g . p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(z2 * (h1 * g2)) . p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
f4 . ((z2 * (h1 * g2)) . p1) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
(h1 * g2) . p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
z2 . ((h1 * g2) . p1) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
f4 . (z2 . ((h1 * g2) . p1)) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P is non empty functional closed compact Element of K6( the carrier of (TOP-REAL 2))
C0 is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
f is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
C0 . p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
C0 . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
h is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
C0 . p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
f2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
C0 . p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
f `1 is V11() real ext-real Element of REAL
f `2 is V11() real ext-real Element of REAL
g `1 is V11() real ext-real Element of REAL
g `2 is V11() real ext-real Element of REAL
h `1 is V11() real ext-real Element of REAL
h `2 is V11() real ext-real Element of REAL
f2 `1 is V11() real ext-real Element of REAL
f2 `2 is V11() real ext-real Element of REAL
dom C0 is functional Element of K6( the carrier of (TOP-REAL 2))
g2 is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
g2 . f is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g2 . g is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g2 . h is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g2 . f2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g2 * C0 is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
h1 is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
dom h1 is functional Element of K6( the carrier of (TOP-REAL 2))
h1 . p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
h1 . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
h1 . O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.(h1 . O).| is V11() real ext-real non negative Element of REAL
|.O.| is V11() real ext-real non negative Element of REAL
C0 . O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
g2 . (C0 . O) is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.(g2 . (C0 . O)).| is V11() real ext-real non negative Element of REAL
|.(C0 . O).| is V11() real ext-real non negative Element of REAL
h1 . p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
h1 . p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|[(- 1),0]| `1 is V11() real ext-real Element of REAL
|[(- 1),0]| `2 is V11() real ext-real Element of REAL
|[1,0]| `1 is V11() real ext-real Element of REAL
|[1,0]| `2 is V11() real ext-real Element of REAL
|[0,(- 1)]| `1 is V11() real ext-real Element of REAL
|[0,(- 1)]| `2 is V11() real ext-real Element of REAL
|[0,1]| `1 is V11() real ext-real Element of REAL
|[0,1]| `2 is V11() real ext-real Element of REAL
|.|[(- 1),0]|.| is V11() real ext-real non negative Element of REAL
(- 1) ^2 is V11() real ext-real Element of REAL
K37((- 1),(- 1)) is V11() real ext-real non negative set
0 ^2 is V11() real ext-real Element of REAL
K37(0,0) is empty V11() real ext-real non positive non negative Function-like functional V142() V143() V144() V145() V146() V147() V148() V201() V204() set
((- 1) ^2) + (0 ^2) is V11() real ext-real Element of REAL
sqrt (((- 1) ^2) + (0 ^2)) is V11() real ext-real Element of REAL
|.|[1,0]|.| is V11() real ext-real non negative Element of REAL
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is V11() real ext-real non negative set
(1 ^2) + (0 ^2) is V11() real ext-real Element of REAL
sqrt ((1 ^2) + (0 ^2)) is V11() real ext-real Element of REAL
|.|[0,(- 1)]|.| is V11() real ext-real non negative Element of REAL
(0 ^2) + ((- 1) ^2) is V11() real ext-real Element of REAL
sqrt ((0 ^2) + ((- 1) ^2)) is V11() real ext-real Element of REAL
|.|[0,1]|.| is V11() real ext-real non negative Element of REAL
(0 ^2) + (1 ^2) is V11() real ext-real Element of REAL
sqrt ((0 ^2) + (1 ^2)) is V11() real ext-real Element of REAL
p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P is non empty functional closed compact Element of K6( the carrier of (TOP-REAL 2))
C0 is functional Element of K6( the carrier of (TOP-REAL 2))
f is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f . 0 is Relation-like Function-like set
f . 1 is Relation-like Function-like set
g . 0 is Relation-like Function-like set
g . 1 is Relation-like Function-like set
rng f is functional Element of K6( the carrier of (TOP-REAL 2))
rng g is functional Element of K6( the carrier of (TOP-REAL 2))
dom g is V142() V143() V144() Element of K6( the carrier of I[01])
dom f is V142() V143() V144() Element of K6( the carrier of I[01])
h is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
h . p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
h . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
h . p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
h . p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : S1[b1] } is set
dom h is functional Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : S2[b1] } is set
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : S3[b1] } is set
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : S4[b1] } is set
- (|[0,1]| `1) is V11() real ext-real Element of REAL
h * g is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
- (|[0,(- 1)]| `1) is V11() real ext-real Element of REAL
KYP is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
dom KYP is V142() V143() V144() Element of K6( the carrier of I[01])
KYP . 0 is Relation-like Function-like set
g2 is V11() real ext-real Element of the carrier of I[01]
KYP . g2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KXP is functional Element of K6( the carrier of (TOP-REAL 2))
rng KYP is functional Element of K6( the carrier of (TOP-REAL 2))
KYN is set
x2 is set
KYP . x2 is Relation-like Function-like set
g . x2 is Relation-like Function-like set
z3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
h . z3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.(h . z3).| is V11() real ext-real non negative Element of REAL
|.z3.| is V11() real ext-real non negative Element of REAL
h . (g . x2) is Relation-like Function-like set
z2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.z2.| is V11() real ext-real non negative Element of REAL
h * f is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
- (|[(- 1),0]| `1) is V11() real ext-real Element of REAL
KYN is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
dom KYN is V142() V143() V144() Element of K6( the carrier of I[01])
KYN . 1 is Relation-like Function-like set
h1 is V11() real ext-real Element of the carrier of I[01]
KYN . h1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
O is functional Element of K6( the carrier of (TOP-REAL 2))
rng KYN is functional Element of K6( the carrier of (TOP-REAL 2))
x2 is set
z3 is set
KYN . z3 is Relation-like Function-like set
f . z3 is Relation-like Function-like set
z2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
h . z2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.(h . z2).| is V11() real ext-real non negative Element of REAL
|.z2.| is V11() real ext-real non negative Element of REAL
h . (f . z3) is Relation-like Function-like set
f4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.f4.| is V11() real ext-real non negative Element of REAL
KYP . 1 is Relation-like Function-like set
KYP . h1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KXN is functional Element of K6( the carrier of (TOP-REAL 2))
KYN . 0 is Relation-like Function-like set
KYN . g2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
I is functional Element of K6( the carrier of (TOP-REAL 2))
x2 is set
z3 is set
KYP . z3 is Relation-like Function-like set
g . z3 is Relation-like Function-like set
f2 is Relation-like Function-like set
f2 " is Relation-like Function-like set
(f2 ") . x2 is set
h . (g . z3) is Relation-like Function-like set
(f2 ") . (h . (g . z3)) is set
z2 is set
KYN . z2 is Relation-like Function-like set
f . z2 is Relation-like Function-like set
h . (f . z2) is Relation-like Function-like set
(f2 ") . (h . (f . z2)) is set
p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P is non empty functional closed compact Element of K6( the carrier of (TOP-REAL 2))
C0 is functional Element of K6( the carrier of (TOP-REAL 2))
f is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f . 0 is Relation-like Function-like set
f . 1 is Relation-like Function-like set
g . 0 is Relation-like Function-like set
g . 1 is Relation-like Function-like set
rng f is functional Element of K6( the carrier of (TOP-REAL 2))
rng g is functional Element of K6( the carrier of (TOP-REAL 2))
dom g is V142() V143() V144() Element of K6( the carrier of I[01])
dom f is V142() V143() V144() Element of K6( the carrier of I[01])
h is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
h . p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
h . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
h . p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
h . p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : S1[b1] } is set
dom h is functional Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : S2[b1] } is set
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : S3[b1] } is set
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : S4[b1] } is set
- (|[0,1]| `1) is V11() real ext-real Element of REAL
h * g is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
- (|[0,(- 1)]| `1) is V11() real ext-real Element of REAL
KYP is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
dom KYP is V142() V143() V144() Element of K6( the carrier of I[01])
KYP . 0 is Relation-like Function-like set
g2 is V11() real ext-real Element of the carrier of I[01]
KYP . g2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KXN is functional Element of K6( the carrier of (TOP-REAL 2))
rng KYP is functional Element of K6( the carrier of (TOP-REAL 2))
KYN is set
x2 is set
KYP . x2 is Relation-like Function-like set
g . x2 is Relation-like Function-like set
z3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
h . z3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.(h . z3).| is V11() real ext-real non negative Element of REAL
|.z3.| is V11() real ext-real non negative Element of REAL
h . (g . x2) is Relation-like Function-like set
z2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.z2.| is V11() real ext-real non negative Element of REAL
h * f is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
- (|[(- 1),0]| `1) is V11() real ext-real Element of REAL
KYN is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
dom KYN is V142() V143() V144() Element of K6( the carrier of I[01])
KYN . 1 is Relation-like Function-like set
h1 is V11() real ext-real Element of the carrier of I[01]
KYN . h1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
O is functional Element of K6( the carrier of (TOP-REAL 2))
rng KYN is functional Element of K6( the carrier of (TOP-REAL 2))
x2 is set
z3 is set
KYN . z3 is Relation-like Function-like set
f . z3 is Relation-like Function-like set
z2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
h . z2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.(h . z2).| is V11() real ext-real non negative Element of REAL
|.z2.| is V11() real ext-real non negative Element of REAL
h . (f . z3) is Relation-like Function-like set
f4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.f4.| is V11() real ext-real non negative Element of REAL
KYP . 1 is Relation-like Function-like set
KYP . h1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KXP is functional Element of K6( the carrier of (TOP-REAL 2))
KYN . 0 is Relation-like Function-like set
KYN . g2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
I is functional Element of K6( the carrier of (TOP-REAL 2))
x2 is set
z3 is set
KYP . z3 is Relation-like Function-like set
g . z3 is Relation-like Function-like set
f2 is Relation-like Function-like set
f2 " is Relation-like Function-like set
(f2 ") . x2 is set
h . (g . z3) is Relation-like Function-like set
(f2 ") . (h . (g . z3)) is set
z2 is set
KYN . z2 is Relation-like Function-like set
f . z2 is Relation-like Function-like set
h . (f . z2) is Relation-like Function-like set
(f2 ") . (h . (f . z2)) is set
p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P is non empty functional closed compact Element of K6( the carrier of (TOP-REAL 2))
C0 is functional Element of K6( the carrier of (TOP-REAL 2))
f is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f . 0 is Relation-like Function-like set
f . 1 is Relation-like Function-like set
g . 0 is Relation-like Function-like set
g . 1 is Relation-like Function-like set
rng f is functional Element of K6( the carrier of (TOP-REAL 2))
rng g is functional Element of K6( the carrier of (TOP-REAL 2))
dom g is V142() V143() V144() Element of K6( the carrier of I[01])
dom f is V142() V143() V144() Element of K6( the carrier of I[01])
h is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
h . p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
h . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
h . p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
h . p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : S1[b1] } is set
dom h is functional Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : S2[b1] } is set
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : S3[b1] } is set
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : S4[b1] } is set
- (|[0,1]| `1) is V11() real ext-real Element of REAL
h * g is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
- (|[0,(- 1)]| `1) is V11() real ext-real Element of REAL
KYP is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
dom KYP is V142() V143() V144() Element of K6( the carrier of I[01])
KYP . 0 is Relation-like Function-like set
g2 is V11() real ext-real Element of the carrier of I[01]
KYP . g2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KXN is functional Element of K6( the carrier of (TOP-REAL 2))
rng KYP is functional Element of K6( the carrier of (TOP-REAL 2))
KYN is set
x2 is set
KYP . x2 is Relation-like Function-like set
g . x2 is Relation-like Function-like set
z3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
h . z3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.(h . z3).| is V11() real ext-real non negative Element of REAL
|.z3.| is V11() real ext-real non negative Element of REAL
h . (g . x2) is Relation-like Function-like set
z2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.z2.| is V11() real ext-real non negative Element of REAL
h * f is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
- (|[(- 1),0]| `1) is V11() real ext-real Element of REAL
KYN is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
dom KYN is V142() V143() V144() Element of K6( the carrier of I[01])
KYN . 1 is Relation-like Function-like set
h1 is V11() real ext-real Element of the carrier of I[01]
KYN . h1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
O is functional Element of K6( the carrier of (TOP-REAL 2))
rng KYN is functional Element of K6( the carrier of (TOP-REAL 2))
x2 is set
z3 is set
KYN . z3 is Relation-like Function-like set
f . z3 is Relation-like Function-like set
z2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
h . z2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.(h . z2).| is V11() real ext-real non negative Element of REAL
|.z2.| is V11() real ext-real non negative Element of REAL
h . (f . z3) is Relation-like Function-like set
f4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.f4.| is V11() real ext-real non negative Element of REAL
KYP . 1 is Relation-like Function-like set
KYP . h1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KXP is functional Element of K6( the carrier of (TOP-REAL 2))
KYN . 0 is Relation-like Function-like set
KYN . g2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
I is functional Element of K6( the carrier of (TOP-REAL 2))
x2 is set
z3 is set
KYP . z3 is Relation-like Function-like set
g . z3 is Relation-like Function-like set
f2 is Relation-like Function-like set
f2 " is Relation-like Function-like set
(f2 ") . x2 is set
h . (g . z3) is Relation-like Function-like set
(f2 ") . (h . (g . z3)) is set
z2 is set
KYN . z2 is Relation-like Function-like set
f . z2 is Relation-like Function-like set
h . (f . z2) is Relation-like Function-like set
(f2 ") . (h . (f . z2)) is set
p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
P is non empty functional closed compact Element of K6( the carrier of (TOP-REAL 2))
C0 is functional Element of K6( the carrier of (TOP-REAL 2))
f is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f . 0 is Relation-like Function-like set
f . 1 is Relation-like Function-like set
g . 0 is Relation-like Function-like set
g . 1 is Relation-like Function-like set
rng f is functional Element of K6( the carrier of (TOP-REAL 2))
rng g is functional Element of K6( the carrier of (TOP-REAL 2))
dom g is V142() V143() V144() Element of K6( the carrier of I[01])
dom f is V142() V143() V144() Element of K6( the carrier of I[01])
h is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
h . p1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
h . p2 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
h . p3 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
h . p4 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
h * f is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
h * g is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
- (|[0,(- 1)]| `1) is V11() real ext-real Element of REAL
g2 is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng g2 is functional Element of K6( the carrier of (TOP-REAL 2))
h1 is set
dom g2 is V142() V143() V144() Element of K6( the carrier of I[01])
O is set
g2 . O is Relation-like Function-like set
g . O is Relation-like Function-like set
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
h . I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.(h . I).| is V11() real ext-real non negative Element of REAL
|.I.| is V11() real ext-real non negative Element of REAL
h . (g . O) is Relation-like Function-like set
KXP is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.KXP.| is V11() real ext-real non negative Element of REAL
f2 is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f2 is functional Element of K6( the carrier of (TOP-REAL 2))
h1 is set
dom f2 is V142() V143() V144() Element of K6( the carrier of I[01])
O is set
f2 . O is Relation-like Function-like set
f . O is Relation-like Function-like set
I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
h . I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.(h . I).| is V11() real ext-real non negative Element of REAL
|.I.| is V11() real ext-real non negative Element of REAL
h . (f . O) is Relation-like Function-like set
KXP is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
|.KXP.| is V11() real ext-real non negative Element of REAL
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : S1[b1] } is set
dom h is functional Element of K6( the carrier of (TOP-REAL 2))
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : S2[b1] } is set
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : S3[b1] } is set
{ b1 where b1 is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2) : S4[b1] } is set
- (|[(- 1),0]| `1) is V11() real ext-real Element of REAL
- (|[0,1]| `1) is V11() real ext-real Element of REAL
dom g2 is V142() V143() V144() Element of K6( the carrier of I[01])
g2 . 0 is Relation-like Function-like set
O is V11() real ext-real Element of the carrier of I[01]
g2 . O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KYP is functional Element of K6( the carrier of (TOP-REAL 2))
g2 . 1 is Relation-like Function-like set
I is V11() real ext-real Element of the carrier of I[01]
g2 . I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KYN is functional Element of K6( the carrier of (TOP-REAL 2))
dom f2 is V142() V143() V144() Element of K6( the carrier of I[01])
f2 . 1 is Relation-like Function-like set
f2 . I is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KXP is functional Element of K6( the carrier of (TOP-REAL 2))
f2 . 0 is Relation-like Function-like set
f2 . O is Relation-like Function-like V43(2) V76() V134() Element of the carrier of (TOP-REAL 2)
KXN is functional Element of K6( the carrier of (TOP-REAL 2))
x2 is set
z3 is set
g2 . z3 is Relation-like Function-like set
g . z3 is Relation-like Function-like set
h1 is Relation-like Function-like set
h1 " is Relation-like Function-like set
(h1 ") . x2 is set
h . (g . z3) is Relation-like Function-like set
(h1 ") . (h . (g . z3)) is set
z2 is set
f2 . z2 is Relation-like Function-like set
f . z2 is Relation-like Function-like set
h . (f . z2) is Relation-like Function-like set
(h1 ") . (h . (f . z2)) is set