:: JGRAPH_4 semantic presentation

REAL is non empty V35() V126() V127() V128() V132() set
NAT is V126() V127() V128() V129() V130() V131() V132() Element of K19(REAL)
K19(REAL) is set
COMPLEX is non empty V35() V126() V132() set
RAT is non empty V35() V126() V127() V128() V129() V132() set
INT is non empty V35() V126() V127() V128() V129() V130() V132() set
K20(COMPLEX,COMPLEX) is set
K19(K20(COMPLEX,COMPLEX)) is set
K20(K20(COMPLEX,COMPLEX),COMPLEX) is set
K19(K20(K20(COMPLEX,COMPLEX),COMPLEX)) is set
K20(REAL,REAL) is set
K19(K20(REAL,REAL)) is set
K20(K20(REAL,REAL),REAL) is set
K19(K20(K20(REAL,REAL),REAL)) is set
K20(RAT,RAT) is set
K19(K20(RAT,RAT)) is set
K20(K20(RAT,RAT),RAT) is set
K19(K20(K20(RAT,RAT),RAT)) is set
K20(INT,INT) is set
K19(K20(INT,INT)) is set
K20(K20(INT,INT),INT) is set
K19(K20(K20(INT,INT),INT)) is set
K20(NAT,NAT) is set
K20(K20(NAT,NAT),NAT) is set
K19(K20(K20(NAT,NAT),NAT)) is set
omega is V126() V127() V128() V129() V130() V131() V132() set
K19(omega) is set
1 is non empty natural V28() real ext-real positive non negative V33() V34() V126() V127() V128() V129() V130() V131() Element of NAT
K20(1,1) is set
K19(K20(1,1)) is set
K20(K20(1,1),1) is set
K19(K20(K20(1,1),1)) is set
K20(K20(1,1),REAL) is set
K19(K20(K20(1,1),REAL)) is set
2 is non empty natural V28() real ext-real positive non negative V33() V34() V126() V127() V128() V129() V130() V131() Element of NAT
K20(2,2) is set
K20(K20(2,2),REAL) is set
K19(K20(K20(2,2),REAL)) is set
K334() is V115() TopStruct
the carrier of K334() is V126() V127() V128() set
RealSpace is strict V115() MetrStruct
R^1 is non empty strict TopSpace-like V115() TopStruct
K19(NAT) is set
TOP-REAL 2 is non empty TopSpace-like T_0 T_1 T_2 V152() V177() V178() V179() V180() V181() V182() V183() strict V190() V191() L15()
the carrier of (TOP-REAL 2) is functional non empty set
K20( the carrier of (TOP-REAL 2),REAL) is set
K19(K20( the carrier of (TOP-REAL 2),REAL)) is set
K19( the carrier of (TOP-REAL 2)) is set
{} is Function-like functional empty V126() V127() V128() V129() V130() V131() V132() set
0 is Function-like functional empty natural V28() real ext-real non positive non negative V33() V34() V126() V127() V128() V129() V130() V131() V132() Element of NAT
the carrier of R^1 is non empty V126() V127() V128() set
sqrt 0 is V28() real ext-real Element of REAL
sqrt 1 is V28() real ext-real Element of REAL
- 1 is V28() real ext-real non positive set
proj1 is Relation-like the carrier of (TOP-REAL 2) -defined REAL -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of (TOP-REAL 2),REAL))
proj2 is Relation-like the carrier of (TOP-REAL 2) -defined REAL -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of (TOP-REAL 2),REAL))
0. (TOP-REAL 2) is Relation-like Function-like V42(2) V51( TOP-REAL 2) V118() V137() Element of the carrier of (TOP-REAL 2)
the ZeroF of (TOP-REAL 2) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(0. (TOP-REAL 2)) `1 is V28() real ext-real Element of REAL
(0. (TOP-REAL 2)) `2 is V28() real ext-real Element of REAL
{(0. (TOP-REAL 2))} is functional non empty Element of K19( the carrier of (TOP-REAL 2))
NonZero (TOP-REAL 2) is functional Element of K19( the carrier of (TOP-REAL 2))
[#] (TOP-REAL 2) is functional non empty non proper closed Element of K19( the carrier of (TOP-REAL 2))
{(0. (TOP-REAL 2))} is functional non empty set
([#] (TOP-REAL 2)) \ {(0. (TOP-REAL 2))} is functional Element of K19( the carrier of (TOP-REAL 2))
K19( the carrier of R^1) is set
cn is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.cn.| is V28() real ext-real non negative Element of REAL
cn is non empty TopStruct
the carrier of cn is non empty set
K20( the carrier of cn, the carrier of R^1) is set
K19(K20( the carrier of cn, the carrier of R^1)) is set
K19( the carrier of cn) is set
q is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
p is Element of K19( the carrier of cn)
p1 is V28() real ext-real set
{ b₁ where b₁ is Element of the carrier of cn : not q /. b₁ <= p1 } is set
{ b₁ where b₁ is V28() real ext-real Element of REAL : not b₁ <= p1 } is set
p2 is set
q3 is V28() real ext-real Element of REAL
p2 is V126() V127() V128() Element of K19( the carrier of R^1)
q " p2 is Element of K19( the carrier of cn)
q3 is set
q . q3 is set
VV0 is Element of the carrier of cn
q /. VV0 is V28() real ext-real Element of the carrier of R^1
q . VV0 is V28() real ext-real Element of the carrier of R^1
u2 is V28() real ext-real Element of REAL
[#] R^1 is non empty non proper closed V126() V127() V128() Element of K19( the carrier of R^1)
q3 is set
VV0 is Element of the carrier of cn
q /. VV0 is V28() real ext-real Element of the carrier of R^1
q . VV0 is V28() real ext-real Element of the carrier of R^1
dom q is Element of K19( the carrier of cn)
q . q3 is set
cn is non empty TopStruct
the carrier of cn is non empty set
K20( the carrier of cn, the carrier of R^1) is set
K19(K20( the carrier of cn, the carrier of R^1)) is set
K19( the carrier of cn) is set
q is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
p is Element of K19( the carrier of cn)
p1 is V28() real ext-real Element of REAL
{ b₁ where b₁ is Element of the carrier of cn : not p1 <= q /. b₁ } is set
{ b₁ where b₁ is V28() real ext-real Element of REAL : not p1 <= b₁ } is set
p2 is set
q3 is V28() real ext-real Element of REAL
p2 is V126() V127() V128() Element of K19( the carrier of R^1)
q " p2 is Element of K19( the carrier of cn)
q3 is set
q . q3 is set
VV0 is Element of the carrier of cn
q /. VV0 is V28() real ext-real Element of the carrier of R^1
q . VV0 is V28() real ext-real Element of the carrier of R^1
u2 is V28() real ext-real Element of REAL
[#] R^1 is non empty non proper closed V126() V127() V128() Element of K19( the carrier of R^1)
q3 is set
VV0 is Element of the carrier of cn
q /. VV0 is V28() real ext-real Element of the carrier of R^1
q . VV0 is V28() real ext-real Element of the carrier of R^1
dom q is Element of K19( the carrier of cn)
q . q3 is set
K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)) is set
K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2))) is set
cn is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
rng cn is functional Element of K19( the carrier of (TOP-REAL 2))
cn " is Relation-like Function-like set
dom cn is functional Element of K19( the carrier of (TOP-REAL 2))
q is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q . p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 is functional Element of K19( the carrier of (TOP-REAL 2))
cn . (q . p) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 is functional non empty closed compact bounded Element of K19( the carrier of (TOP-REAL 2))
cn .: p2 is functional Element of K19( the carrier of (TOP-REAL 2))
q3 is functional Element of K19( the carrier of (TOP-REAL 2))
q3 is functional Element of K19( the carrier of (TOP-REAL 2))
cn | p2 is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
dom (cn | p2) is functional Element of K19( the carrier of (TOP-REAL 2))
(dom cn) /\ p2 is functional Element of K19( the carrier of (TOP-REAL 2))
p1 /\ q3 is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | p2 is non empty strict TopSpace-like T_0 T_1 T_2 compact V195() SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | p2) is non empty set
K19( the carrier of ((TOP-REAL 2) | p2)) is set
(p1 /\ q3) /\ p2 is functional Element of K19( the carrier of (TOP-REAL 2))
VV0 is Element of K19( the carrier of ((TOP-REAL 2) | p2))
[#] ((TOP-REAL 2) | p2) is non empty non proper closed Element of K19( the carrier of ((TOP-REAL 2) | p2))
(p1 /\ q3) /\ ([#] ((TOP-REAL 2) | p2)) is Element of K19( the carrier of ((TOP-REAL 2) | p2))
rng (cn | p2) is functional Element of K19( the carrier of (TOP-REAL 2))
the carrier of (TOP-REAL 2) /\ p2 is functional Element of K19( the carrier of (TOP-REAL 2))
K20( the carrier of ((TOP-REAL 2) | p2), the carrier of (TOP-REAL 2)) is set
K19(K20( the carrier of ((TOP-REAL 2) | p2), the carrier of (TOP-REAL 2))) is set
u3 is Relation-like the carrier of ((TOP-REAL 2) | p2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | p2), the carrier of (TOP-REAL 2)))
(cn | p2) .: p2 is functional Element of K19( the carrier of (TOP-REAL 2))
K20( the carrier of ((TOP-REAL 2) | p2), the carrier of ((TOP-REAL 2) | p2)) is set
K19(K20( the carrier of ((TOP-REAL 2) | p2), the carrier of ((TOP-REAL 2) | p2))) is set
y is Relation-like the carrier of ((TOP-REAL 2) | p2) -defined the carrier of ((TOP-REAL 2) | p2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | p2), the carrier of ((TOP-REAL 2) | p2)))
rng y is Element of K19( the carrier of ((TOP-REAL 2) | p2))
y " is Relation-like Function-like set
dom (y ") is set
rng (y ") is set
dom y is Element of K19( the carrier of ((TOP-REAL 2) | p2))
q4 is Relation-like the carrier of ((TOP-REAL 2) | p2) -defined the carrier of ((TOP-REAL 2) | p2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | p2), the carrier of ((TOP-REAL 2) | p2)))
y " is Relation-like the carrier of ((TOP-REAL 2) | p2) -defined the carrier of ((TOP-REAL 2) | p2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | p2), the carrier of ((TOP-REAL 2) | p2)))
y . (q . p) is set
(y ") . p is set
y . ((y ") . p) is set
y is functional Element of K19( the carrier of (TOP-REAL 2))
u2 is Element of the carrier of ((TOP-REAL 2) | p2)
y is Element of K19( the carrier of ((TOP-REAL 2) | p2))
(y ") .: y is set
q3 /\ p2 is functional Element of K19( the carrier of (TOP-REAL 2))
p1 /\ (q3 /\ p2) is functional Element of K19( the carrier of (TOP-REAL 2))
x is functional Element of K19( the carrier of (TOP-REAL 2))
x /\ ([#] ((TOP-REAL 2) | p2)) is Element of K19( the carrier of ((TOP-REAL 2) | p2))
x /\ q3 is functional Element of K19( the carrier of (TOP-REAL 2))
x is functional Element of K19( the carrier of (TOP-REAL 2))
(cn ") .: y is set
q is set
dom (cn ") is set
K004 is set
(cn ") . K004 is set
cn . q is Relation-like Function-like set
K111 is set
cn . K111 is Relation-like Function-like set
y . q is set
(y ") . K004 is set
x /\ (q3 /\ p2) is functional Element of K19( the carrier of (TOP-REAL 2))
x /\ p2 is functional Element of K19( the carrier of (TOP-REAL 2))
(x /\ p2) /\ q3 is functional Element of K19( the carrier of (TOP-REAL 2))
y /\ q3 is functional Element of K19( the carrier of (TOP-REAL 2))
q .: x is functional Element of K19( the carrier of (TOP-REAL 2))
q .: y is functional Element of K19( the carrier of (TOP-REAL 2))
q .: q3 is functional Element of K19( the carrier of (TOP-REAL 2))
(q .: y) /\ (q .: q3) is functional Element of K19( the carrier of (TOP-REAL 2))
cn " is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
cn is non empty TopSpace-like TopStruct
the carrier of cn is non empty set
K20( the carrier of cn, the carrier of R^1) is set
K19(K20( the carrier of cn, the carrier of R^1)) is set
q is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
p is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
p2 is V28() real ext-real set
p1 is V28() real ext-real set
q3 is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
VV0 is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
u2 is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
u3 is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
y is Element of the carrier of cn
VV0 . y is V28() real ext-real Element of the carrier of R^1
y is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
q4 is Element of the carrier of cn
q . q4 is V28() real ext-real Element of the carrier of R^1
p . q4 is V28() real ext-real Element of the carrier of R^1
y . q4 is V28() real ext-real Element of the carrier of R^1
y is V28() real ext-real set
x is V28() real ext-real set
y / x is V28() real ext-real Element of COMPLEX
(y / x) - p1 is V28() real ext-real set
((y / x) - p1) / p2 is V28() real ext-real Element of COMPLEX
VV0 . q4 is V28() real ext-real Element of the carrier of R^1
q3 . q4 is V28() real ext-real Element of the carrier of R^1
u2 . q4 is V28() real ext-real Element of the carrier of R^1
u3 . q4 is V28() real ext-real Element of the carrier of R^1
cn is non empty TopSpace-like TopStruct
the carrier of cn is non empty set
K20( the carrier of cn, the carrier of R^1) is set
K19(K20( the carrier of cn, the carrier of R^1)) is set
q is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
p is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
p2 is V28() real ext-real Element of REAL
p1 is V28() real ext-real Element of REAL
q3 is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
VV0 is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
u2 is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
u3 is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
y is Element of the carrier of cn
VV0 . y is V28() real ext-real Element of the carrier of R^1
y is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
q4 is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
y is Element of the carrier of cn
q . y is V28() real ext-real Element of the carrier of R^1
p . y is V28() real ext-real Element of the carrier of R^1
q4 . y is V28() real ext-real Element of the carrier of R^1
x is V28() real ext-real Element of REAL
x is V28() real ext-real Element of REAL
x / x is V28() real ext-real Element of COMPLEX
(x / x) - p1 is V28() real ext-real Element of REAL
((x / x) - p1) / p2 is V28() real ext-real Element of COMPLEX
x * (((x / x) - p1) / p2) is V28() real ext-real Element of REAL
u2 . y is V28() real ext-real Element of the carrier of R^1
VV0 . y is V28() real ext-real Element of the carrier of R^1
q3 . y is V28() real ext-real Element of the carrier of R^1
u3 . y is V28() real ext-real Element of the carrier of R^1
y . y is V28() real ext-real Element of the carrier of R^1
cn is non empty TopSpace-like TopStruct
the carrier of cn is non empty set
K20( the carrier of cn, the carrier of R^1) is set
K19(K20( the carrier of cn, the carrier of R^1)) is set
q is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
p is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
p1 is Element of the carrier of cn
q . p1 is V28() real ext-real Element of the carrier of R^1
p2 is V28() real ext-real set
p . p1 is V28() real ext-real Element of the carrier of R^1
p2 ^2 is V28() real ext-real set
p2 * p2 is V28() real ext-real set
cn is non empty TopSpace-like TopStruct
the carrier of cn is non empty set
K20( the carrier of cn, the carrier of R^1) is set
K19(K20( the carrier of cn, the carrier of R^1)) is set
q is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
p is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
p1 is Element of the carrier of cn
p . p1 is V28() real ext-real Element of the carrier of R^1
q . p1 is V28() real ext-real Element of the carrier of R^1
p2 is V28() real ext-real Element of REAL
p2 ^2 is V28() real ext-real Element of REAL
p2 * p2 is V28() real ext-real set
p1 is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
p2 is Element of the carrier of cn
q . p2 is V28() real ext-real Element of the carrier of R^1
p1 . p2 is V28() real ext-real Element of the carrier of R^1
q3 is V28() real ext-real set
abs q3 is V28() real ext-real Element of REAL
p . p2 is V28() real ext-real Element of the carrier of R^1
q3 ^2 is V28() real ext-real set
q3 * q3 is V28() real ext-real set
sqrt (q3 ^2) is V28() real ext-real set
cn is non empty TopSpace-like TopStruct
the carrier of cn is non empty set
K20( the carrier of cn, the carrier of R^1) is set
K19(K20( the carrier of cn, the carrier of R^1)) is set
q is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
p is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
p1 is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
p2 is Element of the carrier of cn
q . p2 is V28() real ext-real Element of the carrier of R^1
p1 . p2 is V28() real ext-real Element of the carrier of R^1
q3 is V28() real ext-real set
- q3 is V28() real ext-real set
p . p2 is V28() real ext-real Element of the carrier of R^1
0 - q3 is V28() real ext-real Element of REAL
cn is non empty TopSpace-like TopStruct
the carrier of cn is non empty set
K20( the carrier of cn, the carrier of R^1) is set
K19(K20( the carrier of cn, the carrier of R^1)) is set
q is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
p is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
p2 is V28() real ext-real set
p1 is V28() real ext-real set
q3 is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
VV0 is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
u2 is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
u3 is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
y is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
q4 is Element of the carrier of cn
y . q4 is V28() real ext-real Element of the carrier of R^1
u3 . q4 is V28() real ext-real Element of the carrier of R^1
y is V28() real ext-real Element of REAL
abs y is V28() real ext-real Element of REAL
q4 is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
y is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
x is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
x is Element of the carrier of cn
q . x is V28() real ext-real Element of the carrier of R^1
p . x is V28() real ext-real Element of the carrier of R^1
x . x is V28() real ext-real Element of the carrier of R^1
q is V28() real ext-real set
K004 is V28() real ext-real set
q / K004 is V28() real ext-real Element of COMPLEX
(q / K004) - p1 is V28() real ext-real set
((q / K004) - p1) / p2 is V28() real ext-real Element of COMPLEX
(((q / K004) - p1) / p2) ^2 is V28() real ext-real Element of COMPLEX
(((q / K004) - p1) / p2) * (((q / K004) - p1) / p2) is V28() real ext-real set
1 - ((((q / K004) - p1) / p2) ^2) is V28() real ext-real Element of REAL
abs (1 - ((((q / K004) - p1) / p2) ^2)) is V28() real ext-real Element of REAL
sqrt (abs (1 - ((((q / K004) - p1) / p2) ^2))) is V28() real ext-real Element of REAL
- (sqrt (abs (1 - ((((q / K004) - p1) / p2) ^2)))) is V28() real ext-real Element of REAL
K004 * (- (sqrt (abs (1 - ((((q / K004) - p1) / p2) ^2))))) is V28() real ext-real Element of REAL
u2 . x is V28() real ext-real Element of the carrier of R^1
q3 . x is V28() real ext-real Element of the carrier of R^1
VV0 . x is V28() real ext-real Element of the carrier of R^1
u3 . x is V28() real ext-real Element of the carrier of R^1
y . x is V28() real ext-real Element of the carrier of R^1
q4 . x is V28() real ext-real Element of the carrier of R^1
y . x is V28() real ext-real Element of the carrier of R^1
cn is non empty TopSpace-like TopStruct
the carrier of cn is non empty set
K20( the carrier of cn, the carrier of R^1) is set
K19(K20( the carrier of cn, the carrier of R^1)) is set
q is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
p is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
p2 is V28() real ext-real set
p1 is V28() real ext-real set
q3 is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
VV0 is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
u2 is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
u3 is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
y is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
q4 is Element of the carrier of cn
y . q4 is V28() real ext-real Element of the carrier of R^1
u3 . q4 is V28() real ext-real Element of the carrier of R^1
y is V28() real ext-real Element of REAL
abs y is V28() real ext-real Element of REAL
q4 is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
y is Relation-like the carrier of cn -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of cn, the carrier of R^1))
x is Element of the carrier of cn
q . x is V28() real ext-real Element of the carrier of R^1
p . x is V28() real ext-real Element of the carrier of R^1
y . x is V28() real ext-real Element of the carrier of R^1
x is V28() real ext-real set
q is V28() real ext-real set
x / q is V28() real ext-real Element of COMPLEX
(x / q) - p1 is V28() real ext-real set
((x / q) - p1) / p2 is V28() real ext-real Element of COMPLEX
(((x / q) - p1) / p2) ^2 is V28() real ext-real Element of COMPLEX
(((x / q) - p1) / p2) * (((x / q) - p1) / p2) is V28() real ext-real set
1 - ((((x / q) - p1) / p2) ^2) is V28() real ext-real Element of REAL
abs (1 - ((((x / q) - p1) / p2) ^2)) is V28() real ext-real Element of REAL
sqrt (abs (1 - ((((x / q) - p1) / p2) ^2))) is V28() real ext-real Element of REAL
q * (sqrt (abs (1 - ((((x / q) - p1) / p2) ^2)))) is V28() real ext-real Element of REAL
u2 . x is V28() real ext-real Element of the carrier of R^1
q3 . x is V28() real ext-real Element of the carrier of R^1
VV0 . x is V28() real ext-real Element of the carrier of R^1
u3 . x is V28() real ext-real Element of the carrier of R^1
y . x is V28() real ext-real Element of the carrier of R^1
q4 . x is V28() real ext-real Element of the carrier of R^1
cn is natural V28() real ext-real set
TOP-REAL cn is non empty TopSpace-like T_0 T_1 T_2 V152() V177() V178() V179() V180() V181() V182() V183() strict V190() V191() L15()
the carrier of (TOP-REAL cn) is functional non empty set
K20( the carrier of (TOP-REAL cn), the carrier of R^1) is set
K19(K20( the carrier of (TOP-REAL cn), the carrier of R^1)) is set
q is Relation-like Function-like V42(cn) V118() V137() Element of the carrier of (TOP-REAL cn)
|.q.| is V28() real ext-real non negative Element of REAL
cn is natural V28() real ext-real set
TOP-REAL cn is non empty TopSpace-like T_0 T_1 T_2 V152() V177() V178() V179() V180() V181() V182() V183() strict V190() V191() L15()
the carrier of (TOP-REAL cn) is functional non empty set
(cn) is Relation-like the carrier of (TOP-REAL cn) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL cn), the carrier of R^1))
K20( the carrier of (TOP-REAL cn), the carrier of R^1) is set
K19(K20( the carrier of (TOP-REAL cn), the carrier of R^1)) is set
dom (cn) is functional Element of K19( the carrier of (TOP-REAL cn))
K19( the carrier of (TOP-REAL cn)) is set
REAL cn is non empty V139() M17( REAL )
cn is natural V28() real ext-real set
TOP-REAL cn is non empty TopSpace-like T_0 T_1 T_2 V152() V177() V178() V179() V180() V181() V182() V183() strict V190() V191() L15()
(cn) is Relation-like the carrier of (TOP-REAL cn) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL cn), the carrier of R^1))
the carrier of (TOP-REAL cn) is functional non empty set
K20( the carrier of (TOP-REAL cn), the carrier of R^1) is set
K19(K20( the carrier of (TOP-REAL cn), the carrier of R^1)) is set
q is Relation-like Function-like V42(cn) V118() V137() Element of the carrier of (TOP-REAL cn)
(cn) . q is V28() real ext-real Element of the carrier of R^1
|.q.| is V28() real ext-real non negative Element of REAL
cn is natural V28() real ext-real set
TOP-REAL cn is non empty TopSpace-like T_0 T_1 T_2 V152() V177() V178() V179() V180() V181() V182() V183() strict V190() V191() L15()
(cn) is Relation-like the carrier of (TOP-REAL cn) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL cn), the carrier of R^1))
the carrier of (TOP-REAL cn) is functional non empty set
K20( the carrier of (TOP-REAL cn), the carrier of R^1) is set
K19(K20( the carrier of (TOP-REAL cn), the carrier of R^1)) is set
cn is natural V28() real ext-real V33() V34() V126() V127() V128() V129() V130() V131() Element of NAT
TOP-REAL cn is non empty TopSpace-like T_0 T_1 T_2 V152() V177() V178() V179() V180() V181() V182() V183() strict V190() V191() L15()
the carrier of (TOP-REAL cn) is functional non empty set
K19( the carrier of (TOP-REAL cn)) is set
(cn) is Relation-like the carrier of (TOP-REAL cn) -defined the carrier of R^1 -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of (TOP-REAL cn), the carrier of R^1))
K20( the carrier of (TOP-REAL cn), the carrier of R^1) is set
K19(K20( the carrier of (TOP-REAL cn), the carrier of R^1)) is set
q is functional Element of K19( the carrier of (TOP-REAL cn))
(TOP-REAL cn) | q is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL cn
the carrier of ((TOP-REAL cn) | q) is set
K20( the carrier of ((TOP-REAL cn) | q), the carrier of R^1) is set
K19(K20( the carrier of ((TOP-REAL cn) | q), the carrier of R^1)) is set
p is Relation-like the carrier of ((TOP-REAL cn) | q) -defined the carrier of R^1 -valued Function-like total quasi_total Element of K19(K20( the carrier of ((TOP-REAL cn) | q), the carrier of R^1))
the carrier of (TOP-REAL cn) /\ q is functional Element of K19( the carrier of (TOP-REAL cn))
dom p is Element of K19( the carrier of ((TOP-REAL cn) | q))
K19( the carrier of ((TOP-REAL cn) | q)) is set
p2 is set
p . p2 is set
(cn) . p2 is set
dom (cn) is functional Element of K19( the carrier of (TOP-REAL cn))
(dom (cn)) /\ q is functional Element of K19( the carrier of (TOP-REAL cn))
p1 is Relation-like the carrier of (TOP-REAL cn) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL cn), the carrier of R^1))
p1 | q is Relation-like the carrier of (TOP-REAL cn) -defined the carrier of R^1 -valued Function-like Element of K19(K20( the carrier of (TOP-REAL cn), the carrier of R^1))
cn is natural V28() real ext-real V33() V34() V126() V127() V128() V129() V130() V131() Element of NAT
Euclid cn is non empty strict Reflexive discerning V85() triangle MetrStruct
the carrier of (Euclid cn) is non empty set
TOP-REAL cn is non empty TopSpace-like T_0 T_1 T_2 V152() V177() V178() V179() V180() V181() V182() V183() strict V190() V191() L15()
the carrier of (TOP-REAL cn) is functional non empty set
K19( the carrier of (TOP-REAL cn)) is set
q is Element of the carrier of (Euclid cn)
p is V28() real ext-real Element of REAL
cl_Ball (q,p) is Element of K19( the carrier of (Euclid cn))
K19( the carrier of (Euclid cn)) is set
p1 is functional Element of K19( the carrier of (TOP-REAL cn))
p + 1 is V28() real ext-real Element of REAL
Ball (q,(p + 1)) is bounded Element of K19( the carrier of (Euclid cn))
p2 is set
q3 is Element of the carrier of (Euclid cn)
dist (q,q3) is V28() real ext-real Element of REAL
the topology of (TOP-REAL cn) is non empty open Element of K19(K19( the carrier of (TOP-REAL cn)))
K19(K19( the carrier of (TOP-REAL cn))) is set
TopStruct(# the carrier of (TOP-REAL cn), the topology of (TOP-REAL cn) #) is non empty strict TopSpace-like TopStruct
TopSpaceMetr (Euclid cn) is TopStruct
Family_open_set (Euclid cn) is Element of K19(K19( the carrier of (Euclid cn)))
K19(K19( the carrier of (Euclid cn))) is set
TopStruct(# the carrier of (Euclid cn),(Family_open_set (Euclid cn)) #) is non empty strict TopStruct
the carrier of (TopSpaceMetr (Euclid cn)) is set
K19( the carrier of (TopSpaceMetr (Euclid cn))) is set
p2 is Element of K19( the carrier of (TopSpaceMetr (Euclid cn)))
Euclid 2 is non empty strict Reflexive discerning V85() triangle MetrStruct
the carrier of (Euclid 2) is non empty set
cn is Element of the carrier of (Euclid 2)
q is V28() real ext-real Element of REAL
cl_Ball (cn,q) is Element of K19( the carrier of (Euclid 2))
K19( the carrier of (Euclid 2)) is set
p is functional Element of K19( the carrier of (TOP-REAL 2))
cn is V28() real ext-real set
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q `2 is V28() real ext-real Element of REAL
|.q.| is V28() real ext-real non negative Element of REAL
(q `2) / |.q.| is V28() real ext-real Element of COMPLEX
q `1 is V28() real ext-real Element of REAL
((q `2) / |.q.|) - cn is V28() real ext-real set
1 - cn is V28() real ext-real Element of REAL
(((q `2) / |.q.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
((((q `2) / |.q.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((q `2) / |.q.|) - cn) / (1 - cn)) * ((((q `2) / |.q.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((q `2) / |.q.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|[(- (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 - cn)) ^2)))),((((q `2) / |.q.|) - cn) / (1 - cn))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.q.| * |[(- (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 - cn)) ^2)))),((((q `2) / |.q.|) - cn) / (1 - cn))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
1 + cn is V28() real ext-real Element of REAL
(((q `2) / |.q.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
((((q `2) / |.q.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((q `2) / |.q.|) - cn) / (1 + cn)) * ((((q `2) / |.q.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|[(- (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2)))),((((q `2) / |.q.|) - cn) / (1 + cn))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.q.| * |[(- (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2)))),((((q `2) / |.q.|) - cn) / (1 + cn))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn is V28() real ext-real set
cn is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn `2 is V28() real ext-real Element of REAL
|.cn.| is V28() real ext-real non negative Element of REAL
(cn `2) / |.cn.| is V28() real ext-real Element of COMPLEX
cn `1 is V28() real ext-real Element of REAL
q is V28() real ext-real set
(q) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(q) . cn is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((cn `2) / |.cn.|) - q is V28() real ext-real set
1 - q is V28() real ext-real Element of REAL
(((cn `2) / |.cn.|) - q) / (1 - q) is V28() real ext-real Element of COMPLEX
((((cn `2) / |.cn.|) - q) / (1 - q)) ^2 is V28() real ext-real Element of COMPLEX
((((cn `2) / |.cn.|) - q) / (1 - q)) * ((((cn `2) / |.cn.|) - q) / (1 - q)) is V28() real ext-real set
1 - (((((cn `2) / |.cn.|) - q) / (1 - q)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((cn `2) / |.cn.|) - q) / (1 - q)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((cn `2) / |.cn.|) - q) / (1 - q)) ^2))) is V28() real ext-real Element of REAL
|.cn.| * (- (sqrt (1 - (((((cn `2) / |.cn.|) - q) / (1 - q)) ^2)))) is V28() real ext-real Element of REAL
|.cn.| * ((((cn `2) / |.cn.|) - q) / (1 - q)) is V28() real ext-real Element of REAL
|[(|.cn.| * (- (sqrt (1 - (((((cn `2) / |.cn.|) - q) / (1 - q)) ^2))))),(|.cn.| * ((((cn `2) / |.cn.|) - q) / (1 - q)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(q,cn) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(- (sqrt (1 - (((((cn `2) / |.cn.|) - q) / (1 - q)) ^2)))),((((cn `2) / |.cn.|) - q) / (1 - q))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.cn.| * |[(- (sqrt (1 - (((((cn `2) / |.cn.|) - q) / (1 - q)) ^2)))),((((cn `2) / |.cn.|) - q) / (1 - q))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn `2 is V28() real ext-real Element of REAL
|.cn.| is V28() real ext-real non negative Element of REAL
(cn `2) / |.cn.| is V28() real ext-real Element of COMPLEX
cn `1 is V28() real ext-real Element of REAL
q is V28() real ext-real Element of REAL
(q) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(q) . cn is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((cn `2) / |.cn.|) - q is V28() real ext-real Element of REAL
1 + q is V28() real ext-real Element of REAL
(((cn `2) / |.cn.|) - q) / (1 + q) is V28() real ext-real Element of COMPLEX
((((cn `2) / |.cn.|) - q) / (1 + q)) ^2 is V28() real ext-real Element of COMPLEX
((((cn `2) / |.cn.|) - q) / (1 + q)) * ((((cn `2) / |.cn.|) - q) / (1 + q)) is V28() real ext-real set
1 - (((((cn `2) / |.cn.|) - q) / (1 + q)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((cn `2) / |.cn.|) - q) / (1 + q)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((cn `2) / |.cn.|) - q) / (1 + q)) ^2))) is V28() real ext-real Element of REAL
|.cn.| * (- (sqrt (1 - (((((cn `2) / |.cn.|) - q) / (1 + q)) ^2)))) is V28() real ext-real Element of REAL
|.cn.| * ((((cn `2) / |.cn.|) - q) / (1 + q)) is V28() real ext-real Element of REAL
|[(|.cn.| * (- (sqrt (1 - (((((cn `2) / |.cn.|) - q) / (1 + q)) ^2))))),(|.cn.| * ((((cn `2) / |.cn.|) - q) / (1 + q)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(q,cn) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(- (sqrt (1 - (((((cn `2) / |.cn.|) - q) / (1 + q)) ^2)))),((((cn `2) / |.cn.|) - q) / (1 + q))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.cn.| * |[(- (sqrt (1 - (((((cn `2) / |.cn.|) - q) / (1 + q)) ^2)))),((((cn `2) / |.cn.|) - q) / (1 + q))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
1 - q is V28() real ext-real Element of REAL
(((cn `2) / |.cn.|) - q) / (1 - q) is V28() real ext-real Element of COMPLEX
- 1 is V28() real ext-real non positive Element of REAL
cn is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn `2 is V28() real ext-real Element of REAL
|.cn.| is V28() real ext-real non negative Element of REAL
(cn `2) / |.cn.| is V28() real ext-real Element of COMPLEX
cn `1 is V28() real ext-real Element of REAL
q is V28() real ext-real Element of REAL
(q) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(q) . cn is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((cn `2) / |.cn.|) - q is V28() real ext-real Element of REAL
1 - q is V28() real ext-real Element of REAL
(((cn `2) / |.cn.|) - q) / (1 - q) is V28() real ext-real Element of COMPLEX
((((cn `2) / |.cn.|) - q) / (1 - q)) ^2 is V28() real ext-real Element of COMPLEX
((((cn `2) / |.cn.|) - q) / (1 - q)) * ((((cn `2) / |.cn.|) - q) / (1 - q)) is V28() real ext-real set
1 - (((((cn `2) / |.cn.|) - q) / (1 - q)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((cn `2) / |.cn.|) - q) / (1 - q)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((cn `2) / |.cn.|) - q) / (1 - q)) ^2))) is V28() real ext-real Element of REAL
|.cn.| * (- (sqrt (1 - (((((cn `2) / |.cn.|) - q) / (1 - q)) ^2)))) is V28() real ext-real Element of REAL
|.cn.| * ((((cn `2) / |.cn.|) - q) / (1 - q)) is V28() real ext-real Element of REAL
|[(|.cn.| * (- (sqrt (1 - (((((cn `2) / |.cn.|) - q) / (1 - q)) ^2))))),(|.cn.| * ((((cn `2) / |.cn.|) - q) / (1 - q)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
1 + q is V28() real ext-real Element of REAL
(((cn `2) / |.cn.|) - q) / (1 + q) is V28() real ext-real Element of COMPLEX
((((cn `2) / |.cn.|) - q) / (1 + q)) ^2 is V28() real ext-real Element of COMPLEX
((((cn `2) / |.cn.|) - q) / (1 + q)) * ((((cn `2) / |.cn.|) - q) / (1 + q)) is V28() real ext-real set
1 - (((((cn `2) / |.cn.|) - q) / (1 + q)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((cn `2) / |.cn.|) - q) / (1 + q)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((cn `2) / |.cn.|) - q) / (1 + q)) ^2))) is V28() real ext-real Element of REAL
|.cn.| * (- (sqrt (1 - (((((cn `2) / |.cn.|) - q) / (1 + q)) ^2)))) is V28() real ext-real Element of REAL
|.cn.| * ((((cn `2) / |.cn.|) - q) / (1 + q)) is V28() real ext-real Element of REAL
|[(|.cn.| * (- (sqrt (1 - (((((cn `2) / |.cn.|) - q) / (1 + q)) ^2))))),(|.cn.| * ((((cn `2) / |.cn.|) - q) / (1 + q)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(q,cn) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(- (sqrt (1 - (((((cn `2) / |.cn.|) - q) / (1 - q)) ^2)))),((((cn `2) / |.cn.|) - q) / (1 - q))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.cn.| * |[(- (sqrt (1 - (((((cn `2) / |.cn.|) - q) / (1 - q)) ^2)))),((((cn `2) / |.cn.|) - q) / (1 - q))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.cn.| ^2 is V28() real ext-real Element of REAL
|.cn.| * |.cn.| is V28() real ext-real non negative set
(cn `1) ^2 is V28() real ext-real Element of REAL
(cn `1) * (cn `1) is V28() real ext-real set
(cn `2) ^2 is V28() real ext-real Element of REAL
(cn `2) * (cn `2) is V28() real ext-real set
((cn `1) ^2) + ((cn `2) ^2) is V28() real ext-real Element of REAL
((cn `2) ^2) / (|.cn.| ^2) is V28() real ext-real Element of COMPLEX
1 ^2 is V28() real ext-real Element of REAL
1 * 1 is V28() real ext-real non negative set
((cn `2) / |.cn.|) ^2 is V28() real ext-real Element of COMPLEX
((cn `2) / |.cn.|) * ((cn `2) / |.cn.|) is V28() real ext-real set
sqrt (((cn `2) / |.cn.|) ^2) is V28() real ext-real set
- ((cn `2) / |.cn.|) is V28() real ext-real Element of COMPLEX
sqrt (|.cn.| ^2) is V28() real ext-real Element of REAL
1 * |.cn.| is V28() real ext-real non negative Element of REAL
((cn `2) / |.cn.|) * |.cn.| is V28() real ext-real Element of REAL
|.cn.| ^2 is V28() real ext-real Element of REAL
|.cn.| * |.cn.| is V28() real ext-real non negative set
(cn `1) ^2 is V28() real ext-real Element of REAL
(cn `1) * (cn `1) is V28() real ext-real set
(cn `2) ^2 is V28() real ext-real Element of REAL
(cn `2) * (cn `2) is V28() real ext-real set
((cn `1) ^2) + ((cn `2) ^2) is V28() real ext-real Element of REAL
- |.cn.| is V28() real ext-real non positive Element of REAL
- (1 + q) is V28() real ext-real Element of REAL
(- (1 + q)) / (1 + q) is V28() real ext-real Element of COMPLEX
- (cn `2) is V28() real ext-real Element of REAL
cn is functional non empty Element of K19( the carrier of (TOP-REAL 2))
proj1 | cn is Relation-like the carrier of ((TOP-REAL 2) | cn) -defined REAL -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | cn),REAL))
(TOP-REAL 2) | cn is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | cn) is non empty set
K20( the carrier of ((TOP-REAL 2) | cn),REAL) is set
K19(K20( the carrier of ((TOP-REAL 2) | cn),REAL)) is set
K20( the carrier of ((TOP-REAL 2) | cn), the carrier of R^1) is set
K19(K20( the carrier of ((TOP-REAL 2) | cn), the carrier of R^1)) is set
q is Relation-like the carrier of ((TOP-REAL 2) | cn) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | cn), the carrier of R^1))
p is Element of the carrier of ((TOP-REAL 2) | cn)
q . p is V28() real ext-real Element of the carrier of R^1
proj1 . p is set
dom proj1 is functional Element of K19( the carrier of (TOP-REAL 2))
(dom proj1) /\ cn is functional Element of K19( the carrier of (TOP-REAL 2))
p is Element of the carrier of ((TOP-REAL 2) | cn)
(proj1 | cn) . p is V28() real ext-real Element of REAL
proj1 . p is set
cn is functional non empty Element of K19( the carrier of (TOP-REAL 2))
proj2 | cn is Relation-like the carrier of ((TOP-REAL 2) | cn) -defined REAL -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | cn),REAL))
(TOP-REAL 2) | cn is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | cn) is non empty set
K20( the carrier of ((TOP-REAL 2) | cn),REAL) is set
K19(K20( the carrier of ((TOP-REAL 2) | cn),REAL)) is set
K20( the carrier of ((TOP-REAL 2) | cn), the carrier of R^1) is set
K19(K20( the carrier of ((TOP-REAL 2) | cn), the carrier of R^1)) is set
q is Relation-like the carrier of ((TOP-REAL 2) | cn) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | cn), the carrier of R^1))
p is Element of the carrier of ((TOP-REAL 2) | cn)
q . p is V28() real ext-real Element of the carrier of R^1
proj2 . p is set
dom proj2 is functional Element of K19( the carrier of (TOP-REAL 2))
(dom proj2) /\ cn is functional Element of K19( the carrier of (TOP-REAL 2))
p is Element of the carrier of ((TOP-REAL 2) | cn)
(proj2 | cn) . p is V28() real ext-real Element of REAL
proj2 . p is set
(2) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of R^1))
K20( the carrier of (TOP-REAL 2), the carrier of R^1) is set
K19(K20( the carrier of (TOP-REAL 2), the carrier of R^1)) is set
dom (2) is functional Element of K19( the carrier of (TOP-REAL 2))
cn is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(2) | cn is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of R^1))
(TOP-REAL 2) | cn is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | cn) is non empty set
K20( the carrier of ((TOP-REAL 2) | cn), the carrier of R^1) is set
K19(K20( the carrier of ((TOP-REAL 2) | cn), the carrier of R^1)) is set
q is Relation-like the carrier of ((TOP-REAL 2) | cn) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | cn), the carrier of R^1))
p is Element of the carrier of ((TOP-REAL 2) | cn)
q . p is V28() real ext-real Element of the carrier of R^1
(2) . p is set
(dom (2)) /\ cn is functional Element of K19( the carrier of (TOP-REAL 2))
p is Element of the carrier of ((TOP-REAL 2) | cn)
((2) | cn) . p is set
(2) . p is set
cn is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | cn is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | cn) is non empty set
K20( the carrier of ((TOP-REAL 2) | cn), the carrier of R^1) is set
K19(K20( the carrier of ((TOP-REAL 2) | cn), the carrier of R^1)) is set
(2) | cn is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of R^1))
q is Relation-like the carrier of ((TOP-REAL 2) | cn) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | cn), the carrier of R^1))
p is Element of the carrier of ((TOP-REAL 2) | cn)
q . p is V28() real ext-real Element of the carrier of R^1
(2) . p is set
p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.p1.| is V28() real ext-real non negative Element of REAL
cn is V28() real ext-real Element of REAL
1 - cn is V28() real ext-real Element of REAL
q is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | q is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | q) is non empty set
K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1) is set
K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1)) is set
p is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
(2) | q is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of R^1))
proj2 | q is Relation-like the carrier of ((TOP-REAL 2) | q) -defined REAL -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q),REAL))
K20( the carrier of ((TOP-REAL 2) | q),REAL) is set
K19(K20( the carrier of ((TOP-REAL 2) | q),REAL)) is set
u2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
u2 is Element of the carrier of ((TOP-REAL 2) | q)
p1 . u2 is V28() real ext-real Element of the carrier of R^1
VV0 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
u2 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
dom u2 is Element of K19( the carrier of ((TOP-REAL 2) | q))
K19( the carrier of ((TOP-REAL 2) | q)) is set
dom p is Element of K19( the carrier of ((TOP-REAL 2) | q))
u3 is set
p . u3 is set
u2 . u3 is set
q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
proj2 . q4 is V28() real ext-real Element of REAL
q4 `2 is V28() real ext-real Element of REAL
(2) . q4 is V28() real ext-real Element of the carrier of R^1
|.q4.| is V28() real ext-real non negative Element of REAL
y is Element of the carrier of ((TOP-REAL 2) | q)
VV0 . y is V28() real ext-real Element of the carrier of R^1
proj2 . y is set
p1 . y is V28() real ext-real Element of the carrier of R^1
(2) . y is set
p . q4 is set
(q4 `2) / |.q4.| is V28() real ext-real Element of COMPLEX
((q4 `2) / |.q4.|) - cn is V28() real ext-real Element of REAL
(((q4 `2) / |.q4.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
|.q4.| * ((((q4 `2) / |.q4.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
cn is V28() real ext-real Element of REAL
1 + cn is V28() real ext-real Element of REAL
q is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | q is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | q) is non empty set
K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1) is set
K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1)) is set
p is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
(2) | q is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of R^1))
proj2 | q is Relation-like the carrier of ((TOP-REAL 2) | q) -defined REAL -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q),REAL))
K20( the carrier of ((TOP-REAL 2) | q),REAL) is set
K19(K20( the carrier of ((TOP-REAL 2) | q),REAL)) is set
u2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
u2 is Element of the carrier of ((TOP-REAL 2) | q)
p1 . u2 is V28() real ext-real Element of the carrier of R^1
VV0 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
u2 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
dom u2 is Element of K19( the carrier of ((TOP-REAL 2) | q))
K19( the carrier of ((TOP-REAL 2) | q)) is set
dom p is Element of K19( the carrier of ((TOP-REAL 2) | q))
u3 is set
p . u3 is set
u2 . u3 is set
q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
proj2 . q4 is V28() real ext-real Element of REAL
q4 `2 is V28() real ext-real Element of REAL
(2) . q4 is V28() real ext-real Element of the carrier of R^1
|.q4.| is V28() real ext-real non negative Element of REAL
y is Element of the carrier of ((TOP-REAL 2) | q)
VV0 . y is V28() real ext-real Element of the carrier of R^1
proj2 . y is set
p1 . y is V28() real ext-real Element of the carrier of R^1
(2) . y is set
p . q4 is set
(q4 `2) / |.q4.| is V28() real ext-real Element of COMPLEX
((q4 `2) / |.q4.|) - cn is V28() real ext-real Element of REAL
(((q4 `2) / |.q4.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
|.q4.| * ((((q4 `2) / |.q4.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
cn is V28() real ext-real Element of REAL
1 - cn is V28() real ext-real Element of REAL
q is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | q is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | q) is non empty set
K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1) is set
K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1)) is set
p is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
(2) | q is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of R^1))
proj2 | q is Relation-like the carrier of ((TOP-REAL 2) | q) -defined REAL -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q),REAL))
K20( the carrier of ((TOP-REAL 2) | q),REAL) is set
K19(K20( the carrier of ((TOP-REAL 2) | q),REAL)) is set
u2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
u2 is Element of the carrier of ((TOP-REAL 2) | q)
p1 . u2 is V28() real ext-real Element of the carrier of R^1
VV0 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
u2 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
dom u2 is Element of K19( the carrier of ((TOP-REAL 2) | q))
K19( the carrier of ((TOP-REAL 2) | q)) is set
dom p is Element of K19( the carrier of ((TOP-REAL 2) | q))
u3 is set
p . u3 is set
u2 . u3 is set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.y.| is V28() real ext-real non negative Element of REAL
|.y.| ^2 is V28() real ext-real Element of REAL
|.y.| * |.y.| is V28() real ext-real non negative set
y `1 is V28() real ext-real Element of REAL
(y `1) ^2 is V28() real ext-real Element of REAL
(y `1) * (y `1) is V28() real ext-real set
y `2 is V28() real ext-real Element of REAL
(y `2) ^2 is V28() real ext-real Element of REAL
(y `2) * (y `2) is V28() real ext-real set
((y `1) ^2) + ((y `2) ^2) is V28() real ext-real Element of REAL
(y `2) - |.y.| is V28() real ext-real Element of REAL
(y `2) + |.y.| is V28() real ext-real Element of REAL
((y `2) - |.y.|) * ((y `2) + |.y.|) is V28() real ext-real Element of REAL
- ((y `1) ^2) is V28() real ext-real Element of REAL
(y `2) / |.y.| is V28() real ext-real Element of COMPLEX
|.y.| / |.y.| is V28() real ext-real non negative Element of COMPLEX
((y `2) / |.y.|) - cn is V28() real ext-real Element of REAL
(1 - cn) ^2 is V28() real ext-real Element of REAL
(1 - cn) * (1 - cn) is V28() real ext-real set
(1 - cn) + cn is V28() real ext-real Element of REAL
0 + cn is V28() real ext-real Element of REAL
cn - ((y `2) / |.y.|) is V28() real ext-real Element of REAL
- (1 - cn) is V28() real ext-real Element of REAL
- (cn - ((y `2) / |.y.|)) is V28() real ext-real Element of REAL
(((y `2) / |.y.|) - cn) ^2 is V28() real ext-real Element of REAL
(((y `2) / |.y.|) - cn) * (((y `2) / |.y.|) - cn) is V28() real ext-real set
((((y `2) / |.y.|) - cn) ^2) / ((1 - cn) ^2) is V28() real ext-real Element of COMPLEX
((1 - cn) ^2) / ((1 - cn) ^2) is V28() real ext-real Element of COMPLEX
(((y `2) / |.y.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
((((y `2) / |.y.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((y `2) / |.y.|) - cn) / (1 - cn)) * ((((y `2) / |.y.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((y `2) / |.y.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
abs (1 - (((((y `2) / |.y.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
p . y is set
sqrt (abs (1 - (((((y `2) / |.y.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
- (sqrt (abs (1 - (((((y `2) / |.y.|) - cn) / (1 - cn)) ^2)))) is V28() real ext-real Element of REAL
|.y.| * (- (sqrt (abs (1 - (((((y `2) / |.y.|) - cn) / (1 - cn)) ^2))))) is V28() real ext-real Element of REAL
proj2 . y is V28() real ext-real Element of REAL
(2) . y is V28() real ext-real Element of the carrier of R^1
q4 is Element of the carrier of ((TOP-REAL 2) | q)
VV0 . q4 is V28() real ext-real Element of the carrier of R^1
proj2 . q4 is set
p1 . q4 is V28() real ext-real Element of the carrier of R^1
(2) . q4 is set
cn is V28() real ext-real Element of REAL
1 + cn is V28() real ext-real Element of REAL
q is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | q is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | q) is non empty set
K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1) is set
K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1)) is set
p is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
(2) | q is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of R^1))
proj2 | q is Relation-like the carrier of ((TOP-REAL 2) | q) -defined REAL -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q),REAL))
K20( the carrier of ((TOP-REAL 2) | q),REAL) is set
K19(K20( the carrier of ((TOP-REAL 2) | q),REAL)) is set
u2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
u2 is Element of the carrier of ((TOP-REAL 2) | q)
p1 . u2 is V28() real ext-real Element of the carrier of R^1
VV0 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
u2 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
dom u2 is Element of K19( the carrier of ((TOP-REAL 2) | q))
K19( the carrier of ((TOP-REAL 2) | q)) is set
dom p is Element of K19( the carrier of ((TOP-REAL 2) | q))
u3 is set
p . u3 is set
u2 . u3 is set
(1 + cn) ^2 is V28() real ext-real Element of REAL
(1 + cn) * (1 + cn) is V28() real ext-real set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.y.| is V28() real ext-real non negative Element of REAL
|.y.| ^2 is V28() real ext-real Element of REAL
|.y.| * |.y.| is V28() real ext-real non negative set
y `1 is V28() real ext-real Element of REAL
(y `1) ^2 is V28() real ext-real Element of REAL
(y `1) * (y `1) is V28() real ext-real set
y `2 is V28() real ext-real Element of REAL
(y `2) ^2 is V28() real ext-real Element of REAL
(y `2) * (y `2) is V28() real ext-real set
((y `1) ^2) + ((y `2) ^2) is V28() real ext-real Element of REAL
(y `2) - |.y.| is V28() real ext-real Element of REAL
(y `2) + |.y.| is V28() real ext-real Element of REAL
((y `2) - |.y.|) * ((y `2) + |.y.|) is V28() real ext-real Element of REAL
- ((y `1) ^2) is V28() real ext-real Element of REAL
- |.y.| is V28() real ext-real non positive Element of REAL
(- |.y.|) / |.y.| is V28() real ext-real non positive Element of COMPLEX
(y `2) / |.y.| is V28() real ext-real Element of COMPLEX
(- 1) - cn is V28() real ext-real Element of REAL
((y `2) / |.y.|) - cn is V28() real ext-real Element of REAL
- (1 + cn) is V28() real ext-real Element of REAL
cn - ((y `2) / |.y.|) is V28() real ext-real Element of REAL
- (cn - ((y `2) / |.y.|)) is V28() real ext-real Element of REAL
- 0 is Function-like functional empty V28() real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() Element of REAL
(((y `2) / |.y.|) - cn) ^2 is V28() real ext-real Element of REAL
(((y `2) / |.y.|) - cn) * (((y `2) / |.y.|) - cn) is V28() real ext-real set
((((y `2) / |.y.|) - cn) ^2) / ((1 + cn) ^2) is V28() real ext-real Element of COMPLEX
((1 + cn) ^2) / ((1 + cn) ^2) is V28() real ext-real Element of COMPLEX
(((y `2) / |.y.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
((((y `2) / |.y.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((y `2) / |.y.|) - cn) / (1 + cn)) * ((((y `2) / |.y.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((y `2) / |.y.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
abs (1 - (((((y `2) / |.y.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
p . y is set
sqrt (abs (1 - (((((y `2) / |.y.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
- (sqrt (abs (1 - (((((y `2) / |.y.|) - cn) / (1 + cn)) ^2)))) is V28() real ext-real Element of REAL
|.y.| * (- (sqrt (abs (1 - (((((y `2) / |.y.|) - cn) / (1 + cn)) ^2))))) is V28() real ext-real Element of REAL
proj2 . y is V28() real ext-real Element of REAL
(2) . y is V28() real ext-real Element of the carrier of R^1
q4 is Element of the carrier of ((TOP-REAL 2) | q)
VV0 . q4 is V28() real ext-real Element of the carrier of R^1
proj2 . q4 is set
p1 . q4 is V28() real ext-real Element of the carrier of R^1
(2) . q4 is set
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( b₁ `1 <= 0 & not b<sub>1</sub> = 0. (TOP-REAL 2) ) } is set
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( cn <= (b<sub>1</sub> `2) / |.b₁.| & b₁ `1 <= 0 & not b₁ = 0. (TOP-REAL 2) ) } is set
q is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | q is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | q) is set
p is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | p is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | p) is set
K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p)) is set
K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p))) is set
(cn) | q is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p1 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of ((TOP-REAL 2) | p) -valued Function-like quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p)))
cn ^2 is V28() real ext-real Element of REAL
cn * cn is V28() real ext-real set
1 - (cn ^2) is V28() real ext-real Element of REAL
sqrt (1 - (cn ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (cn ^2))) is V28() real ext-real Element of REAL
|[(- (sqrt (1 - (cn ^2)))),cn]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(- (sqrt (1 - (cn ^2)))),cn]| `1 is V28() real ext-real Element of REAL
|[(- (sqrt (1 - (cn ^2)))),cn]| `2 is V28() real ext-real Element of REAL
|.|[(- (sqrt (1 - (cn ^2)))),cn]|.| is V28() real ext-real non negative Element of REAL
(- (sqrt (1 - (cn ^2)))) ^2 is V28() real ext-real Element of REAL
(- (sqrt (1 - (cn ^2)))) * (- (sqrt (1 - (cn ^2)))) is V28() real ext-real set
((- (sqrt (1 - (cn ^2)))) ^2) + (cn ^2) is V28() real ext-real Element of REAL
sqrt (((- (sqrt (1 - (cn ^2)))) ^2) + (cn ^2)) is V28() real ext-real Element of REAL
(sqrt (1 - (cn ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (cn ^2))) * (sqrt (1 - (cn ^2))) is V28() real ext-real set
((sqrt (1 - (cn ^2))) ^2) + (cn ^2) is V28() real ext-real Element of REAL
sqrt (((sqrt (1 - (cn ^2))) ^2) + (cn ^2)) is V28() real ext-real Element of REAL
1 ^2 is V28() real ext-real Element of REAL
1 * 1 is V28() real ext-real non negative set
- (- (sqrt (1 - (cn ^2)))) is V28() real ext-real Element of REAL
- 0 is Function-like functional empty V28() real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() Element of REAL
(|[(- (sqrt (1 - (cn ^2)))),cn]| `2) / |.|[(- (sqrt (1 - (cn ^2)))),cn]|.| is V28() real ext-real Element of COMPLEX
VV0 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(cn) | VV0 is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
proj1 * ((cn) | VV0) is Relation-like the carrier of (TOP-REAL 2) -defined REAL -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2),REAL))
rng (proj1 * ((cn) | VV0)) is V126() V127() V128() Element of K19(REAL)
u2 is set
u3 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
u3 `2 is V28() real ext-real Element of REAL
|.u3.| is V28() real ext-real non negative Element of REAL
(u3 `2) / |.u3.| is V28() real ext-real Element of COMPLEX
u3 `1 is V28() real ext-real Element of REAL
dom ((cn) | VV0) is functional Element of K19( the carrier of (TOP-REAL 2))
proj2 * ((cn) | VV0) is Relation-like the carrier of (TOP-REAL 2) -defined REAL -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2),REAL))
dom (proj2 * ((cn) | VV0)) is functional Element of K19( the carrier of (TOP-REAL 2))
u2 is set
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
(dom (cn)) /\ VV0 is functional Element of K19( the carrier of (TOP-REAL 2))
dom proj2 is functional Element of K19( the carrier of (TOP-REAL 2))
(cn) . u2 is Relation-like Function-like set
rng (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
((cn) | VV0) . u2 is Relation-like Function-like set
rng (proj2 * ((cn) | VV0)) is V126() V127() V128() Element of K19(REAL)
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
(dom (cn)) /\ VV0 is functional Element of K19( the carrier of (TOP-REAL 2))
the carrier of (TOP-REAL 2) /\ VV0 is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | VV0 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | VV0) is non empty set
K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1) is set
K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1)) is set
u2 is Relation-like the carrier of ((TOP-REAL 2) | VV0) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1))
1 - cn is V28() real ext-real Element of REAL
u3 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
u2 . u3 is set
|.u3.| is V28() real ext-real non negative Element of REAL
u3 `2 is V28() real ext-real Element of REAL
(u3 `2) / |.u3.| is V28() real ext-real Element of COMPLEX
((u3 `2) / |.u3.|) - cn is V28() real ext-real Element of REAL
(((u3 `2) / |.u3.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
|.u3.| * ((((u3 `2) / |.u3.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
(cn) . u3 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((((u3 `2) / |.u3.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((u3 `2) / |.u3.|) - cn) / (1 - cn)) * ((((u3 `2) / |.u3.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((u3 `2) / |.u3.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((u3 `2) / |.u3.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((u3 `2) / |.u3.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.u3.| * (- (sqrt (1 - (((((u3 `2) / |.u3.|) - cn) / (1 - cn)) ^2)))) is V28() real ext-real Element of REAL
|[(|.u3.| * (- (sqrt (1 - (((((u3 `2) / |.u3.|) - cn) / (1 - cn)) ^2))))),(|.u3.| * ((((u3 `2) / |.u3.|) - cn) / (1 - cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `2 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `2) / |.y.| is V28() real ext-real Element of COMPLEX
y `1 is V28() real ext-real Element of REAL
((cn) | VV0) . u3 is Relation-like Function-like set
proj2 . |[(|.u3.| * (- (sqrt (1 - (((((u3 `2) / |.u3.|) - cn) / (1 - cn)) ^2))))),(|.u3.| * ((((u3 `2) / |.u3.|) - cn) / (1 - cn)))]| is V28() real ext-real Element of REAL
|[(|.u3.| * (- (sqrt (1 - (((((u3 `2) / |.u3.|) - cn) / (1 - cn)) ^2))))),(|.u3.| * ((((u3 `2) / |.u3.|) - cn) / (1 - cn)))]| `2 is V28() real ext-real Element of REAL
u3 is Relation-like the carrier of ((TOP-REAL 2) | VV0) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1))
dom (proj1 * ((cn) | VV0)) is functional Element of K19( the carrier of (TOP-REAL 2))
y is set
dom proj1 is functional Element of K19( the carrier of (TOP-REAL 2))
(cn) . y is Relation-like Function-like set
rng (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
((cn) | VV0) . y is Relation-like Function-like set
y is Relation-like the carrier of ((TOP-REAL 2) | VV0) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1))
q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y . q4 is set
|.q4.| is V28() real ext-real non negative Element of REAL
q4 `2 is V28() real ext-real Element of REAL
(q4 `2) / |.q4.| is V28() real ext-real Element of COMPLEX
((q4 `2) / |.q4.|) - cn is V28() real ext-real Element of REAL
(((q4 `2) / |.q4.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
((((q4 `2) / |.q4.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((q4 `2) / |.q4.|) - cn) / (1 - cn)) * ((((q4 `2) / |.q4.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((q4 `2) / |.q4.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((q4 `2) / |.q4.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((q4 `2) / |.q4.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.q4.| * (- (sqrt (1 - (((((q4 `2) / |.q4.|) - cn) / (1 - cn)) ^2)))) is V28() real ext-real Element of REAL
(cn) . q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.q4.| * ((((q4 `2) / |.q4.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
|[(|.q4.| * (- (sqrt (1 - (((((q4 `2) / |.q4.|) - cn) / (1 - cn)) ^2))))),(|.q4.| * ((((q4 `2) / |.q4.|) - cn) / (1 - cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `2 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `2) / |.y.| is V28() real ext-real Element of COMPLEX
y `1 is V28() real ext-real Element of REAL
((cn) | VV0) . q4 is Relation-like Function-like set
proj1 . |[(|.q4.| * (- (sqrt (1 - (((((q4 `2) / |.q4.|) - cn) / (1 - cn)) ^2))))),(|.q4.| * ((((q4 `2) / |.q4.|) - cn) / (1 - cn)))]| is V28() real ext-real Element of REAL
|[(|.q4.| * (- (sqrt (1 - (((((q4 `2) / |.q4.|) - cn) / (1 - cn)) ^2))))),(|.q4.| * ((((q4 `2) / |.q4.|) - cn) / (1 - cn)))]| `1 is V28() real ext-real Element of REAL
q4 is Relation-like the carrier of ((TOP-REAL 2) | VV0) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1))
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `1 is V28() real ext-real Element of REAL
y `2 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `2) / |.y.| is V28() real ext-real Element of COMPLEX
x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x `2 is V28() real ext-real Element of REAL
|.x.| is V28() real ext-real non negative Element of REAL
(x `2) / |.x.| is V28() real ext-real Element of COMPLEX
x `1 is V28() real ext-real Element of REAL
y is V28() real ext-real set
x is V28() real ext-real set
|[y,x]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x is V28() real ext-real set
q4 . |[y,x]| is set
q is V28() real ext-real set
u3 . |[y,x]| is set
p1 . |[y,x]| is set
|[x,q]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.|[y,x]|.| is V28() real ext-real non negative Element of REAL
|[y,x]| `2 is V28() real ext-real Element of REAL
(|[y,x]| `2) / |.|[y,x]|.| is V28() real ext-real Element of COMPLEX
((|[y,x]| `2) / |.|[y,x]|.|) - cn is V28() real ext-real Element of REAL
(((|[y,x]| `2) / |.|[y,x]|.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
((((|[y,x]| `2) / |.|[y,x]|.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((|[y,x]| `2) / |.|[y,x]|.|) - cn) / (1 - cn)) * ((((|[y,x]| `2) / |.|[y,x]|.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((|[y,x]| `2) / |.|[y,x]|.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((|[y,x]| `2) / |.|[y,x]|.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((|[y,x]| `2) / |.|[y,x]|.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.|[y,x]|.| * (- (sqrt (1 - (((((|[y,x]| `2) / |.|[y,x]|.|) - cn) / (1 - cn)) ^2)))) is V28() real ext-real Element of REAL
((cn) | q) . |[y,x]| is Relation-like Function-like set
(cn) . |[y,x]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.|[y,x]|.| * ((((|[y,x]| `2) / |.|[y,x]|.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
|[(|.|[y,x]|.| * (- (sqrt (1 - (((((|[y,x]| `2) / |.|[y,x]|.|) - cn) / (1 - cn)) ^2))))),(|.|[y,x]|.| * ((((|[y,x]| `2) / |.|[y,x]|.|) - cn) / (1 - cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K111 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K111 `2 is V28() real ext-real Element of REAL
|.K111.| is V28() real ext-real non negative Element of REAL
(K111 `2) / |.K111.| is V28() real ext-real Element of COMPLEX
K111 `1 is V28() real ext-real Element of REAL
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `1 is V28() real ext-real Element of REAL
x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x `2 is V28() real ext-real Element of REAL
|.x.| is V28() real ext-real non negative Element of REAL
(x `2) / |.x.| is V28() real ext-real Element of COMPLEX
x `1 is V28() real ext-real Element of REAL
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( (b₁ `2) / |.b<sub>1</sub>.| <= cn & b<sub>1</sub> `1 <= 0 & not b₁ = 0. (TOP-REAL 2) ) } is set
q is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | q is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | q) is set
p is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | p is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | p) is set
K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p)) is set
K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p))) is set
(cn) | q is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p1 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of ((TOP-REAL 2) | p) -valued Function-like quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p)))
cn ^2 is V28() real ext-real Element of REAL
cn * cn is V28() real ext-real set
1 - (cn ^2) is V28() real ext-real Element of REAL
sqrt (1 - (cn ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (cn ^2))) is V28() real ext-real Element of REAL
|[(- (sqrt (1 - (cn ^2)))),cn]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(- (sqrt (1 - (cn ^2)))),cn]| `1 is V28() real ext-real Element of REAL
|[(- (sqrt (1 - (cn ^2)))),cn]| `2 is V28() real ext-real Element of REAL
|.|[(- (sqrt (1 - (cn ^2)))),cn]|.| is V28() real ext-real non negative Element of REAL
(- (sqrt (1 - (cn ^2)))) ^2 is V28() real ext-real Element of REAL
(- (sqrt (1 - (cn ^2)))) * (- (sqrt (1 - (cn ^2)))) is V28() real ext-real set
((- (sqrt (1 - (cn ^2)))) ^2) + (cn ^2) is V28() real ext-real Element of REAL
sqrt (((- (sqrt (1 - (cn ^2)))) ^2) + (cn ^2)) is V28() real ext-real Element of REAL
(sqrt (1 - (cn ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (cn ^2))) * (sqrt (1 - (cn ^2))) is V28() real ext-real set
((sqrt (1 - (cn ^2))) ^2) + (cn ^2) is V28() real ext-real Element of REAL
sqrt (((sqrt (1 - (cn ^2))) ^2) + (cn ^2)) is V28() real ext-real Element of REAL
1 ^2 is V28() real ext-real Element of REAL
1 * 1 is V28() real ext-real non negative set
- (- (sqrt (1 - (cn ^2)))) is V28() real ext-real Element of REAL
- 0 is Function-like functional empty V28() real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() Element of REAL
(|[(- (sqrt (1 - (cn ^2)))),cn]| `2) / |.|[(- (sqrt (1 - (cn ^2)))),cn]|.| is V28() real ext-real Element of COMPLEX
VV0 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(cn) | VV0 is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
proj1 * ((cn) | VV0) is Relation-like the carrier of (TOP-REAL 2) -defined REAL -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2),REAL))
rng (proj1 * ((cn) | VV0)) is V126() V127() V128() Element of K19(REAL)
u2 is set
u3 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
u3 `2 is V28() real ext-real Element of REAL
|.u3.| is V28() real ext-real non negative Element of REAL
(u3 `2) / |.u3.| is V28() real ext-real Element of COMPLEX
u3 `1 is V28() real ext-real Element of REAL
dom ((cn) | VV0) is functional Element of K19( the carrier of (TOP-REAL 2))
proj2 * ((cn) | VV0) is Relation-like the carrier of (TOP-REAL 2) -defined REAL -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2),REAL))
dom (proj2 * ((cn) | VV0)) is functional Element of K19( the carrier of (TOP-REAL 2))
u2 is set
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
(dom (cn)) /\ VV0 is functional Element of K19( the carrier of (TOP-REAL 2))
dom proj2 is functional Element of K19( the carrier of (TOP-REAL 2))
(cn) . u2 is Relation-like Function-like set
rng (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
((cn) | VV0) . u2 is Relation-like Function-like set
rng (proj2 * ((cn) | VV0)) is V126() V127() V128() Element of K19(REAL)
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
(dom (cn)) /\ VV0 is functional Element of K19( the carrier of (TOP-REAL 2))
the carrier of (TOP-REAL 2) /\ VV0 is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | VV0 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | VV0) is non empty set
K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1) is set
K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1)) is set
u2 is Relation-like the carrier of ((TOP-REAL 2) | VV0) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1))
1 + cn is V28() real ext-real Element of REAL
u3 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
u2 . u3 is set
|.u3.| is V28() real ext-real non negative Element of REAL
u3 `2 is V28() real ext-real Element of REAL
(u3 `2) / |.u3.| is V28() real ext-real Element of COMPLEX
((u3 `2) / |.u3.|) - cn is V28() real ext-real Element of REAL
(((u3 `2) / |.u3.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
|.u3.| * ((((u3 `2) / |.u3.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
(cn) . u3 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((((u3 `2) / |.u3.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((u3 `2) / |.u3.|) - cn) / (1 + cn)) * ((((u3 `2) / |.u3.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((u3 `2) / |.u3.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((u3 `2) / |.u3.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((u3 `2) / |.u3.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|.u3.| * (- (sqrt (1 - (((((u3 `2) / |.u3.|) - cn) / (1 + cn)) ^2)))) is V28() real ext-real Element of REAL
|[(|.u3.| * (- (sqrt (1 - (((((u3 `2) / |.u3.|) - cn) / (1 + cn)) ^2))))),(|.u3.| * ((((u3 `2) / |.u3.|) - cn) / (1 + cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `2 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `2) / |.y.| is V28() real ext-real Element of COMPLEX
y `1 is V28() real ext-real Element of REAL
((cn) | VV0) . u3 is Relation-like Function-like set
proj2 . |[(|.u3.| * (- (sqrt (1 - (((((u3 `2) / |.u3.|) - cn) / (1 + cn)) ^2))))),(|.u3.| * ((((u3 `2) / |.u3.|) - cn) / (1 + cn)))]| is V28() real ext-real Element of REAL
|[(|.u3.| * (- (sqrt (1 - (((((u3 `2) / |.u3.|) - cn) / (1 + cn)) ^2))))),(|.u3.| * ((((u3 `2) / |.u3.|) - cn) / (1 + cn)))]| `2 is V28() real ext-real Element of REAL
u3 is Relation-like the carrier of ((TOP-REAL 2) | VV0) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1))
dom (proj1 * ((cn) | VV0)) is functional Element of K19( the carrier of (TOP-REAL 2))
y is set
dom proj1 is functional Element of K19( the carrier of (TOP-REAL 2))
(cn) . y is Relation-like Function-like set
rng (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
((cn) | VV0) . y is Relation-like Function-like set
y is Relation-like the carrier of ((TOP-REAL 2) | VV0) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1))
q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y . q4 is set
|.q4.| is V28() real ext-real non negative Element of REAL
q4 `2 is V28() real ext-real Element of REAL
(q4 `2) / |.q4.| is V28() real ext-real Element of COMPLEX
((q4 `2) / |.q4.|) - cn is V28() real ext-real Element of REAL
(((q4 `2) / |.q4.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
((((q4 `2) / |.q4.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((q4 `2) / |.q4.|) - cn) / (1 + cn)) * ((((q4 `2) / |.q4.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((q4 `2) / |.q4.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((q4 `2) / |.q4.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((q4 `2) / |.q4.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|.q4.| * (- (sqrt (1 - (((((q4 `2) / |.q4.|) - cn) / (1 + cn)) ^2)))) is V28() real ext-real Element of REAL
(cn) . q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.q4.| * ((((q4 `2) / |.q4.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
|[(|.q4.| * (- (sqrt (1 - (((((q4 `2) / |.q4.|) - cn) / (1 + cn)) ^2))))),(|.q4.| * ((((q4 `2) / |.q4.|) - cn) / (1 + cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `2 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `2) / |.y.| is V28() real ext-real Element of COMPLEX
y `1 is V28() real ext-real Element of REAL
((cn) | VV0) . q4 is Relation-like Function-like set
proj1 . |[(|.q4.| * (- (sqrt (1 - (((((q4 `2) / |.q4.|) - cn) / (1 + cn)) ^2))))),(|.q4.| * ((((q4 `2) / |.q4.|) - cn) / (1 + cn)))]| is V28() real ext-real Element of REAL
|[(|.q4.| * (- (sqrt (1 - (((((q4 `2) / |.q4.|) - cn) / (1 + cn)) ^2))))),(|.q4.| * ((((q4 `2) / |.q4.|) - cn) / (1 + cn)))]| `1 is V28() real ext-real Element of REAL
q4 is Relation-like the carrier of ((TOP-REAL 2) | VV0) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1))
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `1 is V28() real ext-real Element of REAL
y `2 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `2) / |.y.| is V28() real ext-real Element of COMPLEX
x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x `2 is V28() real ext-real Element of REAL
|.x.| is V28() real ext-real non negative Element of REAL
(x `2) / |.x.| is V28() real ext-real Element of COMPLEX
x `1 is V28() real ext-real Element of REAL
y is V28() real ext-real set
x is V28() real ext-real set
|[y,x]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x is V28() real ext-real set
q4 . |[y,x]| is set
q is V28() real ext-real set
u3 . |[y,x]| is set
p1 . |[y,x]| is set
|[x,q]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.|[y,x]|.| is V28() real ext-real non negative Element of REAL
|[y,x]| `2 is V28() real ext-real Element of REAL
(|[y,x]| `2) / |.|[y,x]|.| is V28() real ext-real Element of COMPLEX
((|[y,x]| `2) / |.|[y,x]|.|) - cn is V28() real ext-real Element of REAL
(((|[y,x]| `2) / |.|[y,x]|.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
((((|[y,x]| `2) / |.|[y,x]|.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((|[y,x]| `2) / |.|[y,x]|.|) - cn) / (1 + cn)) * ((((|[y,x]| `2) / |.|[y,x]|.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((|[y,x]| `2) / |.|[y,x]|.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((|[y,x]| `2) / |.|[y,x]|.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((|[y,x]| `2) / |.|[y,x]|.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|.|[y,x]|.| * (- (sqrt (1 - (((((|[y,x]| `2) / |.|[y,x]|.|) - cn) / (1 + cn)) ^2)))) is V28() real ext-real Element of REAL
((cn) | q) . |[y,x]| is Relation-like Function-like set
(cn) . |[y,x]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.|[y,x]|.| * ((((|[y,x]| `2) / |.|[y,x]|.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
|[(|.|[y,x]|.| * (- (sqrt (1 - (((((|[y,x]| `2) / |.|[y,x]|.|) - cn) / (1 + cn)) ^2))))),(|.|[y,x]|.| * ((((|[y,x]| `2) / |.|[y,x]|.|) - cn) / (1 + cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K111 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K111 `2 is V28() real ext-real Element of REAL
|.K111.| is V28() real ext-real non negative Element of REAL
(K111 `2) / |.K111.| is V28() real ext-real Element of COMPLEX
K111 `1 is V28() real ext-real Element of REAL
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `1 is V28() real ext-real Element of REAL
x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x `2 is V28() real ext-real Element of REAL
|.x.| is V28() real ext-real non negative Element of REAL
(x `2) / |.x.| is V28() real ext-real Element of COMPLEX
x `1 is V28() real ext-real Element of REAL
(TOP-REAL 2) | ([#] (TOP-REAL 2)) is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))) is non empty set
K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of R^1) is set
K19(K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of R^1)) is set
(2) | ([#] (TOP-REAL 2)) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of R^1))
proj2 | ([#] (TOP-REAL 2)) is Relation-like the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))) -defined REAL -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))),REAL))
K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))),REAL) is set
K19(K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))),REAL)) is set
p1 is V28() real ext-real Element of REAL
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : p1 * |.b₁.| <= b₁ `2 } is set
p2 is functional Element of K19( the carrier of (TOP-REAL 2))
q is Relation-like the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))) -defined the carrier of R^1 -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of R^1))
q3 is Relation-like the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of R^1))
p is Relation-like the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))) -defined the carrier of R^1 -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of R^1))
VV0 is Relation-like the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of R^1))
the topology of (TOP-REAL 2) is non empty open Element of K19(K19( the carrier of (TOP-REAL 2)))
K19(K19( 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
K19( the carrier of TopStruct(# the carrier of (TOP-REAL 2), the topology of (TOP-REAL 2) #)) is set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S<sub>1</sub>[b<sub>1</sub>] } is set
p2 ` is functional Element of K19( the carrier of (TOP-REAL 2))
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : not S₁[b₁] } is set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
VV0 . y is set
|.y.| is V28() real ext-real non negative Element of REAL
p1 * |.y.| is V28() real ext-real Element of REAL
y `2 is V28() real ext-real Element of REAL
(p1 * |.y.|) - (y `2) is V28() real ext-real Element of REAL
q . y is set
(2) . y is V28() real ext-real Element of the carrier of R^1
q3 . y is set
p . y is set
proj2 . y is V28() real ext-real Element of REAL
u2 is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of R^1))
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : not u2 /. b₁ <= 0 } is set
y is set
q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.q4.| is V28() real ext-real non negative Element of REAL
p1 * |.q4.| is V28() real ext-real Element of REAL
q4 `2 is V28() real ext-real Element of REAL
u2 /. q4 is V28() real ext-real Element of the carrier of R^1
u2 . q4 is V28() real ext-real Element of the carrier of R^1
(p1 * |.q4.|) - (q4 `2) is V28() real ext-real Element of REAL
y is set
q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
u2 /. q4 is V28() real ext-real Element of the carrier of R^1
u2 . q4 is V28() real ext-real Element of the carrier of R^1
|.q4.| is V28() real ext-real non negative Element of REAL
p1 * |.q4.| is V28() real ext-real Element of REAL
q4 `2 is V28() real ext-real Element of REAL
(p1 * |.q4.|) - (q4 `2) is V28() real ext-real Element of REAL
((p1 * |.q4.|) - (q4 `2)) + (q4 `2) is V28() real ext-real Element of REAL
0 + (q4 `2) is V28() real ext-real Element of REAL
u3 is Element of K19( the carrier of TopStruct(# the carrier of (TOP-REAL 2), the topology of (TOP-REAL 2) #))
u3 ` is Element of K19( the carrier of TopStruct(# the carrier of (TOP-REAL 2), the topology 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
the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))) is non empty set
K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of R^1) is set
K19(K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of R^1)) is set
(2) | ([#] (TOP-REAL 2)) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of R^1))
proj1 | ([#] (TOP-REAL 2)) is Relation-like the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))) -defined REAL -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))),REAL))
K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))),REAL) is set
K19(K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))),REAL)) is set
p1 is V28() real ext-real Element of REAL
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : p1 * |.b₁.| <= b₁ `1 } is set
p2 is functional Element of K19( the carrier of (TOP-REAL 2))
q is Relation-like the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))) -defined the carrier of R^1 -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of R^1))
q3 is Relation-like the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of R^1))
p is Relation-like the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))) -defined the carrier of R^1 -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of R^1))
VV0 is Relation-like the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of R^1))
the topology of (TOP-REAL 2) is non empty open Element of K19(K19( the carrier of (TOP-REAL 2)))
K19(K19( 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
K19( the carrier of TopStruct(# the carrier of (TOP-REAL 2), the topology of (TOP-REAL 2) #)) is set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S<sub>1</sub>[b<sub>1</sub>] } is set
p2 ` is functional Element of K19( the carrier of (TOP-REAL 2))
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : not S₁[b₁] } is set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
VV0 . y is set
|.y.| is V28() real ext-real non negative Element of REAL
p1 * |.y.| is V28() real ext-real Element of REAL
y `1 is V28() real ext-real Element of REAL
(p1 * |.y.|) - (y `1) is V28() real ext-real Element of REAL
q . y is set
(2) . y is V28() real ext-real Element of the carrier of R^1
q3 . y is set
p . y is set
proj1 . y is V28() real ext-real Element of REAL
u2 is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of R^1))
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : not u2 /. b₁ <= 0 } is set
y is set
q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.q4.| is V28() real ext-real non negative Element of REAL
p1 * |.q4.| is V28() real ext-real Element of REAL
q4 `1 is V28() real ext-real Element of REAL
u2 /. q4 is V28() real ext-real Element of the carrier of R^1
u2 . q4 is V28() real ext-real Element of the carrier of R^1
(p1 * |.q4.|) - (q4 `1) is V28() real ext-real Element of REAL
y is set
q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
u2 /. q4 is V28() real ext-real Element of the carrier of R^1
u2 . q4 is V28() real ext-real Element of the carrier of R^1
|.q4.| is V28() real ext-real non negative Element of REAL
p1 * |.q4.| is V28() real ext-real Element of REAL
q4 `1 is V28() real ext-real Element of REAL
(p1 * |.q4.|) - (q4 `1) is V28() real ext-real Element of REAL
((p1 * |.q4.|) - (q4 `1)) + (q4 `1) is V28() real ext-real Element of REAL
0 + (q4 `1) is V28() real ext-real Element of REAL
u3 is Element of K19( the carrier of TopStruct(# the carrier of (TOP-REAL 2), the topology of (TOP-REAL 2) #))
u3 ` is Element of K19( the carrier of TopStruct(# the carrier of (TOP-REAL 2), the topology of (TOP-REAL 2) #))
cn is V28() real ext-real Element of REAL
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( cn * |.b₁.| <= b₁ `2 & b<sub>1</sub> `1 <= 0 ) } is set
q is functional Element of K19( the carrier of (TOP-REAL 2))
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₁[b₁] } is set
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₂[b₁] } is set
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( S₂[b₁] & S₁[b₁] ) } is set
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₂[b₁] } /\ { b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₁[b₁] } is set
p1 is functional Element of K19( the carrier of (TOP-REAL 2))
p is functional Element of K19( 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
the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))) is non empty set
K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of R^1) is set
K19(K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of R^1)) is set
(2) | ([#] (TOP-REAL 2)) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of R^1))
proj2 | ([#] (TOP-REAL 2)) is Relation-like the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))) -defined REAL -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))),REAL))
K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))),REAL) is set
K19(K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))),REAL)) is set
p1 is V28() real ext-real Element of REAL
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : b₁ `2 <= p1 * |.b<sub>1</sub>.| } is set
p2 is functional Element of K19( the carrier of (TOP-REAL 2))
q is Relation-like the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))) -defined the carrier of R^1 -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of R^1))
q3 is Relation-like the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of R^1))
p is Relation-like the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))) -defined the carrier of R^1 -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of R^1))
VV0 is Relation-like the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of R^1))
the topology of (TOP-REAL 2) is non empty open Element of K19(K19( the carrier of (TOP-REAL 2)))
K19(K19( 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
K19( the carrier of TopStruct(# the carrier of (TOP-REAL 2), the topology of (TOP-REAL 2) #)) is set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S<sub>1</sub>[b<sub>1</sub>] } is set
p2 ` is functional Element of K19( the carrier of (TOP-REAL 2))
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : not S₁[b₁] } is set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
VV0 . y is set
|.y.| is V28() real ext-real non negative Element of REAL
p1 * |.y.| is V28() real ext-real Element of REAL
y `2 is V28() real ext-real Element of REAL
(p1 * |.y.|) - (y `2) is V28() real ext-real Element of REAL
q . y is set
(2) . y is V28() real ext-real Element of the carrier of R^1
q3 . y is set
p . y is set
proj2 . y is V28() real ext-real Element of REAL
u2 is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of R^1))
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : not 0 <= u2 /. b₁ } is set
y is set
q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q4 `2 is V28() real ext-real Element of REAL
|.q4.| is V28() real ext-real non negative Element of REAL
p1 * |.q4.| is V28() real ext-real Element of REAL
u2 /. q4 is V28() real ext-real Element of the carrier of R^1
u2 . q4 is V28() real ext-real Element of the carrier of R^1
(p1 * |.q4.|) - (q4 `2) is V28() real ext-real Element of REAL
y is set
q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
u2 /. q4 is V28() real ext-real Element of the carrier of R^1
u2 . q4 is V28() real ext-real Element of the carrier of R^1
|.q4.| is V28() real ext-real non negative Element of REAL
p1 * |.q4.| is V28() real ext-real Element of REAL
q4 `2 is V28() real ext-real Element of REAL
(p1 * |.q4.|) - (q4 `2) is V28() real ext-real Element of REAL
0 + (q4 `2) is V28() real ext-real Element of REAL
((p1 * |.q4.|) - (q4 `2)) + (q4 `2) is V28() real ext-real Element of REAL
u3 is Element of K19( the carrier of TopStruct(# the carrier of (TOP-REAL 2), the topology of (TOP-REAL 2) #))
u3 ` is Element of K19( the carrier of TopStruct(# the carrier of (TOP-REAL 2), the topology 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
the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))) is non empty set
K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of R^1) is set
K19(K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of R^1)) is set
(2) | ([#] (TOP-REAL 2)) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of R^1))
proj1 | ([#] (TOP-REAL 2)) is Relation-like the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))) -defined REAL -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))),REAL))
K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))),REAL) is set
K19(K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))),REAL)) is set
p1 is V28() real ext-real Element of REAL
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : b₁ `1 <= p1 * |.b<sub>1</sub>.| } is set
p2 is functional Element of K19( the carrier of (TOP-REAL 2))
q is Relation-like the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))) -defined the carrier of R^1 -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of R^1))
q3 is Relation-like the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of R^1))
p is Relation-like the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))) -defined the carrier of R^1 -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of R^1))
VV0 is Relation-like the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of R^1))
the topology of (TOP-REAL 2) is non empty open Element of K19(K19( the carrier of (TOP-REAL 2)))
K19(K19( 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
K19( the carrier of TopStruct(# the carrier of (TOP-REAL 2), the topology of (TOP-REAL 2) #)) is set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S<sub>1</sub>[b<sub>1</sub>] } is set
p2 ` is functional Element of K19( the carrier of (TOP-REAL 2))
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : not S₁[b₁] } is set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
VV0 . y is set
|.y.| is V28() real ext-real non negative Element of REAL
p1 * |.y.| is V28() real ext-real Element of REAL
y `1 is V28() real ext-real Element of REAL
(p1 * |.y.|) - (y `1) is V28() real ext-real Element of REAL
q . y is set
(2) . y is V28() real ext-real Element of the carrier of R^1
q3 . y is set
p . y is set
proj1 . y is V28() real ext-real Element of REAL
u2 is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of R^1))
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : not 0 <= u2 /. b₁ } is set
y is set
q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q4 `1 is V28() real ext-real Element of REAL
|.q4.| is V28() real ext-real non negative Element of REAL
p1 * |.q4.| is V28() real ext-real Element of REAL
u2 /. q4 is V28() real ext-real Element of the carrier of R^1
u2 . q4 is V28() real ext-real Element of the carrier of R^1
(p1 * |.q4.|) - (q4 `1) is V28() real ext-real Element of REAL
y is set
q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
u2 /. q4 is V28() real ext-real Element of the carrier of R^1
u2 . q4 is V28() real ext-real Element of the carrier of R^1
|.q4.| is V28() real ext-real non negative Element of REAL
p1 * |.q4.| is V28() real ext-real Element of REAL
q4 `1 is V28() real ext-real Element of REAL
(p1 * |.q4.|) - (q4 `1) is V28() real ext-real Element of REAL
0 + (q4 `1) is V28() real ext-real Element of REAL
((p1 * |.q4.|) - (q4 `1)) + (q4 `1) is V28() real ext-real Element of REAL
u3 is Element of K19( the carrier of TopStruct(# the carrier of (TOP-REAL 2), the topology of (TOP-REAL 2) #))
u3 ` is Element of K19( the carrier of TopStruct(# the carrier of (TOP-REAL 2), the topology of (TOP-REAL 2) #))
cn is V28() real ext-real Element of REAL
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( b₁ `2 <= cn * |.b<sub>1</sub>.| & b<sub>1</sub> `1 <= 0 ) } is set
q is functional Element of K19( the carrier of (TOP-REAL 2))
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( S₂[b₁] & S₁[b₁] ) } is set
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₁[b₁] } is set
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₂[b₁] } is set
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₂[b₁] } /\ { b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₁[b₁] } is set
p1 is functional Element of K19( the carrier of (TOP-REAL 2))
p is functional Element of K19( the carrier of (TOP-REAL 2))
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | q is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | q) is set
p is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | p is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | p) is set
K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p)) is set
K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p))) is set
(cn) | q is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p1 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of ((TOP-REAL 2) | p) -valued Function-like quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p)))
cn ^2 is V28() real ext-real Element of REAL
cn * cn is V28() real ext-real set
1 - (cn ^2) is V28() real ext-real Element of REAL
sqrt (1 - (cn ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (cn ^2))) is V28() real ext-real Element of REAL
|[(- (sqrt (1 - (cn ^2)))),cn]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(- (sqrt (1 - (cn ^2)))),cn]| `1 is V28() real ext-real Element of REAL
|[(- (sqrt (1 - (cn ^2)))),cn]| `2 is V28() real ext-real Element of REAL
|.|[(- (sqrt (1 - (cn ^2)))),cn]|.| is V28() real ext-real non negative Element of REAL
(- (sqrt (1 - (cn ^2)))) ^2 is V28() real ext-real Element of REAL
(- (sqrt (1 - (cn ^2)))) * (- (sqrt (1 - (cn ^2)))) is V28() real ext-real set
((- (sqrt (1 - (cn ^2)))) ^2) + (cn ^2) is V28() real ext-real Element of REAL
sqrt (((- (sqrt (1 - (cn ^2)))) ^2) + (cn ^2)) is V28() real ext-real Element of REAL
(sqrt (1 - (cn ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (cn ^2))) * (sqrt (1 - (cn ^2))) is V28() real ext-real set
((sqrt (1 - (cn ^2))) ^2) + (cn ^2) is V28() real ext-real Element of REAL
sqrt (((sqrt (1 - (cn ^2))) ^2) + (cn ^2)) is V28() real ext-real Element of REAL
1 ^2 is V28() real ext-real Element of REAL
1 * 1 is V28() real ext-real non negative set
- (- (sqrt (1 - (cn ^2)))) is V28() real ext-real Element of REAL
- 0 is Function-like functional empty V28() real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() Element of REAL
(|[(- (sqrt (1 - (cn ^2)))),cn]| `2) / |.|[(- (sqrt (1 - (cn ^2)))),cn]|.| is V28() real ext-real Element of COMPLEX
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( cn <= (b<sub>1</sub> `2) / |.b₁.| & b₁ `1 <= 0 & not b<sub>1</sub> = 0. (TOP-REAL 2) ) } is set
VV0 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
u2 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
u3 is set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `1 is V28() real ext-real Element of REAL
VV0 \/ u2 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | VV0 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
(TOP-REAL 2) | u2 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( (b₁ `2) / |.b<sub>1</sub>.| <= cn & b<sub>1</sub> `1 <= 0 & not b₁ = 0. (TOP-REAL 2) ) } is set
u3 is set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `2 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `2) / |.y.| is V28() real ext-real Element of COMPLEX
y `1 is V28() real ext-real Element of REAL
u3 is set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `2 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `2) / |.y.| is V28() real ext-real Element of COMPLEX
y `1 is V28() real ext-real Element of REAL
the carrier of ((TOP-REAL 2) | VV0) is non empty set
K19( the carrier of ((TOP-REAL 2) | VV0)) is set
the carrier of ((TOP-REAL 2) | u2) is non empty set
u3 is non empty Element of K19( the carrier of ((TOP-REAL 2) | VV0))
p1 | u3 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of ((TOP-REAL 2) | p) -valued Function-like Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p)))
rng (p1 | u3) is Element of K19( the carrier of ((TOP-REAL 2) | p))
K19( the carrier of ((TOP-REAL 2) | p)) is set
y is non empty Element of K19( the carrier of ((TOP-REAL 2) | VV0))
p1 | y is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of ((TOP-REAL 2) | p) -valued Function-like Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p)))
rng (p1 | y) is Element of K19( the carrier of ((TOP-REAL 2) | p))
dom p1 is Element of K19( the carrier of ((TOP-REAL 2) | q))
K19( the carrier of ((TOP-REAL 2) | q)) is set
dom (p1 | u3) is Element of K19( the carrier of ((TOP-REAL 2) | q))
((TOP-REAL 2) | VV0) | u3 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of (TOP-REAL 2) | VV0
the carrier of (((TOP-REAL 2) | VV0) | u3) is non empty set
K20( the carrier of (((TOP-REAL 2) | VV0) | u3), the carrier of ((TOP-REAL 2) | u2)) is set
K19(K20( the carrier of (((TOP-REAL 2) | VV0) | u3), the carrier of ((TOP-REAL 2) | u2))) is set
dom (p1 | y) is Element of K19( the carrier of ((TOP-REAL 2) | q))
((TOP-REAL 2) | VV0) | y is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of (TOP-REAL 2) | VV0
the carrier of (((TOP-REAL 2) | VV0) | y) is non empty set
K20( the carrier of (((TOP-REAL 2) | VV0) | y), the carrier of ((TOP-REAL 2) | u2)) is set
K19(K20( the carrier of (((TOP-REAL 2) | VV0) | y), the carrier of ((TOP-REAL 2) | u2))) is set
y is Relation-like the carrier of (((TOP-REAL 2) | VV0) | y) -defined the carrier of ((TOP-REAL 2) | u2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (((TOP-REAL 2) | VV0) | y), the carrier of ((TOP-REAL 2) | u2)))
dom y is Element of K19( the carrier of (((TOP-REAL 2) | VV0) | y))
K19( the carrier of (((TOP-REAL 2) | VV0) | y)) is set
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₁[b₁] } is set
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₂[b₁] } is set
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( cn * |.b₁.| <= b₁ `2 & b<sub>1</sub> `1 <= 0 ) } is set
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₃[b₁] } is set
x is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(cn) | x is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
rng ((cn) | x) is functional Element of K19( the carrier of (TOP-REAL 2))
q is set
dom ((cn) | x) is functional Element of K19( the carrier of (TOP-REAL 2))
K004 is set
((cn) | x) . K004 is Relation-like Function-like set
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
K111 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(cn) . K111 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(dom (cn)) /\ x is functional Element of K19( the carrier of (TOP-REAL 2))
the carrier of (TOP-REAL 2) /\ x is functional Element of K19( the carrier of (TOP-REAL 2))
K111 `2 is V28() real ext-real Element of REAL
|.K111.| is V28() real ext-real non negative Element of REAL
(K111 `2) / |.K111.| is V28() real ext-real Element of COMPLEX
((K111 `2) / |.K111.|) - cn is V28() real ext-real Element of REAL
f4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
f4 `2 is V28() real ext-real Element of REAL
|.f4.| is V28() real ext-real non negative Element of REAL
(f4 `2) / |.f4.| is V28() real ext-real Element of COMPLEX
f4 `1 is V28() real ext-real Element of REAL
f4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
f4 `2 is V28() real ext-real Element of REAL
|.f4.| is V28() real ext-real non negative Element of REAL
(f4 `2) / |.f4.| is V28() real ext-real Element of COMPLEX
f4 `1 is V28() real ext-real Element of REAL
|.K111.| ^2 is V28() real ext-real Element of REAL
|.K111.| * |.K111.| is V28() real ext-real non negative set
0 ^2 is V28() real ext-real Element of REAL
0 * 0 is Function-like functional empty V28() real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() set
1 - cn is V28() real ext-real Element of REAL
(((K111 `2) / |.K111.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
((((K111 `2) / |.K111.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((K111 `2) / |.K111.|) - cn) / (1 - cn)) * ((((K111 `2) / |.K111.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((K111 `2) / |.K111.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((K111 `2) / |.K111.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((K111 `2) / |.K111.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.K111.| * (- (sqrt (1 - (((((K111 `2) / |.K111.|) - cn) / (1 - cn)) ^2)))) is V28() real ext-real Element of REAL
|.K111.| * ((((K111 `2) / |.K111.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
|[(|.K111.| * (- (sqrt (1 - (((((K111 `2) / |.K111.|) - cn) / (1 - cn)) ^2))))),(|.K111.| * ((((K111 `2) / |.K111.|) - cn) / (1 - cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.K111.| * (- (sqrt (1 - (((((K111 `2) / |.K111.|) - cn) / (1 - cn)) ^2))))),(|.K111.| * ((((K111 `2) / |.K111.|) - cn) / (1 - cn)))]| `2 is V28() real ext-real Element of REAL
K111 `1 is V28() real ext-real Element of REAL
(K111 `1) ^2 is V28() real ext-real Element of REAL
(K111 `1) * (K111 `1) is V28() real ext-real set
(K111 `2) ^2 is V28() real ext-real Element of REAL
(K111 `2) * (K111 `2) is V28() real ext-real set
0 + ((K111 `2) ^2) is V28() real ext-real Element of REAL
((K111 `1) ^2) + ((K111 `2) ^2) is V28() real ext-real Element of REAL
((K111 `2) ^2) / (|.K111.| ^2) is V28() real ext-real Element of COMPLEX
(|.K111.| ^2) / (|.K111.| ^2) is V28() real ext-real Element of COMPLEX
((K111 `2) / |.K111.|) ^2 is V28() real ext-real Element of COMPLEX
((K111 `2) / |.K111.|) * ((K111 `2) / |.K111.|) is V28() real ext-real set
- (1 - cn) is V28() real ext-real Element of REAL
- (((K111 `2) / |.K111.|) - cn) is V28() real ext-real Element of REAL
(- (1 - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
(- (((K111 `2) / |.K111.|) - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
((- (((K111 `2) / |.K111.|) - cn)) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((K111 `2) / |.K111.|) - cn)) / (1 - cn)) * ((- (((K111 `2) / |.K111.|) - cn)) / (1 - cn)) is V28() real ext-real set
1 - (((- (((K111 `2) / |.K111.|) - cn)) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
- ((((K111 `2) / |.K111.|) - cn) / (1 - cn)) is V28() real ext-real Element of COMPLEX
(- ((((K111 `2) / |.K111.|) - cn) / (1 - cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((K111 `2) / |.K111.|) - cn) / (1 - cn))) * (- ((((K111 `2) / |.K111.|) - cn) / (1 - cn))) is V28() real ext-real set
1 - ((- ((((K111 `2) / |.K111.|) - cn) / (1 - cn))) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((K111 `2) / |.K111.|) - cn)) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
(- (((K111 `2) / |.K111.|) - cn)) ^2 is V28() real ext-real Element of REAL
(- (((K111 `2) / |.K111.|) - cn)) * (- (((K111 `2) / |.K111.|) - cn)) is V28() real ext-real set
(1 - cn) ^2 is V28() real ext-real Element of REAL
(1 - cn) * (1 - cn) is V28() real ext-real set
((- (((K111 `2) / |.K111.|) - cn)) ^2) / ((1 - cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((- (((K111 `2) / |.K111.|) - cn)) ^2) / ((1 - cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((K111 `2) / |.K111.|) - cn)) ^2) / ((1 - cn) ^2))) is V28() real ext-real Element of REAL
(((K111 `2) / |.K111.|) - cn) ^2 is V28() real ext-real Element of REAL
(((K111 `2) / |.K111.|) - cn) * (((K111 `2) / |.K111.|) - cn) is V28() real ext-real set
((((K111 `2) / |.K111.|) - cn) ^2) / ((1 - cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((((K111 `2) / |.K111.|) - cn) ^2) / ((1 - cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((((K111 `2) / |.K111.|) - cn) ^2) / ((1 - cn) ^2))) is V28() real ext-real Element of REAL
|[(|.K111.| * (- (sqrt (1 - (((((K111 `2) / |.K111.|) - cn) / (1 - cn)) ^2))))),(|.K111.| * ((((K111 `2) / |.K111.|) - cn) / (1 - cn)))]| `1 is V28() real ext-real Element of REAL
(|[(|.K111.| * (- (sqrt (1 - (((((K111 `2) / |.K111.|) - cn) / (1 - cn)) ^2))))),(|.K111.| * ((((K111 `2) / |.K111.|) - cn) / (1 - cn)))]| `1) ^2 is V28() real ext-real Element of REAL
(|[(|.K111.| * (- (sqrt (1 - (((((K111 `2) / |.K111.|) - cn) / (1 - cn)) ^2))))),(|.K111.| * ((((K111 `2) / |.K111.|) - cn) / (1 - cn)))]| `1) * (|[(|.K111.| * (- (sqrt (1 - (((((K111 `2) / |.K111.|) - cn) / (1 - cn)) ^2))))),(|.K111.| * ((((K111 `2) / |.K111.|) - cn) / (1 - cn)))]| `1) is V28() real ext-real set
(sqrt (1 - (((((K111 `2) / |.K111.|) - cn) / (1 - cn)) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((K111 `2) / |.K111.|) - cn) / (1 - cn)) ^2))) * (sqrt (1 - (((((K111 `2) / |.K111.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real set
(|.K111.| ^2) * ((sqrt (1 - (((((K111 `2) / |.K111.|) - cn) / (1 - cn)) ^2))) ^2) is V28() real ext-real Element of REAL
(|.K111.| ^2) * (1 - (((((K111 `2) / |.K111.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.|[(|.K111.| * (- (sqrt (1 - (((((K111 `2) / |.K111.|) - cn) / (1 - cn)) ^2))))),(|.K111.| * ((((K111 `2) / |.K111.|) - cn) / (1 - cn)))]|.| is V28() real ext-real non negative Element of REAL
|.|[(|.K111.| * (- (sqrt (1 - (((((K111 `2) / |.K111.|) - cn) / (1 - cn)) ^2))))),(|.K111.| * ((((K111 `2) / |.K111.|) - cn) / (1 - cn)))]|.| ^2 is V28() real ext-real Element of REAL
|.|[(|.K111.| * (- (sqrt (1 - (((((K111 `2) / |.K111.|) - cn) / (1 - cn)) ^2))))),(|.K111.| * ((((K111 `2) / |.K111.|) - cn) / (1 - cn)))]|.| * |.|[(|.K111.| * (- (sqrt (1 - (((((K111 `2) / |.K111.|) - cn) / (1 - cn)) ^2))))),(|.K111.| * ((((K111 `2) / |.K111.|) - cn) / (1 - cn)))]|.| is V28() real ext-real non negative set
(|[(|.K111.| * (- (sqrt (1 - (((((K111 `2) / |.K111.|) - cn) / (1 - cn)) ^2))))),(|.K111.| * ((((K111 `2) / |.K111.|) - cn) / (1 - cn)))]| `2) ^2 is V28() real ext-real Element of REAL
(|[(|.K111.| * (- (sqrt (1 - (((((K111 `2) / |.K111.|) - cn) / (1 - cn)) ^2))))),(|.K111.| * ((((K111 `2) / |.K111.|) - cn) / (1 - cn)))]| `2) * (|[(|.K111.| * (- (sqrt (1 - (((((K111 `2) / |.K111.|) - cn) / (1 - cn)) ^2))))),(|.K111.| * ((((K111 `2) / |.K111.|) - cn) / (1 - cn)))]| `2) is V28() real ext-real set
((|[(|.K111.| * (- (sqrt (1 - (((((K111 `2) / |.K111.|) - cn) / (1 - cn)) ^2))))),(|.K111.| * ((((K111 `2) / |.K111.|) - cn) / (1 - cn)))]| `1) ^2) + ((|[(|.K111.| * (- (sqrt (1 - (((((K111 `2) / |.K111.|) - cn) / (1 - cn)) ^2))))),(|.K111.| * ((((K111 `2) / |.K111.|) - cn) / (1 - cn)))]| `2) ^2) is V28() real ext-real Element of REAL
T1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
T1 `2 is V28() real ext-real Element of REAL
|.T1.| is V28() real ext-real non negative Element of REAL
(T1 `2) / |.T1.| is V28() real ext-real Element of COMPLEX
T1 `1 is V28() real ext-real Element of REAL
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
dom ((cn) | x) is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | x is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | x) is non empty set
K20( the carrier of ((TOP-REAL 2) | x), the carrier of ((TOP-REAL 2) | VV0)) is set
K19(K20( the carrier of ((TOP-REAL 2) | x), the carrier of ((TOP-REAL 2) | VV0))) is set
x is functional Element of K19( the carrier of (TOP-REAL 2))
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S<sub>4</sub>[b<sub>1</sub>] } is set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( b<sub>1</sub> `2 <= cn * |.b₁.| & b₁ `1 <= 0 ) } is set
K004 is functional Element of K19( the carrier of (TOP-REAL 2))
K004 /\ VV0 is functional Element of K19( the carrier of (TOP-REAL 2))
K111 is set
f4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
f4 `2 is V28() real ext-real Element of REAL
|.f4.| is V28() real ext-real non negative Element of REAL
cn * |.f4.| is V28() real ext-real Element of REAL
f4 `1 is V28() real ext-real Element of REAL
(f4 `2) / |.f4.| is V28() real ext-real Element of COMPLEX
(cn * |.f4.|) / |.f4.| is V28() real ext-real Element of COMPLEX
T1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
T1 `1 is V28() real ext-real Element of REAL
T1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
T1 `1 is V28() real ext-real Element of REAL
q4 is Relation-like the carrier of (((TOP-REAL 2) | VV0) | u3) -defined the carrier of ((TOP-REAL 2) | u2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (((TOP-REAL 2) | VV0) | u3), the carrier of ((TOP-REAL 2) | u2)))
q is Relation-like the carrier of ((TOP-REAL 2) | x) -defined the carrier of ((TOP-REAL 2) | VV0) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | x), the carrier of ((TOP-REAL 2) | VV0)))
[#] ((TOP-REAL 2) | VV0) is non empty non proper closed Element of K19( the carrier of ((TOP-REAL 2) | VV0))
K111 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(cn) | K111 is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
rng ((cn) | K111) is functional Element of K19( the carrier of (TOP-REAL 2))
f4 is set
dom ((cn) | K111) is functional Element of K19( the carrier of (TOP-REAL 2))
T1 is set
((cn) | K111) . T1 is Relation-like Function-like set
T2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(cn) . T2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(dom (cn)) /\ K111 is functional Element of K19( the carrier of (TOP-REAL 2))
the carrier of (TOP-REAL 2) /\ K111 is functional Element of K19( the carrier of (TOP-REAL 2))
T2 `2 is V28() real ext-real Element of REAL
|.T2.| is V28() real ext-real non negative Element of REAL
(T2 `2) / |.T2.| is V28() real ext-real Element of COMPLEX
((T2 `2) / |.T2.|) - cn is V28() real ext-real Element of REAL
h is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
h `2 is V28() real ext-real Element of REAL
|.h.| is V28() real ext-real non negative Element of REAL
(h `2) / |.h.| is V28() real ext-real Element of COMPLEX
h `1 is V28() real ext-real Element of REAL
h is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
h `2 is V28() real ext-real Element of REAL
|.h.| is V28() real ext-real non negative Element of REAL
(h `2) / |.h.| is V28() real ext-real Element of COMPLEX
h `1 is V28() real ext-real Element of REAL
|.T2.| ^2 is V28() real ext-real Element of REAL
|.T2.| * |.T2.| is V28() real ext-real non negative set
0 ^2 is V28() real ext-real Element of REAL
0 * 0 is Function-like functional empty V28() real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() set
1 + cn is V28() real ext-real Element of REAL
(((T2 `2) / |.T2.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
((((T2 `2) / |.T2.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((T2 `2) / |.T2.|) - cn) / (1 + cn)) * ((((T2 `2) / |.T2.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((T2 `2) / |.T2.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((T2 `2) / |.T2.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((T2 `2) / |.T2.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|.T2.| * (- (sqrt (1 - (((((T2 `2) / |.T2.|) - cn) / (1 + cn)) ^2)))) is V28() real ext-real Element of REAL
|.T2.| * ((((T2 `2) / |.T2.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
|[(|.T2.| * (- (sqrt (1 - (((((T2 `2) / |.T2.|) - cn) / (1 + cn)) ^2))))),(|.T2.| * ((((T2 `2) / |.T2.|) - cn) / (1 + cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.T2.| * (- (sqrt (1 - (((((T2 `2) / |.T2.|) - cn) / (1 + cn)) ^2))))),(|.T2.| * ((((T2 `2) / |.T2.|) - cn) / (1 + cn)))]| `2 is V28() real ext-real Element of REAL
T2 `1 is V28() real ext-real Element of REAL
(T2 `1) ^2 is V28() real ext-real Element of REAL
(T2 `1) * (T2 `1) is V28() real ext-real set
(T2 `2) ^2 is V28() real ext-real Element of REAL
(T2 `2) * (T2 `2) is V28() real ext-real set
((T2 `1) ^2) + ((T2 `2) ^2) is V28() real ext-real Element of REAL
0 + ((T2 `2) ^2) is V28() real ext-real Element of REAL
((T2 `2) ^2) / (|.T2.| ^2) is V28() real ext-real Element of COMPLEX
(|.T2.| ^2) / (|.T2.| ^2) is V28() real ext-real Element of COMPLEX
((T2 `2) / |.T2.|) ^2 is V28() real ext-real Element of COMPLEX
((T2 `2) / |.T2.|) * ((T2 `2) / |.T2.|) is V28() real ext-real set
(- 1) - cn is V28() real ext-real Element of REAL
- (1 + cn) is V28() real ext-real Element of REAL
(- (1 + cn)) / (1 + cn) is V28() real ext-real Element of COMPLEX
- ((((T2 `2) / |.T2.|) - cn) / (1 + cn)) is V28() real ext-real Element of COMPLEX
(- ((((T2 `2) / |.T2.|) - cn) / (1 + cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((T2 `2) / |.T2.|) - cn) / (1 + cn))) * (- ((((T2 `2) / |.T2.|) - cn) / (1 + cn))) is V28() real ext-real set
1 - ((- ((((T2 `2) / |.T2.|) - cn) / (1 + cn))) ^2) is V28() real ext-real Element of REAL
- (((T2 `2) / |.T2.|) - cn) is V28() real ext-real Element of REAL
(- (((T2 `2) / |.T2.|) - cn)) / (1 + cn) is V28() real ext-real Element of COMPLEX
((- (((T2 `2) / |.T2.|) - cn)) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((T2 `2) / |.T2.|) - cn)) / (1 + cn)) * ((- (((T2 `2) / |.T2.|) - cn)) / (1 + cn)) is V28() real ext-real set
1 - (((- (((T2 `2) / |.T2.|) - cn)) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((T2 `2) / |.T2.|) - cn)) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
(- (((T2 `2) / |.T2.|) - cn)) ^2 is V28() real ext-real Element of REAL
(- (((T2 `2) / |.T2.|) - cn)) * (- (((T2 `2) / |.T2.|) - cn)) is V28() real ext-real set
(1 + cn) ^2 is V28() real ext-real Element of REAL
(1 + cn) * (1 + cn) is V28() real ext-real set
((- (((T2 `2) / |.T2.|) - cn)) ^2) / ((1 + cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((- (((T2 `2) / |.T2.|) - cn)) ^2) / ((1 + cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((T2 `2) / |.T2.|) - cn)) ^2) / ((1 + cn) ^2))) is V28() real ext-real Element of REAL
(((T2 `2) / |.T2.|) - cn) ^2 is V28() real ext-real Element of REAL
(((T2 `2) / |.T2.|) - cn) * (((T2 `2) / |.T2.|) - cn) is V28() real ext-real set
((((T2 `2) / |.T2.|) - cn) ^2) / ((1 + cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((((T2 `2) / |.T2.|) - cn) ^2) / ((1 + cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((((T2 `2) / |.T2.|) - cn) ^2) / ((1 + cn) ^2))) is V28() real ext-real Element of REAL
|[(|.T2.| * (- (sqrt (1 - (((((T2 `2) / |.T2.|) - cn) / (1 + cn)) ^2))))),(|.T2.| * ((((T2 `2) / |.T2.|) - cn) / (1 + cn)))]| `1 is V28() real ext-real Element of REAL
(|[(|.T2.| * (- (sqrt (1 - (((((T2 `2) / |.T2.|) - cn) / (1 + cn)) ^2))))),(|.T2.| * ((((T2 `2) / |.T2.|) - cn) / (1 + cn)))]| `1) ^2 is V28() real ext-real Element of REAL
(|[(|.T2.| * (- (sqrt (1 - (((((T2 `2) / |.T2.|) - cn) / (1 + cn)) ^2))))),(|.T2.| * ((((T2 `2) / |.T2.|) - cn) / (1 + cn)))]| `1) * (|[(|.T2.| * (- (sqrt (1 - (((((T2 `2) / |.T2.|) - cn) / (1 + cn)) ^2))))),(|.T2.| * ((((T2 `2) / |.T2.|) - cn) / (1 + cn)))]| `1) is V28() real ext-real set
(sqrt (1 - (((((T2 `2) / |.T2.|) - cn) / (1 + cn)) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((T2 `2) / |.T2.|) - cn) / (1 + cn)) ^2))) * (sqrt (1 - (((((T2 `2) / |.T2.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real set
(|.T2.| ^2) * ((sqrt (1 - (((((T2 `2) / |.T2.|) - cn) / (1 + cn)) ^2))) ^2) is V28() real ext-real Element of REAL
(|.T2.| ^2) * (1 - (((((T2 `2) / |.T2.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
|.|[(|.T2.| * (- (sqrt (1 - (((((T2 `2) / |.T2.|) - cn) / (1 + cn)) ^2))))),(|.T2.| * ((((T2 `2) / |.T2.|) - cn) / (1 + cn)))]|.| is V28() real ext-real non negative Element of REAL
|.|[(|.T2.| * (- (sqrt (1 - (((((T2 `2) / |.T2.|) - cn) / (1 + cn)) ^2))))),(|.T2.| * ((((T2 `2) / |.T2.|) - cn) / (1 + cn)))]|.| ^2 is V28() real ext-real Element of REAL
|.|[(|.T2.| * (- (sqrt (1 - (((((T2 `2) / |.T2.|) - cn) / (1 + cn)) ^2))))),(|.T2.| * ((((T2 `2) / |.T2.|) - cn) / (1 + cn)))]|.| * |.|[(|.T2.| * (- (sqrt (1 - (((((T2 `2) / |.T2.|) - cn) / (1 + cn)) ^2))))),(|.T2.| * ((((T2 `2) / |.T2.|) - cn) / (1 + cn)))]|.| is V28() real ext-real non negative set
(|[(|.T2.| * (- (sqrt (1 - (((((T2 `2) / |.T2.|) - cn) / (1 + cn)) ^2))))),(|.T2.| * ((((T2 `2) / |.T2.|) - cn) / (1 + cn)))]| `2) ^2 is V28() real ext-real Element of REAL
(|[(|.T2.| * (- (sqrt (1 - (((((T2 `2) / |.T2.|) - cn) / (1 + cn)) ^2))))),(|.T2.| * ((((T2 `2) / |.T2.|) - cn) / (1 + cn)))]| `2) * (|[(|.T2.| * (- (sqrt (1 - (((((T2 `2) / |.T2.|) - cn) / (1 + cn)) ^2))))),(|.T2.| * ((((T2 `2) / |.T2.|) - cn) / (1 + cn)))]| `2) is V28() real ext-real set
((|[(|.T2.| * (- (sqrt (1 - (((((T2 `2) / |.T2.|) - cn) / (1 + cn)) ^2))))),(|.T2.| * ((((T2 `2) / |.T2.|) - cn) / (1 + cn)))]| `1) ^2) + ((|[(|.T2.| * (- (sqrt (1 - (((((T2 `2) / |.T2.|) - cn) / (1 + cn)) ^2))))),(|.T2.| * ((((T2 `2) / |.T2.|) - cn) / (1 + cn)))]| `2) ^2) is V28() real ext-real Element of REAL
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `2 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `2) / |.y.| is V28() real ext-real Element of COMPLEX
y `1 is V28() real ext-real Element of REAL
dom ((cn) | K111) is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | K111 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | K111) is non empty set
K20( the carrier of ((TOP-REAL 2) | K111), the carrier of ((TOP-REAL 2) | VV0)) is set
K19(K20( the carrier of ((TOP-REAL 2) | K111), the carrier of ((TOP-REAL 2) | VV0))) is set
f4 is Relation-like the carrier of ((TOP-REAL 2) | K111) -defined the carrier of ((TOP-REAL 2) | VV0) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | K111), the carrier of ((TOP-REAL 2) | VV0)))
[#] (((TOP-REAL 2) | VV0) | y) is non empty non proper closed Element of K19( the carrier of (((TOP-REAL 2) | VV0) | y))
h is set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `2 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `2) / |.y.| is V28() real ext-real Element of COMPLEX
y `1 is V28() real ext-real Element of REAL
((y `2) / |.y.|) * |.y.| is V28() real ext-real Element of REAL
cn * |.y.| is V28() real ext-real Element of REAL
K004 /\ ([#] ((TOP-REAL 2) | VV0)) is Element of K19( the carrier of ((TOP-REAL 2) | VV0))
x /\ VV0 is functional Element of K19( the carrier of (TOP-REAL 2))
h is set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.y.| is V28() real ext-real non negative Element of REAL
cn * |.y.| is V28() real ext-real Element of REAL
y `2 is V28() real ext-real Element of REAL
y `1 is V28() real ext-real Element of REAL
(cn * |.y.|) / |.y.| is V28() real ext-real Element of COMPLEX
(y `2) / |.y.| is V28() real ext-real Element of COMPLEX
c<sub>23</sub> is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
c<sub>23</sub> `1 is V28() real ext-real Element of REAL
c₂₃ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
c₂₃ `1 is V28() real ext-real Element of REAL
[#] (((TOP-REAL 2) | VV0) | u3) is non empty non proper closed Element of K19( the carrier of (((TOP-REAL 2) | VV0) | u3))
K19( the carrier of (((TOP-REAL 2) | VV0) | u3)) is set
([#] (((TOP-REAL 2) | VV0) | u3)) /\ ([#] (((TOP-REAL 2) | VV0) | y)) is Element of K19( the carrier of (((TOP-REAL 2) | VV0) | y))
h is set
q4 . h is set
y . h is set
p1 . h is set
h is set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `2 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `2) / |.y.| is V28() real ext-real Element of COMPLEX
y `1 is V28() real ext-real Element of REAL
cn * |.y.| is V28() real ext-real Element of REAL
((y `2) / |.y.|) * |.y.| is V28() real ext-real Element of REAL
x /\ ([#] ((TOP-REAL 2) | VV0)) is Element of K19( the carrier of ((TOP-REAL 2) | VV0))
u3 \/ y is non empty Element of K19( the carrier of ((TOP-REAL 2) | VV0))
h is set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `1 is V28() real ext-real Element of REAL
y `2 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `2) / |.y.| is V28() real ext-real Element of COMPLEX
y `2 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `2) / |.y.| is V28() real ext-real Element of COMPLEX
y `2 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `2) / |.y.| is V28() real ext-real Element of COMPLEX
([#] (((TOP-REAL 2) | VV0) | u3)) \/ ([#] (((TOP-REAL 2) | VV0) | y)) is non empty set
K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of ((TOP-REAL 2) | u2)) is set
K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of ((TOP-REAL 2) | u2))) is set
q4 +* y is Relation-like Function-like set
h is Relation-like the carrier of ((TOP-REAL 2) | VV0) -defined the carrier of ((TOP-REAL 2) | u2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of ((TOP-REAL 2) | u2)))
dom h is Element of K19( the carrier of ((TOP-REAL 2) | VV0))
dom q4 is Element of K19( the carrier of (((TOP-REAL 2) | VV0) | u3))
y is set
h . y is set
p1 . y is set
(dom q4) \/ (dom y) is set
q4 . y is set
(dom q4) \/ (dom y) is set
y . y is set
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( 0 <= b₁ `1 & not b₁ = 0. (TOP-REAL 2) ) } is set
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | q is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | q) is set
p is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | p is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | p) is set
K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p)) is set
K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p))) is set
(cn) | q is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p1 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of ((TOP-REAL 2) | p) -valued Function-like quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p)))
cn ^2 is V28() real ext-real Element of REAL
cn * cn is V28() real ext-real set
1 - (cn ^2) is V28() real ext-real Element of REAL
sqrt (1 - (cn ^2)) is V28() real ext-real Element of REAL
- cn is V28() real ext-real Element of REAL
|[(sqrt (1 - (cn ^2))),(- cn)]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
1 ^2 is V28() real ext-real Element of REAL
1 * 1 is V28() real ext-real non negative set
|[(sqrt (1 - (cn ^2))),(- cn)]| `1 is V28() real ext-real Element of REAL
u2 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
VV0 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
u3 is set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `1 is V28() real ext-real Element of REAL
(TOP-REAL 2) | u2 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | u2) is non empty set
(TOP-REAL 2) | VV0 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | VV0) is non empty set
K19( the carrier of ((TOP-REAL 2) | VV0)) is set
K19( the carrier of ((TOP-REAL 2) | u2)) is set
u3 is Element of the carrier of ((TOP-REAL 2) | u2)
p1 . u3 is set
y is Element of K19( the carrier of ((TOP-REAL 2) | VV0))
[#] ((TOP-REAL 2) | VV0) is non empty non proper closed Element of K19( the carrier of ((TOP-REAL 2) | VV0))
q4 is functional Element of K19( the carrier of (TOP-REAL 2))
q4 /\ ([#] ((TOP-REAL 2) | VV0)) is Element of K19( the carrier of ((TOP-REAL 2) | VV0))
[#] ((TOP-REAL 2) | u2) is non empty non proper closed Element of K19( the carrier of ((TOP-REAL 2) | u2))
q4 /\ ([#] ((TOP-REAL 2) | u2)) is Element of K19( the carrier of ((TOP-REAL 2) | u2))
(cn) . u3 is Relation-like Function-like set
y is Element of K19( the carrier of ((TOP-REAL 2) | u2))
p1 .: y is Element of K19( the carrier of ((TOP-REAL 2) | p))
K19( the carrier of ((TOP-REAL 2) | p)) is set
x is set
dom p1 is Element of K19( the carrier of ((TOP-REAL 2) | q))
K19( the carrier of ((TOP-REAL 2) | q)) is set
x is set
p1 . x is set
K20( the carrier of ((TOP-REAL 2) | u2), the carrier of ((TOP-REAL 2) | VV0)) is set
K19(K20( the carrier of ((TOP-REAL 2) | u2), the carrier of ((TOP-REAL 2) | VV0))) is set
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q `1 is V28() real ext-real Element of REAL
p1 . q is set
(cn) . q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x `1 is V28() real ext-real Element of REAL
(cn) . x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( S₁[b₁] & not b₁ = 0. (TOP-REAL 2) ) } is set
p is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | p is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | p) is set
K19( the carrier of ((TOP-REAL 2) | p)) is set
p1 is Element of K19( the carrier of ((TOP-REAL 2) | p))
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₁[b₁] } is set
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₁[b₁] } /\ (NonZero (TOP-REAL 2)) is functional Element of K19( the carrier of (TOP-REAL 2))
p2 is functional Element of K19( the carrier of (TOP-REAL 2))
[#] ((TOP-REAL 2) | p) is non proper closed Element of K19( the carrier of ((TOP-REAL 2) | p))
p2 /\ ([#] ((TOP-REAL 2) | p)) is Element of K19( the carrier of ((TOP-REAL 2) | p))
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | q is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | q) is set
K19( the carrier of ((TOP-REAL 2) | q)) is set
p is Element of K19( the carrier of ((TOP-REAL 2) | q))
((TOP-REAL 2) | q) | p is strict TopSpace-like T_0 T_1 T_2 SubSpace of (TOP-REAL 2) | q
the carrier of (((TOP-REAL 2) | q) | p) is set
K20( the carrier of (((TOP-REAL 2) | q) | p), the carrier of ((TOP-REAL 2) | q)) is set
K19(K20( the carrier of (((TOP-REAL 2) | q) | p), the carrier of ((TOP-REAL 2) | q))) is set
(cn) | p is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p1 is Relation-like the carrier of (((TOP-REAL 2) | q) | p) -defined the carrier of ((TOP-REAL 2) | q) -valued Function-like quasi_total Element of K19(K20( the carrier of (((TOP-REAL 2) | q) | p), the carrier of ((TOP-REAL 2) | q)))
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₁[b₁] } is set
q3 is set
VV0 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
VV0 `1 is V28() real ext-real Element of REAL
VV0 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
VV0 `1 is V28() real ext-real Element of REAL
p2 is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | p2 is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( S₁[b₁] & not b₁ = 0. (TOP-REAL 2) ) } is set
p is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | p is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | p) is set
K19( the carrier of ((TOP-REAL 2) | p)) is set
p1 is Element of K19( the carrier of ((TOP-REAL 2) | p))
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₁[b₁] } is set
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₁[b₁] } /\ (NonZero (TOP-REAL 2)) is functional Element of K19( the carrier of (TOP-REAL 2))
p2 is functional Element of K19( the carrier of (TOP-REAL 2))
[#] ((TOP-REAL 2) | p) is non proper closed Element of K19( the carrier of ((TOP-REAL 2) | p))
p2 /\ ([#] ((TOP-REAL 2) | p)) is Element of K19( the carrier of ((TOP-REAL 2) | p))
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | q is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | q) is set
K19( the carrier of ((TOP-REAL 2) | q)) is set
p is Element of K19( the carrier of ((TOP-REAL 2) | q))
((TOP-REAL 2) | q) | p is strict TopSpace-like T_0 T_1 T_2 SubSpace of (TOP-REAL 2) | q
the carrier of (((TOP-REAL 2) | q) | p) is set
K20( the carrier of (((TOP-REAL 2) | q) | p), the carrier of ((TOP-REAL 2) | q)) is set
K19(K20( the carrier of (((TOP-REAL 2) | q) | p), the carrier of ((TOP-REAL 2) | q))) is set
(cn) | p is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p1 is Relation-like the carrier of (((TOP-REAL 2) | q) | p) -defined the carrier of ((TOP-REAL 2) | q) -valued Function-like quasi_total Element of K19(K20( the carrier of (((TOP-REAL 2) | q) | p), the carrier of ((TOP-REAL 2) | q)))
q3 is set
VV0 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
VV0 `1 is V28() real ext-real Element of REAL
VV0 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
VV0 `1 is V28() real ext-real Element of REAL
p2 is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | p2 is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(cn) . q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.((cn) . q).| is V28() real ext-real non negative Element of REAL
|.q.| is V28() real ext-real non negative Element of REAL
p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 `2 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `1 is V28() real ext-real Element of REAL
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((p1 `2) / |.p1.|) - cn is V28() real ext-real Element of REAL
1 - cn is V28() real ext-real Element of REAL
(((p1 `2) / |.p1.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p1 `2) / |.p1.|) - cn) / (1 - cn)) * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2)))) is V28() real ext-real Element of REAL
|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `1 is V28() real ext-real Element of REAL
p2 `2 is V28() real ext-real Element of REAL
|.p1.| ^2 is V28() real ext-real Element of REAL
|.p1.| * |.p1.| is V28() real ext-real non negative set
(p1 `1) ^2 is V28() real ext-real Element of REAL
(p1 `1) * (p1 `1) is V28() real ext-real set
(p1 `2) ^2 is V28() real ext-real Element of REAL
(p1 `2) * (p1 `2) is V28() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p1 `2) ^2) is V28() real ext-real Element of REAL
((p1 `2) ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
(|.p1.| ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
((p1 `2) / |.p1.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `2) / |.p1.|) * ((p1 `2) / |.p1.|) is V28() real ext-real set
(1 - cn) " is V28() real ext-real Element of REAL
(((p1 `2) / |.p1.|) - cn) * ((1 - cn) ") is V28() real ext-real Element of REAL
(((p1 `2) / |.p1.|) - cn) * 0 is V28() real ext-real Element of REAL
|.p1.| * (- 1) is V28() real ext-real non positive Element of REAL
|.p1.| * 0 is Function-like functional empty V28() real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() Element of REAL
|[(|.p1.| * (- 1)),(|.p1.| * 0)]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
- |.p1.| is V28() real ext-real non positive Element of REAL
|[(- |.p1.|),0]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((cn) . p1) `1 is V28() real ext-real Element of REAL
((cn) . p1) `2 is V28() real ext-real Element of REAL
(- |.p1.|) ^2 is V28() real ext-real Element of REAL
(- |.p1.|) * (- |.p1.|) is V28() real ext-real non negative set
0 ^2 is V28() real ext-real Element of REAL
0 * 0 is Function-like functional empty V28() real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() set
((- |.p1.|) ^2) + (0 ^2) is V28() real ext-real Element of REAL
sqrt (((- |.p1.|) ^2) + (0 ^2)) is V28() real ext-real Element of REAL
sqrt (|.p1.| ^2) is V28() real ext-real Element of REAL
- (1 - cn) is V28() real ext-real Element of REAL
- (((p1 `2) / |.p1.|) - cn) is V28() real ext-real Element of REAL
(- (1 - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
(- (((p1 `2) / |.p1.|) - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
((- (((p1 `2) / |.p1.|) - cn)) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((p1 `2) / |.p1.|) - cn)) / (1 - cn)) * ((- (((p1 `2) / |.p1.|) - cn)) / (1 - cn)) is V28() real ext-real set
1 ^2 is V28() real ext-real Element of REAL
1 * 1 is V28() real ext-real non negative set
1 - (((- (((p1 `2) / |.p1.|) - cn)) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
- ((((p1 `2) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real Element of COMPLEX
(- ((((p1 `2) / |.p1.|) - cn) / (1 - cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((p1 `2) / |.p1.|) - cn) / (1 - cn))) * (- ((((p1 `2) / |.p1.|) - cn) / (1 - cn))) is V28() real ext-real set
1 - ((- ((((p1 `2) / |.p1.|) - cn) / (1 - cn))) ^2) is V28() real ext-real Element of REAL
(p2 `1) ^2 is V28() real ext-real Element of REAL
(p2 `1) * (p2 `1) is V28() real ext-real set
(sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))) * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real set
(|.p1.| ^2) * ((sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))) ^2) is V28() real ext-real Element of REAL
(|.p1.| ^2) * (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
|.p2.| ^2 is V28() real ext-real Element of REAL
|.p2.| * |.p2.| is V28() real ext-real non negative set
(p2 `2) ^2 is V28() real ext-real Element of REAL
(p2 `2) * (p2 `2) is V28() real ext-real set
((p2 `1) ^2) + ((p2 `2) ^2) is V28() real ext-real Element of REAL
sqrt (|.p2.| ^2) is V28() real ext-real Element of REAL
(p1 `2) / |.q.| is V28() real ext-real Element of COMPLEX
p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 `2 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `1 is V28() real ext-real Element of REAL
|.p1.| ^2 is V28() real ext-real Element of REAL
|.p1.| * |.p1.| is V28() real ext-real non negative set
((p1 `2) / |.p1.|) - cn is V28() real ext-real Element of REAL
(p1 `1) ^2 is V28() real ext-real Element of REAL
(p1 `1) * (p1 `1) is V28() real ext-real set
(p1 `2) ^2 is V28() real ext-real Element of REAL
(p1 `2) * (p1 `2) is V28() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p1 `2) ^2) is V28() real ext-real Element of REAL
((p1 `2) ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
(|.p1.| ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
((p1 `2) / |.p1.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `2) / |.p1.|) * ((p1 `2) / |.p1.|) is V28() real ext-real set
(- 1) - cn is V28() real ext-real Element of REAL
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
1 + cn is V28() real ext-real Element of REAL
(((p1 `2) / |.p1.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p1 `2) / |.p1.|) - cn) / (1 + cn)) * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2)))) is V28() real ext-real Element of REAL
|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `1 is V28() real ext-real Element of REAL
p2 `2 is V28() real ext-real Element of REAL
(1 + cn) " is V28() real ext-real Element of REAL
(((p1 `2) / |.p1.|) - cn) * ((1 + cn) ") is V28() real ext-real Element of REAL
(((p1 `2) / |.p1.|) - cn) * 0 is V28() real ext-real Element of REAL
((cn) . p1) `1 is V28() real ext-real Element of REAL
- |.p1.| is V28() real ext-real non positive Element of REAL
((cn) . p1) `2 is V28() real ext-real Element of REAL
(- |.p1.|) ^2 is V28() real ext-real Element of REAL
(- |.p1.|) * (- |.p1.|) is V28() real ext-real non negative set
0 ^2 is V28() real ext-real Element of REAL
0 * 0 is Function-like functional empty V28() real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() set
((- |.p1.|) ^2) + (0 ^2) is V28() real ext-real Element of REAL
sqrt (((- |.p1.|) ^2) + (0 ^2)) is V28() real ext-real Element of REAL
sqrt (|.p1.| ^2) is V28() real ext-real Element of REAL
- (1 + cn) is V28() real ext-real Element of REAL
(- (1 + cn)) / (1 + cn) is V28() real ext-real Element of COMPLEX
1 ^2 is V28() real ext-real Element of REAL
1 * 1 is V28() real ext-real non negative set
(p2 `1) ^2 is V28() real ext-real Element of REAL
(p2 `1) * (p2 `1) is V28() real ext-real set
(sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))) * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real set
(|.p1.| ^2) * ((sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))) ^2) is V28() real ext-real Element of REAL
(|.p1.| ^2) * (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
|.p2.| ^2 is V28() real ext-real Element of REAL
|.p2.| * |.p2.| is V28() real ext-real non negative set
(p2 `2) ^2 is V28() real ext-real Element of REAL
(p2 `2) * (p2 `2) is V28() real ext-real set
((p2 `1) ^2) + ((p2 `2) ^2) is V28() real ext-real Element of REAL
sqrt (|.p2.| ^2) is V28() real ext-real Element of REAL
(p1 `2) / |.q.| is V28() real ext-real Element of COMPLEX
- (1 + cn) is V28() real ext-real Element of REAL
- 0 is Function-like functional empty V28() real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() Element of REAL
p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 `2 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `1 is V28() real ext-real Element of REAL
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is set
p is set
(cn) . q is Relation-like Function-like set
p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
|.p1.| ^2 is V28() real ext-real Element of REAL
|.p1.| * |.p1.| is V28() real ext-real non negative set
p1 `2 is V28() real ext-real Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((p1 `2) / |.p1.|) - cn is V28() real ext-real Element of REAL
1 + cn is V28() real ext-real Element of REAL
(((p1 `2) / |.p1.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p1 `2) / |.p1.|) - cn) / (1 + cn)) * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2)))) is V28() real ext-real Element of REAL
|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `1 is V28() real ext-real Element of REAL
(p1 `1) ^2 is V28() real ext-real Element of REAL
(p1 `1) * (p1 `1) is V28() real ext-real set
(p1 `2) ^2 is V28() real ext-real Element of REAL
(p1 `2) * (p1 `2) is V28() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p1 `2) ^2) is V28() real ext-real Element of REAL
(|.p1.| ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
((p1 `2) ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
((p1 `2) / |.p1.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `2) / |.p1.|) * ((p1 `2) / |.p1.|) is V28() real ext-real set
(- 1) - cn is V28() real ext-real Element of REAL
(- 1) * (1 + cn) is V28() real ext-real Element of REAL
((- 1) * (1 + cn)) / (1 + cn) is V28() real ext-real Element of COMPLEX
1 ^2 is V28() real ext-real Element of REAL
1 * 1 is V28() real ext-real non negative set
- (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2)))) is V28() real ext-real Element of REAL
p1 `2 is V28() real ext-real Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((p1 `2) / |.p1.|) - cn is V28() real ext-real Element of REAL
1 - cn is V28() real ext-real Element of REAL
(((p1 `2) / |.p1.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p1 `2) / |.p1.|) - cn) / (1 - cn)) * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2)))) is V28() real ext-real Element of REAL
|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `1 is V28() real ext-real Element of REAL
(p1 `1) ^2 is V28() real ext-real Element of REAL
(p1 `1) * (p1 `1) is V28() real ext-real set
(p1 `2) ^2 is V28() real ext-real Element of REAL
(p1 `2) * (p1 `2) is V28() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p1 `2) ^2) is V28() real ext-real Element of REAL
(|.p1.| ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
((p1 `2) ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
((p1 `2) / |.p1.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `2) / |.p1.|) * ((p1 `2) / |.p1.|) is V28() real ext-real set
(1 - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
- 0 is Function-like functional empty V28() real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() Element of REAL
- (1 - cn) is V28() real ext-real Element of REAL
cn - cn is V28() real ext-real Element of REAL
(- 1) * (1 - cn) is V28() real ext-real Element of REAL
((- 1) * (1 - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
1 ^2 is V28() real ext-real Element of REAL
1 * 1 is V28() real ext-real non negative set
- (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2)))) is V28() real ext-real Element of REAL
p1 `2 is V28() real ext-real Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is set
p is set
(cn) . q is Relation-like Function-like set
p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() real ext-real Element of REAL
F₁() is functional non empty Element of K19( the carrier of (TOP-REAL 2))
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( P₁[b₁] & not b₁ = 0. (TOP-REAL 2) ) } is set
(TOP-REAL 2) | F₁() is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | F₁()) is non empty set
cn is set
F₁() ` is functional Element of K19( the carrier of (TOP-REAL 2))
the carrier of (TOP-REAL 2) \ F<sub>1</sub>() is functional Element of K19( the carrier of (TOP-REAL 2))
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[0,1]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[0,1]| `1 is V28() real ext-real Element of REAL
|[0,1]| `2 is V28() real ext-real Element of REAL
p is V28() real ext-real Element of REAL
(p) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p1 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
p1 ` is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | p1 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | p1) is non empty set
K20( the carrier of ((TOP-REAL 2) | p1), the carrier of ((TOP-REAL 2) | p1)) is set
K19(K20( the carrier of ((TOP-REAL 2) | p1), the carrier of ((TOP-REAL 2) | p1))) is set
(p) | p1 is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is functional Element of K19( the carrier of (TOP-REAL 2))
q ` is functional Element of K19( the carrier of (TOP-REAL 2))
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( S<sub>1</sub>[b<sub>1</sub>] & not b<sub>1</sub> = 0. (TOP-REAL 2) ) } is set
K19( the carrier of ((TOP-REAL 2) | p1)) is set
p2 is non empty Element of K19( the carrier of ((TOP-REAL 2) | p1))
((TOP-REAL 2) | p1) | p2 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of (TOP-REAL 2) | p1
the carrier of (((TOP-REAL 2) | p1) | p2) is non empty set
(p) | p2 is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
rng ((p) | p2) is functional Element of K19( the carrier of (TOP-REAL 2))
q3 is set
dom ((p) | p2) is functional Element of K19( the carrier of (TOP-REAL 2))
VV0 is set
((p) | p2) . VV0 is Relation-like Function-like set
dom (p) is functional Element of K19( the carrier of (TOP-REAL 2))
(dom (p)) /\ p2 is Element of K19( the carrier of ((TOP-REAL 2) | p1))
u2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(p) . u2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q3 is set
VV0 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
VV0 `1 is V28() real ext-real Element of REAL
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( S₂[b₁] & not b₁ = 0. (TOP-REAL 2) ) } is set
q3 is non empty Element of K19( the carrier of ((TOP-REAL 2) | p1))
dom ((p) | p2) is functional Element of K19( the carrier of (TOP-REAL 2))
dom (p) is functional Element of K19( the carrier of (TOP-REAL 2))
(dom (p)) /\ p2 is Element of K19( the carrier of ((TOP-REAL 2) | p1))
the carrier of (TOP-REAL 2) /\ p2 is Element of K19( the carrier of ((TOP-REAL 2) | p1))
K20( the carrier of (((TOP-REAL 2) | p1) | p2), the carrier of ((TOP-REAL 2) | p1)) is set
K19(K20( the carrier of (((TOP-REAL 2) | p1) | p2), the carrier of ((TOP-REAL 2) | p1))) is set
((TOP-REAL 2) | p1) | q3 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of (TOP-REAL 2) | p1
the carrier of (((TOP-REAL 2) | p1) | q3) is non empty set
(p) | q3 is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
rng ((p) | q3) is functional Element of K19( the carrier of (TOP-REAL 2))
u2 is set
dom ((p) | q3) is functional Element of K19( the carrier of (TOP-REAL 2))
u3 is set
((p) | q3) . u3 is Relation-like Function-like set
(dom (p)) /\ q3 is Element of K19( the carrier of ((TOP-REAL 2) | p1))
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(p) . y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
u2 is set
u3 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
u3 `1 is V28() real ext-real Element of REAL
dom ((p) | q3) is functional Element of K19( the carrier of (TOP-REAL 2))
(dom (p)) /\ q3 is Element of K19( the carrier of ((TOP-REAL 2) | p1))
the carrier of (TOP-REAL 2) /\ q3 is Element of K19( the carrier of ((TOP-REAL 2) | p1))
K20( the carrier of (((TOP-REAL 2) | p1) | q3), the carrier of ((TOP-REAL 2) | p1)) is set
K19(K20( the carrier of (((TOP-REAL 2) | p1) | q3), the carrier of ((TOP-REAL 2) | p1))) is set
[#] (((TOP-REAL 2) | p1) | q3) is non empty non proper closed Element of K19( the carrier of (((TOP-REAL 2) | p1) | q3))
K19( the carrier of (((TOP-REAL 2) | p1) | q3)) is set
p2 \/ q3 is non empty Element of K19( the carrier of ((TOP-REAL 2) | p1))
u3 is set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `1 is V28() real ext-real Element of REAL
VV0 is Relation-like the carrier of (((TOP-REAL 2) | p1) | p2) -defined the carrier of ((TOP-REAL 2) | p1) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (((TOP-REAL 2) | p1) | p2), the carrier of ((TOP-REAL 2) | p1)))
dom VV0 is Element of K19( the carrier of (((TOP-REAL 2) | p1) | p2))
K19( the carrier of (((TOP-REAL 2) | p1) | p2)) is set
[#] (((TOP-REAL 2) | p1) | p2) is non empty non proper closed Element of K19( the carrier of (((TOP-REAL 2) | p1) | p2))
([#] (((TOP-REAL 2) | p1) | p2)) /\ ([#] (((TOP-REAL 2) | p1) | q3)) is Element of K19( the carrier of (((TOP-REAL 2) | p1) | q3))
u2 is Relation-like the carrier of (((TOP-REAL 2) | p1) | q3) -defined the carrier of ((TOP-REAL 2) | p1) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (((TOP-REAL 2) | p1) | q3), the carrier of ((TOP-REAL 2) | p1)))
u3 is set
VV0 . u3 is set
u2 . u3 is set
(p) . u3 is Relation-like Function-like set
[#] ((TOP-REAL 2) | p1) is non empty non proper closed Element of K19( the carrier of ((TOP-REAL 2) | p1))
([#] (((TOP-REAL 2) | p1) | p2)) \/ ([#] (((TOP-REAL 2) | p1) | q3)) is non empty set
VV0 +* u2 is Relation-like Function-like set
u3 is Relation-like the carrier of ((TOP-REAL 2) | p1) -defined the carrier of ((TOP-REAL 2) | p1) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | p1), the carrier of ((TOP-REAL 2) | p1)))
dom u3 is Element of K19( the carrier of ((TOP-REAL 2) | p1))
dom u2 is Element of K19( the carrier of (((TOP-REAL 2) | p1) | q3))
y is set
u3 . y is set
((p) | p1) . y is Relation-like Function-like set
(p1 `) ` is functional Element of K19( the carrier of (TOP-REAL 2))
q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((p) | p1) . q4 is Relation-like Function-like set
(p) . q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
VV0 . q4 is set
u3 . q4 is set
u2 +* VV0 is Relation-like Function-like set
(u2 +* VV0) . q4 is set
q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q4 `1 is V28() real ext-real Element of REAL
((p) | p1) . q4 is Relation-like Function-like set
(p) . q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
u2 . q4 is set
dom ((p) | p1) is functional Element of K19( the carrier of (TOP-REAL 2))
the carrier of (TOP-REAL 2) /\ p1 is functional Element of K19( the carrier of (TOP-REAL 2))
the topology of (TOP-REAL 2) is non empty open Element of K19(K19( the carrier of (TOP-REAL 2)))
K19(K19( 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
TopSpaceMetr (Euclid 2) is TopStruct
Family_open_set (Euclid 2) is Element of K19(K19( the carrier of (Euclid 2)))
K19( the carrier of (Euclid 2)) is set
K19(K19( the carrier of (Euclid 2))) is set
TopStruct(# the carrier of (Euclid 2),(Family_open_set (Euclid 2)) #) is non empty strict TopStruct
q is V28() real ext-real Element of REAL
(q) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p . (0. (TOP-REAL 2)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | cn is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | cn) is non empty set
p1 is Element of the carrier of ((TOP-REAL 2) | cn)
p . p1 is Relation-like Function-like set
[#] ((TOP-REAL 2) | cn) is non empty non proper closed Element of K19( the carrier of ((TOP-REAL 2) | cn))
K19( the carrier of ((TOP-REAL 2) | cn)) is set
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `2 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `2) / |.p2.| is V28() real ext-real Element of COMPLEX
p2 `1 is V28() real ext-real Element of REAL
((p2 `2) / |.p2.|) - q is V28() real ext-real Element of REAL
1 - q is V28() real ext-real Element of REAL
(((p2 `2) / |.p2.|) - q) / (1 - q) is V28() real ext-real Element of COMPLEX
((((p2 `2) / |.p2.|) - q) / (1 - q)) ^2 is V28() real ext-real Element of COMPLEX
((((p2 `2) / |.p2.|) - q) / (1 - q)) * ((((p2 `2) / |.p2.|) - q) / (1 - q)) is V28() real ext-real set
1 - (((((p2 `2) / |.p2.|) - q) / (1 - q)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p2 `2) / |.p2.|) - q) / (1 - q)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((p2 `2) / |.p2.|) - q) / (1 - q)) ^2))) is V28() real ext-real Element of REAL
|.p2.| * (- (sqrt (1 - (((((p2 `2) / |.p2.|) - q) / (1 - q)) ^2)))) is V28() real ext-real Element of REAL
|.p2.| * ((((p2 `2) / |.p2.|) - q) / (1 - q)) is V28() real ext-real Element of REAL
|[(|.p2.| * (- (sqrt (1 - (((((p2 `2) / |.p2.|) - q) / (1 - q)) ^2))))),(|.p2.| * ((((p2 `2) / |.p2.|) - q) / (1 - q)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p2.| * (- (sqrt (1 - (((((p2 `2) / |.p2.|) - q) / (1 - q)) ^2))))),(|.p2.| * ((((p2 `2) / |.p2.|) - q) / (1 - q)))]| `2 is V28() real ext-real Element of REAL
|[(|.p2.| * (- (sqrt (1 - (((((p2 `2) / |.p2.|) - q) / (1 - q)) ^2))))),(|.p2.| * ((((p2 `2) / |.p2.|) - q) / (1 - q)))]| `1 is V28() real ext-real Element of REAL
0 ^2 is V28() real ext-real Element of REAL
0 * 0 is Function-like functional empty V28() real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() set
1 - 0 is non empty V28() real ext-real positive non negative Element of REAL
sqrt (1 - 0) is V28() real ext-real Element of REAL
- (sqrt (1 - 0)) is V28() real ext-real Element of REAL
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `2 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `2) / |.p2.| is V28() real ext-real Element of COMPLEX
p2 `1 is V28() real ext-real Element of REAL
((p2 `2) / |.p2.|) - q is V28() real ext-real Element of REAL
1 + q is V28() real ext-real Element of REAL
(((p2 `2) / |.p2.|) - q) / (1 + q) is V28() real ext-real Element of COMPLEX
((((p2 `2) / |.p2.|) - q) / (1 + q)) ^2 is V28() real ext-real Element of COMPLEX
((((p2 `2) / |.p2.|) - q) / (1 + q)) * ((((p2 `2) / |.p2.|) - q) / (1 + q)) is V28() real ext-real set
1 - (((((p2 `2) / |.p2.|) - q) / (1 + q)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p2 `2) / |.p2.|) - q) / (1 + q)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((p2 `2) / |.p2.|) - q) / (1 + q)) ^2))) is V28() real ext-real Element of REAL
|.p2.| * (- (sqrt (1 - (((((p2 `2) / |.p2.|) - q) / (1 + q)) ^2)))) is V28() real ext-real Element of REAL
|.p2.| * ((((p2 `2) / |.p2.|) - q) / (1 + q)) is V28() real ext-real Element of REAL
|[(|.p2.| * (- (sqrt (1 - (((((p2 `2) / |.p2.|) - q) / (1 + q)) ^2))))),(|.p2.| * ((((p2 `2) / |.p2.|) - q) / (1 + q)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p2.| * (- (sqrt (1 - (((((p2 `2) / |.p2.|) - q) / (1 + q)) ^2))))),(|.p2.| * ((((p2 `2) / |.p2.|) - q) / (1 + q)))]| `2 is V28() real ext-real Element of REAL
|[(|.p2.| * (- (sqrt (1 - (((((p2 `2) / |.p2.|) - q) / (1 + q)) ^2))))),(|.p2.| * ((((p2 `2) / |.p2.|) - q) / (1 + q)))]| `1 is V28() real ext-real Element of REAL
0 ^2 is V28() real ext-real Element of REAL
0 * 0 is Function-like functional empty V28() real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() set
1 - 0 is non empty V28() real ext-real positive non negative Element of REAL
sqrt (1 - 0) is V28() real ext-real Element of REAL
- (sqrt (1 - 0)) is V28() real ext-real Element of REAL
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `1 is V28() real ext-real Element of REAL
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `2 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `2) / |.p2.| is V28() real ext-real Element of COMPLEX
p2 `1 is V28() real ext-real Element of REAL
p2 is functional Element of K19( the carrier of (TOP-REAL 2))
the carrier of (TopSpaceMetr (Euclid 2)) is set
K19( the carrier of (TopSpaceMetr (Euclid 2))) is set
q3 is Element of K19( the carrier of (TopSpaceMetr (Euclid 2)))
p1 is Element of the carrier of (Euclid 2)
VV0 is V28() real ext-real set
Ball (p1,VV0) is bounded Element of K19( the carrier of (Euclid 2))
u2 is V28() real ext-real Element of REAL
Ball (p1,u2) is bounded Element of K19( the carrier of (Euclid 2))
u3 is functional Element of K19( the carrier of (TOP-REAL 2))
p .: u3 is functional Element of K19( the carrier of (TOP-REAL 2))
y is set
dom p is functional Element of K19( the carrier of (TOP-REAL 2))
q4 is set
p . q4 is Relation-like Function-like set
rng p is functional Element of K19( the carrier of (TOP-REAL 2))
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q is Element of the carrier of (Euclid 2)
dist (p1,q) is V28() real ext-real Element of REAL
(0. (TOP-REAL 2)) - x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
- x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K443((TOP-REAL 2),(0. (TOP-REAL 2)),(- x)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is Relation-like K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)) -defined the carrier of (TOP-REAL 2) -valued Function-like total quasi_total Element of K19(K20(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)))
K20(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) is set
K19(K20(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2))) is set
K230( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),(0. (TOP-REAL 2)),(- x)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.((0. (TOP-REAL 2)) - x).| is V28() real ext-real non negative Element of REAL
x `1 is V28() real ext-real Element of REAL
x `2 is V28() real ext-real Element of REAL
|.x.| is V28() real ext-real non negative Element of REAL
(x `2) / |.x.| is V28() real ext-real Element of COMPLEX
x `1 is V28() real ext-real Element of REAL
((x `2) / |.x.|) - q is V28() real ext-real Element of REAL
(x `1) ^2 is V28() real ext-real Element of REAL
(x `1) * (x `1) is V28() real ext-real set
|.x.| ^2 is V28() real ext-real Element of REAL
|.x.| * |.x.| is V28() real ext-real non negative set
(x `2) ^2 is V28() real ext-real Element of REAL
(x `2) * (x `2) is V28() real ext-real set
((x `1) ^2) + ((x `2) ^2) is V28() real ext-real Element of REAL
0 + ((x `2) ^2) is V28() real ext-real Element of REAL
((x `2) ^2) / (|.x.| ^2) is V28() real ext-real Element of COMPLEX
(|.x.| ^2) / (|.x.| ^2) is V28() real ext-real Element of COMPLEX
1 - q is V28() real ext-real Element of REAL
((x `2) / |.x.|) ^2 is V28() real ext-real Element of COMPLEX
((x `2) / |.x.|) * ((x `2) / |.x.|) is V28() real ext-real set
- (1 - q) is V28() real ext-real Element of REAL
- (((x `2) / |.x.|) - q) is V28() real ext-real Element of REAL
(- (1 - q)) / (1 - q) is V28() real ext-real Element of COMPLEX
(- (((x `2) / |.x.|) - q)) / (1 - q) is V28() real ext-real Element of COMPLEX
((- (((x `2) / |.x.|) - q)) / (1 - q)) ^2 is V28() real ext-real Element of COMPLEX
((- (((x `2) / |.x.|) - q)) / (1 - q)) * ((- (((x `2) / |.x.|) - q)) / (1 - q)) is V28() real ext-real set
1 ^2 is V28() real ext-real Element of REAL
1 * 1 is V28() real ext-real non negative set
1 - (((- (((x `2) / |.x.|) - q)) / (1 - q)) ^2) is V28() real ext-real Element of REAL
(((x `2) / |.x.|) - q) / (1 - q) is V28() real ext-real Element of COMPLEX
- ((((x `2) / |.x.|) - q) / (1 - q)) is V28() real ext-real Element of COMPLEX
(- ((((x `2) / |.x.|) - q) / (1 - q))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((x `2) / |.x.|) - q) / (1 - q))) * (- ((((x `2) / |.x.|) - q) / (1 - q))) is V28() real ext-real set
1 - ((- ((((x `2) / |.x.|) - q) / (1 - q))) ^2) is V28() real ext-real Element of REAL
(q) . x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((((x `2) / |.x.|) - q) / (1 - q)) ^2 is V28() real ext-real Element of COMPLEX
((((x `2) / |.x.|) - q) / (1 - q)) * ((((x `2) / |.x.|) - q) / (1 - q)) is V28() real ext-real set
1 - (((((x `2) / |.x.|) - q) / (1 - q)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((x `2) / |.x.|) - q) / (1 - q)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((x `2) / |.x.|) - q) / (1 - q)) ^2))) is V28() real ext-real Element of REAL
|.x.| * (- (sqrt (1 - (((((x `2) / |.x.|) - q) / (1 - q)) ^2)))) is V28() real ext-real Element of REAL
|.x.| * ((((x `2) / |.x.|) - q) / (1 - q)) is V28() real ext-real Element of REAL
|[(|.x.| * (- (sqrt (1 - (((((x `2) / |.x.|) - q) / (1 - q)) ^2))))),(|.x.| * ((((x `2) / |.x.|) - q) / (1 - q)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `2 is V28() real ext-real Element of REAL
y `1 is V28() real ext-real Element of REAL
(y `1) ^2 is V28() real ext-real Element of REAL
(y `1) * (y `1) is V28() real ext-real set
(sqrt (1 - (((((x `2) / |.x.|) - q) / (1 - q)) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((x `2) / |.x.|) - q) / (1 - q)) ^2))) * (sqrt (1 - (((((x `2) / |.x.|) - q) / (1 - q)) ^2))) is V28() real ext-real set
(|.x.| ^2) * ((sqrt (1 - (((((x `2) / |.x.|) - q) / (1 - q)) ^2))) ^2) is V28() real ext-real Element of REAL
(|.x.| ^2) * (1 - (((((x `2) / |.x.|) - q) / (1 - q)) ^2)) is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
|.y.| ^2 is V28() real ext-real Element of REAL
|.y.| * |.y.| is V28() real ext-real non negative set
(y `2) ^2 is V28() real ext-real Element of REAL
(y `2) * (y `2) is V28() real ext-real set
((y `1) ^2) + ((y `2) ^2) is V28() real ext-real Element of REAL
sqrt (|.y.| ^2) is V28() real ext-real Element of REAL
|.(- x).| is V28() real ext-real non negative Element of REAL
- y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.(- y).| is V28() real ext-real non negative Element of REAL
(0. (TOP-REAL 2)) - y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K443((TOP-REAL 2),(0. (TOP-REAL 2)),(- y)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K230( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),(0. (TOP-REAL 2)),(- y)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.((0. (TOP-REAL 2)) - y).| is V28() real ext-real non negative Element of REAL
x is Element of the carrier of (Euclid 2)
dist (p1,x) is V28() real ext-real Element of REAL
x `2 is V28() real ext-real Element of REAL
|.x.| is V28() real ext-real non negative Element of REAL
(x `2) / |.x.| is V28() real ext-real Element of COMPLEX
x `1 is V28() real ext-real Element of REAL
(x `1) ^2 is V28() real ext-real Element of REAL
(x `1) * (x `1) is V28() real ext-real set
|.x.| ^2 is V28() real ext-real Element of REAL
|.x.| * |.x.| is V28() real ext-real non negative set
(x `2) ^2 is V28() real ext-real Element of REAL
(x `2) * (x `2) is V28() real ext-real set
((x `1) ^2) + ((x `2) ^2) is V28() real ext-real Element of REAL
0 + ((x `2) ^2) is V28() real ext-real Element of REAL
((x `2) ^2) / (|.x.| ^2) is V28() real ext-real Element of COMPLEX
(|.x.| ^2) / (|.x.| ^2) is V28() real ext-real Element of COMPLEX
1 + q is V28() real ext-real Element of REAL
((x `2) / |.x.|) ^2 is V28() real ext-real Element of COMPLEX
((x `2) / |.x.|) * ((x `2) / |.x.|) is V28() real ext-real set
- ((x `2) / |.x.|) is V28() real ext-real Element of COMPLEX
- (- 1) is V28() real ext-real non negative Element of REAL
(- ((x `2) / |.x.|)) + q is V28() real ext-real Element of REAL
((x `2) / |.x.|) - q is V28() real ext-real Element of REAL
- (((x `2) / |.x.|) - q) is V28() real ext-real Element of REAL
(- (((x `2) / |.x.|) - q)) / (1 + q) is V28() real ext-real Element of COMPLEX
q - ((x `2) / |.x.|) is V28() real ext-real Element of REAL
((- (((x `2) / |.x.|) - q)) / (1 + q)) ^2 is V28() real ext-real Element of COMPLEX
((- (((x `2) / |.x.|) - q)) / (1 + q)) * ((- (((x `2) / |.x.|) - q)) / (1 + q)) is V28() real ext-real set
1 ^2 is V28() real ext-real Element of REAL
1 * 1 is V28() real ext-real non negative set
1 - (((- (((x `2) / |.x.|) - q)) / (1 + q)) ^2) is V28() real ext-real Element of REAL
(((x `2) / |.x.|) - q) / (1 + q) is V28() real ext-real Element of COMPLEX
- ((((x `2) / |.x.|) - q) / (1 + q)) is V28() real ext-real Element of COMPLEX
(- ((((x `2) / |.x.|) - q) / (1 + q))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((x `2) / |.x.|) - q) / (1 + q))) * (- ((((x `2) / |.x.|) - q) / (1 + q))) is V28() real ext-real set
1 - ((- ((((x `2) / |.x.|) - q) / (1 + q))) ^2) is V28() real ext-real Element of REAL
(q) . x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((((x `2) / |.x.|) - q) / (1 + q)) ^2 is V28() real ext-real Element of COMPLEX
((((x `2) / |.x.|) - q) / (1 + q)) * ((((x `2) / |.x.|) - q) / (1 + q)) is V28() real ext-real set
1 - (((((x `2) / |.x.|) - q) / (1 + q)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((x `2) / |.x.|) - q) / (1 + q)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((x `2) / |.x.|) - q) / (1 + q)) ^2))) is V28() real ext-real Element of REAL
|.x.| * (- (sqrt (1 - (((((x `2) / |.x.|) - q) / (1 + q)) ^2)))) is V28() real ext-real Element of REAL
|.x.| * ((((x `2) / |.x.|) - q) / (1 + q)) is V28() real ext-real Element of REAL
|[(|.x.| * (- (sqrt (1 - (((((x `2) / |.x.|) - q) / (1 + q)) ^2))))),(|.x.| * ((((x `2) / |.x.|) - q) / (1 + q)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `2 is V28() real ext-real Element of REAL
y `1 is V28() real ext-real Element of REAL
(y `1) ^2 is V28() real ext-real Element of REAL
(y `1) * (y `1) is V28() real ext-real set
(sqrt (1 - (((((x `2) / |.x.|) - q) / (1 + q)) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((x `2) / |.x.|) - q) / (1 + q)) ^2))) * (sqrt (1 - (((((x `2) / |.x.|) - q) / (1 + q)) ^2))) is V28() real ext-real set
(|.x.| ^2) * ((sqrt (1 - (((((x `2) / |.x.|) - q) / (1 + q)) ^2))) ^2) is V28() real ext-real Element of REAL
(|.x.| ^2) * (1 - (((((x `2) / |.x.|) - q) / (1 + q)) ^2)) is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
|.y.| ^2 is V28() real ext-real Element of REAL
|.y.| * |.y.| is V28() real ext-real non negative set
(y `2) ^2 is V28() real ext-real Element of REAL
(y `2) * (y `2) is V28() real ext-real set
((y `1) ^2) + ((y `2) ^2) is V28() real ext-real Element of REAL
sqrt (|.y.| ^2) is V28() real ext-real Element of REAL
|.(- x).| is V28() real ext-real non negative Element of REAL
- y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.(- y).| is V28() real ext-real non negative Element of REAL
(0. (TOP-REAL 2)) - y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K443((TOP-REAL 2),(0. (TOP-REAL 2)),(- y)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K230( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),(0. (TOP-REAL 2)),(- y)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.((0. (TOP-REAL 2)) - y).| is V28() real ext-real non negative Element of REAL
x is Element of the carrier of (Euclid 2)
dist (p1,x) is V28() real ext-real Element of REAL
x `1 is V28() real ext-real Element of REAL
x `2 is V28() real ext-real Element of REAL
|.x.| is V28() real ext-real non negative Element of REAL
(x `2) / |.x.| is V28() real ext-real Element of COMPLEX
cn ` is functional Element of K19( the carrier of (TOP-REAL 2))
K20( the carrier of ((TOP-REAL 2) | cn), the carrier of ((TOP-REAL 2) | cn)) is set
K19(K20( the carrier of ((TOP-REAL 2) | cn), the carrier of ((TOP-REAL 2) | cn))) is set
(q) | cn is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p1 is Relation-like the carrier of ((TOP-REAL 2) | cn) -defined the carrier of ((TOP-REAL 2) | cn) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | cn), the carrier of ((TOP-REAL 2) | cn)))
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
q is set
p is set
(cn) . q is Relation-like Function-like set
(cn) . p is Relation-like Function-like set
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
1 - cn is V28() real ext-real Element of REAL
p2 `1 is V28() real ext-real Element of REAL
(cn) . p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() real ext-real Element of REAL
p1 `2 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `1 is V28() real ext-real Element of REAL
((p1 `2) / |.p1.|) - cn is V28() real ext-real Element of REAL
(((p1 `2) / |.p1.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p1 `2) / |.p1.|) - cn) / (1 - cn)) * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2)))) is V28() real ext-real Element of REAL
|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.p1.| ^2 is V28() real ext-real Element of REAL
|.p1.| * |.p1.| is V28() real ext-real non negative set
(p1 `1) ^2 is V28() real ext-real Element of REAL
(p1 `1) * (p1 `1) is V28() real ext-real set
(p1 `2) ^2 is V28() real ext-real Element of REAL
(p1 `2) * (p1 `2) is V28() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p1 `2) ^2) is V28() real ext-real Element of REAL
((p1 `2) ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
(|.p1.| ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
((p1 `2) / |.p1.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `2) / |.p1.|) * ((p1 `2) / |.p1.|) is V28() real ext-real set
- (1 - cn) is V28() real ext-real Element of REAL
- (((p1 `2) / |.p1.|) - cn) is V28() real ext-real Element of REAL
(- (1 - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
(- (((p1 `2) / |.p1.|) - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((- (((p1 `2) / |.p1.|) - cn)) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((p1 `2) / |.p1.|) - cn)) / (1 - cn)) * ((- (((p1 `2) / |.p1.|) - cn)) / (1 - cn)) is V28() real ext-real set
1 ^2 is V28() real ext-real Element of REAL
1 * 1 is V28() real ext-real non negative set
1 - (((- (((p1 `2) / |.p1.|) - cn)) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((p1 `2) / |.p1.|) - cn)) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
(- (((p1 `2) / |.p1.|) - cn)) ^2 is V28() real ext-real Element of REAL
(- (((p1 `2) / |.p1.|) - cn)) * (- (((p1 `2) / |.p1.|) - cn)) is V28() real ext-real set
(1 - cn) ^2 is V28() real ext-real Element of REAL
(1 - cn) * (1 - cn) is V28() real ext-real set
((- (((p1 `2) / |.p1.|) - cn)) ^2) / ((1 - cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((- (((p1 `2) / |.p1.|) - cn)) ^2) / ((1 - cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((p1 `2) / |.p1.|) - cn)) ^2) / ((1 - cn) ^2))) is V28() real ext-real Element of REAL
(((p1 `2) / |.p1.|) - cn) ^2 is V28() real ext-real Element of REAL
(((p1 `2) / |.p1.|) - cn) * (((p1 `2) / |.p1.|) - cn) is V28() real ext-real set
((((p1 `2) / |.p1.|) - cn) ^2) / ((1 - cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((((p1 `2) / |.p1.|) - cn) ^2) / ((1 - cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `2) / |.p1.|) - cn) ^2) / ((1 - cn) ^2))) is V28() real ext-real Element of REAL
|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]| `1 is V28() real ext-real Element of REAL
- ((((p1 `2) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real Element of COMPLEX
(- ((((p1 `2) / |.p1.|) - cn) / (1 - cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((p1 `2) / |.p1.|) - cn) / (1 - cn))) * (- ((((p1 `2) / |.p1.|) - cn) / (1 - cn))) is V28() real ext-real set
1 - ((- ((((p1 `2) / |.p1.|) - cn) / (1 - cn))) ^2) is V28() real ext-real Element of REAL
1 * (1 - cn) is V28() real ext-real Element of REAL
1 * |.p1.| is V28() real ext-real non negative Element of REAL
p1 `2 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `1 is V28() real ext-real Element of REAL
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((p1 `2) / |.p1.|) - cn is V28() real ext-real Element of REAL
1 + cn is V28() real ext-real Element of REAL
(((p1 `2) / |.p1.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p1 `2) / |.p1.|) - cn) / (1 + cn)) * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2)))) is V28() real ext-real Element of REAL
|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.p1.| ^2 is V28() real ext-real Element of REAL
|.p1.| * |.p1.| is V28() real ext-real non negative set
(p1 `1) ^2 is V28() real ext-real Element of REAL
(p1 `1) * (p1 `1) is V28() real ext-real set
(p1 `2) ^2 is V28() real ext-real Element of REAL
(p1 `2) * (p1 `2) is V28() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p1 `2) ^2) is V28() real ext-real Element of REAL
((p1 `2) ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
(|.p1.| ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
- (((p1 `2) / |.p1.|) - cn) is V28() real ext-real Element of REAL
(- (((p1 `2) / |.p1.|) - cn)) / (1 + cn) is V28() real ext-real Element of COMPLEX
((p1 `2) / |.p1.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `2) / |.p1.|) * ((p1 `2) / |.p1.|) is V28() real ext-real set
- ((p1 `2) / |.p1.|) is V28() real ext-real Element of COMPLEX
(- ((p1 `2) / |.p1.|)) ^2 is V28() real ext-real Element of COMPLEX
(- ((p1 `2) / |.p1.|)) * (- ((p1 `2) / |.p1.|)) is V28() real ext-real set
(- ((p1 `2) / |.p1.|)) + cn is V28() real ext-real Element of REAL
((- (((p1 `2) / |.p1.|) - cn)) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((p1 `2) / |.p1.|) - cn)) / (1 + cn)) * ((- (((p1 `2) / |.p1.|) - cn)) / (1 + cn)) is V28() real ext-real set
1 ^2 is V28() real ext-real Element of REAL
1 * 1 is V28() real ext-real non negative set
1 - (((- (((p1 `2) / |.p1.|) - cn)) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((p1 `2) / |.p1.|) - cn)) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
(- (((p1 `2) / |.p1.|) - cn)) ^2 is V28() real ext-real Element of REAL
(- (((p1 `2) / |.p1.|) - cn)) * (- (((p1 `2) / |.p1.|) - cn)) is V28() real ext-real set
(1 + cn) ^2 is V28() real ext-real Element of REAL
(1 + cn) * (1 + cn) is V28() real ext-real set
((- (((p1 `2) / |.p1.|) - cn)) ^2) / ((1 + cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((- (((p1 `2) / |.p1.|) - cn)) ^2) / ((1 + cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((p1 `2) / |.p1.|) - cn)) ^2) / ((1 + cn) ^2))) is V28() real ext-real Element of REAL
(((p1 `2) / |.p1.|) - cn) ^2 is V28() real ext-real Element of REAL
(((p1 `2) / |.p1.|) - cn) * (((p1 `2) / |.p1.|) - cn) is V28() real ext-real set
((((p1 `2) / |.p1.|) - cn) ^2) / ((1 + cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((((p1 `2) / |.p1.|) - cn) ^2) / ((1 + cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `2) / |.p1.|) - cn) ^2) / ((1 + cn) ^2))) is V28() real ext-real Element of REAL
|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]| `1 is V28() real ext-real Element of REAL
- ((((p1 `2) / |.p1.|) - cn) / (1 + cn)) is V28() real ext-real Element of COMPLEX
(- ((((p1 `2) / |.p1.|) - cn) / (1 + cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((p1 `2) / |.p1.|) - cn) / (1 + cn))) * (- ((((p1 `2) / |.p1.|) - cn) / (1 + cn))) is V28() real ext-real set
1 - ((- ((((p1 `2) / |.p1.|) - cn) / (1 + cn))) ^2) is V28() real ext-real Element of REAL
sqrt ((- ((((p1 `2) / |.p1.|) - cn) / (1 + cn))) ^2) is V28() real ext-real set
1 * (1 + cn) is V28() real ext-real Element of REAL
(1 + cn) - cn is V28() real ext-real Element of REAL
- (p1 `2) is V28() real ext-real Element of REAL
(- (p1 `2)) / |.p1.| is V28() real ext-real Element of COMPLEX
1 * |.p1.| is V28() real ext-real non negative Element of REAL
((p1 `2) ^2) - ((p1 `2) ^2) is V28() real ext-real Element of REAL
p1 `1 is V28() real ext-real Element of REAL
p1 `2 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `1 is V28() real ext-real Element of REAL
p1 `2 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
p2 `2 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `2) / |.p2.| is V28() real ext-real Element of COMPLEX
p2 `1 is V28() real ext-real Element of REAL
|.p2.| ^2 is V28() real ext-real Element of REAL
|.p2.| * |.p2.| is V28() real ext-real non negative set
((p2 `2) / |.p2.|) - cn is V28() real ext-real Element of REAL
(((p2 `2) / |.p2.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p2 `2) / |.p2.|) - cn) / (1 - cn)) * ((((p2 `2) / |.p2.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.p2.| * (- (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2)))) is V28() real ext-real Element of REAL
|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
|[(|.p2.| * (- (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2))))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 - cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p2.| * (- (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2))))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 - cn)))]| `2 is V28() real ext-real Element of REAL
(cn) . p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p2.| * (- (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2))))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 - cn)))]| `1 is V28() real ext-real Element of REAL
p1 `1 is V28() real ext-real Element of REAL
(p2 `1) ^2 is V28() real ext-real Element of REAL
(p2 `1) * (p2 `1) is V28() real ext-real set
(p2 `2) ^2 is V28() real ext-real Element of REAL
(p2 `2) * (p2 `2) is V28() real ext-real set
((p2 `1) ^2) + ((p2 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p2 `2) ^2) is V28() real ext-real Element of REAL
((p2 `2) ^2) / (|.p2.| ^2) is V28() real ext-real Element of COMPLEX
(|.p2.| ^2) / (|.p2.| ^2) is V28() real ext-real Element of COMPLEX
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((p2 `2) / |.p2.|) ^2 is V28() real ext-real Element of COMPLEX
((p2 `2) / |.p2.|) * ((p2 `2) / |.p2.|) is V28() real ext-real set
- (1 - cn) is V28() real ext-real Element of REAL
- (((p2 `2) / |.p2.|) - cn) is V28() real ext-real Element of REAL
(- (1 - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
(- (((p2 `2) / |.p2.|) - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
((- (((p2 `2) / |.p2.|) - cn)) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((p2 `2) / |.p2.|) - cn)) / (1 - cn)) * ((- (((p2 `2) / |.p2.|) - cn)) / (1 - cn)) is V28() real ext-real set
1 ^2 is V28() real ext-real Element of REAL
1 * 1 is V28() real ext-real non negative set
1 - (((- (((p2 `2) / |.p2.|) - cn)) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((p2 `2) / |.p2.|) - cn)) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
(- (((p2 `2) / |.p2.|) - cn)) ^2 is V28() real ext-real Element of REAL
(- (((p2 `2) / |.p2.|) - cn)) * (- (((p2 `2) / |.p2.|) - cn)) is V28() real ext-real set
(1 - cn) ^2 is V28() real ext-real Element of REAL
(1 - cn) * (1 - cn) is V28() real ext-real set
((- (((p2 `2) / |.p2.|) - cn)) ^2) / ((1 - cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((- (((p2 `2) / |.p2.|) - cn)) ^2) / ((1 - cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((p2 `2) / |.p2.|) - cn)) ^2) / ((1 - cn) ^2))) is V28() real ext-real Element of REAL
(((p2 `2) / |.p2.|) - cn) ^2 is V28() real ext-real Element of REAL
(((p2 `2) / |.p2.|) - cn) * (((p2 `2) / |.p2.|) - cn) is V28() real ext-real set
((((p2 `2) / |.p2.|) - cn) ^2) / ((1 - cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((((p2 `2) / |.p2.|) - cn) ^2) / ((1 - cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((((p2 `2) / |.p2.|) - cn) ^2) / ((1 - cn) ^2))) is V28() real ext-real Element of REAL
- ((((p2 `2) / |.p2.|) - cn) / (1 - cn)) is V28() real ext-real Element of COMPLEX
(- ((((p2 `2) / |.p2.|) - cn) / (1 - cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((p2 `2) / |.p2.|) - cn) / (1 - cn))) * (- ((((p2 `2) / |.p2.|) - cn) / (1 - cn))) is V28() real ext-real set
1 - ((- ((((p2 `2) / |.p2.|) - cn) / (1 - cn))) ^2) is V28() real ext-real Element of REAL
1 * (1 - cn) is V28() real ext-real Element of REAL
1 * |.p2.| is V28() real ext-real non negative Element of REAL
p1 `2 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `1 is V28() real ext-real Element of REAL
(p2 `1) ^2 is V28() real ext-real Element of REAL
(p2 `1) * (p2 `1) is V28() real ext-real set
(p2 `2) ^2 is V28() real ext-real Element of REAL
(p2 `2) * (p2 `2) is V28() real ext-real set
((p2 `1) ^2) + ((p2 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p2 `2) ^2) is V28() real ext-real Element of REAL
((p2 `2) ^2) / (|.p2.| ^2) is V28() real ext-real Element of COMPLEX
(|.p2.| ^2) / (|.p2.| ^2) is V28() real ext-real Element of COMPLEX
((p2 `2) / |.p2.|) ^2 is V28() real ext-real Element of COMPLEX
((p2 `2) / |.p2.|) * ((p2 `2) / |.p2.|) is V28() real ext-real set
- (1 - cn) is V28() real ext-real Element of REAL
- (((p2 `2) / |.p2.|) - cn) is V28() real ext-real Element of REAL
(- (1 - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
(- (((p2 `2) / |.p2.|) - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
((- (((p2 `2) / |.p2.|) - cn)) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((p2 `2) / |.p2.|) - cn)) / (1 - cn)) * ((- (((p2 `2) / |.p2.|) - cn)) / (1 - cn)) is V28() real ext-real set
1 ^2 is V28() real ext-real Element of REAL
1 * 1 is V28() real ext-real non negative set
1 - (((- (((p2 `2) / |.p2.|) - cn)) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
- ((((p2 `2) / |.p2.|) - cn) / (1 - cn)) is V28() real ext-real Element of COMPLEX
(- ((((p2 `2) / |.p2.|) - cn) / (1 - cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((p2 `2) / |.p2.|) - cn) / (1 - cn))) * (- ((((p2 `2) / |.p2.|) - cn) / (1 - cn))) is V28() real ext-real set
1 - ((- ((((p2 `2) / |.p2.|) - cn) / (1 - cn))) ^2) is V28() real ext-real Element of REAL
(|[(|.p2.| * (- (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2))))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 - cn)))]| `1) ^2 is V28() real ext-real Element of REAL
(|[(|.p2.| * (- (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2))))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 - cn)))]| `1) * (|[(|.p2.| * (- (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2))))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 - cn)))]| `1) is V28() real ext-real set
(sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2))) * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real set
(|.p2.| ^2) * ((sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2))) ^2) is V28() real ext-real Element of REAL
(|.p2.| ^2) * (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.|[(|.p2.| * (- (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2))))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 - cn)))]|.| is V28() real ext-real non negative Element of REAL
|.|[(|.p2.| * (- (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2))))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 - cn)))]|.| ^2 is V28() real ext-real Element of REAL
|.|[(|.p2.| * (- (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2))))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 - cn)))]|.| * |.|[(|.p2.| * (- (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2))))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 - cn)))]|.| is V28() real ext-real non negative set
(|[(|.p2.| * (- (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2))))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 - cn)))]| `2) ^2 is V28() real ext-real Element of REAL
(|[(|.p2.| * (- (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2))))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 - cn)))]| `2) * (|[(|.p2.| * (- (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2))))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 - cn)))]| `2) is V28() real ext-real set
((|[(|.p2.| * (- (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2))))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 - cn)))]| `1) ^2) + ((|[(|.p2.| * (- (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2))))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 - cn)))]| `2) ^2) is V28() real ext-real Element of REAL
sqrt (|.|[(|.p2.| * (- (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2))))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 - cn)))]|.| ^2) is V28() real ext-real Element of REAL
(p1 `1) ^2 is V28() real ext-real Element of REAL
(p1 `1) * (p1 `1) is V28() real ext-real set
|.p1.| ^2 is V28() real ext-real Element of REAL
|.p1.| * |.p1.| is V28() real ext-real non negative set
(p1 `2) ^2 is V28() real ext-real Element of REAL
(p1 `2) * (p1 `2) is V28() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p1 `2) ^2) is V28() real ext-real Element of REAL
((p1 `2) ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
(|.p1.| ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
((p1 `2) / |.p1.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `2) / |.p1.|) * ((p1 `2) / |.p1.|) is V28() real ext-real set
((p1 `2) / |.p1.|) - cn is V28() real ext-real Element of REAL
- (((p1 `2) / |.p1.|) - cn) is V28() real ext-real Element of REAL
(- (((p1 `2) / |.p1.|) - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
(((p1 `2) / |.p1.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p1 `2) / |.p1.|) - cn) / (1 - cn)) * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2)))) is V28() real ext-real Element of REAL
|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]| `2 is V28() real ext-real Element of REAL
((- (((p1 `2) / |.p1.|) - cn)) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((p1 `2) / |.p1.|) - cn)) / (1 - cn)) * ((- (((p1 `2) / |.p1.|) - cn)) / (1 - cn)) is V28() real ext-real set
1 - (((- (((p1 `2) / |.p1.|) - cn)) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
- ((((p1 `2) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real Element of COMPLEX
(- ((((p1 `2) / |.p1.|) - cn) / (1 - cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((p1 `2) / |.p1.|) - cn) / (1 - cn))) * (- ((((p1 `2) / |.p1.|) - cn) / (1 - cn))) is V28() real ext-real set
1 - ((- ((((p1 `2) / |.p1.|) - cn) / (1 - cn))) ^2) is V28() real ext-real Element of REAL
|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]| `1 is V28() real ext-real Element of REAL
(|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]| `1) ^2 is V28() real ext-real Element of REAL
(|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]| `1) * (|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]| `1) is V28() real ext-real set
(sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))) * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real set
(|.p1.| ^2) * ((sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))) ^2) is V28() real ext-real Element of REAL
(|.p1.| ^2) * (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]|.| is V28() real ext-real non negative Element of REAL
|.|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]|.| ^2 is V28() real ext-real Element of REAL
|.|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]|.| * |.|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]|.| is V28() real ext-real non negative set
(|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]| `2) ^2 is V28() real ext-real Element of REAL
(|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]| `2) * (|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]| `2) is V28() real ext-real set
((|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]| `1) ^2) + ((|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]| `2) ^2) is V28() real ext-real Element of REAL
sqrt (|.|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]|.| ^2) is V28() real ext-real Element of REAL
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 - cn))) / |.p1.| is V28() real ext-real Element of COMPLEX
((((p1 `2) / |.p1.|) - cn) / (1 - cn)) * (1 - cn) is V28() real ext-real Element of REAL
((p1 `2) / |.p1.|) * |.p1.| is V28() real ext-real Element of REAL
- (p1 `1) is V28() real ext-real Element of REAL
(- (p1 `1)) ^2 is V28() real ext-real Element of REAL
(- (p1 `1)) * (- (p1 `1)) is V28() real ext-real set
- (p2 `1) is V28() real ext-real Element of REAL
(- (p2 `1)) ^2 is V28() real ext-real Element of REAL
(- (p2 `1)) * (- (p2 `1)) is V28() real ext-real set
sqrt ((- (p2 `1)) ^2) is V28() real ext-real Element of REAL
- (- (p1 `1)) is V28() real ext-real Element of REAL
- (- (p2 `1)) is V28() real ext-real Element of REAL
|[(p1 `1),(p1 `2)]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 `2 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `1 is V28() real ext-real Element of REAL
((p1 `2) / |.p1.|) - cn is V28() real ext-real Element of REAL
1 + cn is V28() real ext-real Element of REAL
(((p1 `2) / |.p1.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p1 `2) / |.p1.|) - cn) / (1 + cn)) * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2)))) is V28() real ext-real Element of REAL
|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]| `2 is V28() real ext-real Element of REAL
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() real ext-real Element of REAL
p1 `2 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `1 is V28() real ext-real Element of REAL
p1 `2 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
p2 `2 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `2) / |.p2.| is V28() real ext-real Element of COMPLEX
p2 `1 is V28() real ext-real Element of REAL
|.p2.| ^2 is V28() real ext-real Element of REAL
|.p2.| * |.p2.| is V28() real ext-real non negative set
((p2 `2) / |.p2.|) - cn is V28() real ext-real Element of REAL
1 + cn is V28() real ext-real Element of REAL
(((p2 `2) / |.p2.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p2 `2) / |.p2.|) - cn) / (1 + cn)) * ((((p2 `2) / |.p2.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|.p2.| * (- (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2)))) is V28() real ext-real Element of REAL
|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
|[(|.p2.| * (- (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2))))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 + cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p2.| * (- (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2))))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 + cn)))]| `1 is V28() real ext-real Element of REAL
|[(|.p2.| * (- (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2))))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 + cn)))]| `2 is V28() real ext-real Element of REAL
(cn) . p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() real ext-real Element of REAL
(p2 `1) ^2 is V28() real ext-real Element of REAL
(p2 `1) * (p2 `1) is V28() real ext-real set
(p2 `2) ^2 is V28() real ext-real Element of REAL
(p2 `2) * (p2 `2) is V28() real ext-real set
((p2 `1) ^2) + ((p2 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p2 `2) ^2) is V28() real ext-real Element of REAL
((p2 `2) ^2) / (|.p2.| ^2) is V28() real ext-real Element of COMPLEX
(|.p2.| ^2) / (|.p2.| ^2) is V28() real ext-real Element of COMPLEX
((p2 `2) / |.p2.|) ^2 is V28() real ext-real Element of COMPLEX
((p2 `2) / |.p2.|) * ((p2 `2) / |.p2.|) is V28() real ext-real set
- ((p2 `2) / |.p2.|) is V28() real ext-real Element of COMPLEX
(- ((p2 `2) / |.p2.|)) ^2 is V28() real ext-real Element of COMPLEX
(- ((p2 `2) / |.p2.|)) * (- ((p2 `2) / |.p2.|)) is V28() real ext-real set
(- ((p2 `2) / |.p2.|)) + cn is V28() real ext-real Element of REAL
- (((p2 `2) / |.p2.|) - cn) is V28() real ext-real Element of REAL
(- (((p2 `2) / |.p2.|) - cn)) / (1 + cn) is V28() real ext-real Element of COMPLEX
((- (((p2 `2) / |.p2.|) - cn)) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((p2 `2) / |.p2.|) - cn)) / (1 + cn)) * ((- (((p2 `2) / |.p2.|) - cn)) / (1 + cn)) is V28() real ext-real set
1 ^2 is V28() real ext-real Element of REAL
1 * 1 is V28() real ext-real non negative set
1 - (((- (((p2 `2) / |.p2.|) - cn)) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
- ((((p2 `2) / |.p2.|) - cn) / (1 + cn)) is V28() real ext-real Element of COMPLEX
(- ((((p2 `2) / |.p2.|) - cn) / (1 + cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((p2 `2) / |.p2.|) - cn) / (1 + cn))) * (- ((((p2 `2) / |.p2.|) - cn) / (1 + cn))) is V28() real ext-real set
1 - ((- ((((p2 `2) / |.p2.|) - cn) / (1 + cn))) ^2) is V28() real ext-real Element of REAL
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
sqrt (1 - (((- (((p2 `2) / |.p2.|) - cn)) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
(- (((p2 `2) / |.p2.|) - cn)) ^2 is V28() real ext-real Element of REAL
(- (((p2 `2) / |.p2.|) - cn)) * (- (((p2 `2) / |.p2.|) - cn)) is V28() real ext-real set
(1 + cn) ^2 is V28() real ext-real Element of REAL
(1 + cn) * (1 + cn) is V28() real ext-real set
((- (((p2 `2) / |.p2.|) - cn)) ^2) / ((1 + cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((- (((p2 `2) / |.p2.|) - cn)) ^2) / ((1 + cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((p2 `2) / |.p2.|) - cn)) ^2) / ((1 + cn) ^2))) is V28() real ext-real Element of REAL
(((p2 `2) / |.p2.|) - cn) ^2 is V28() real ext-real Element of REAL
(((p2 `2) / |.p2.|) - cn) * (((p2 `2) / |.p2.|) - cn) is V28() real ext-real set
((((p2 `2) / |.p2.|) - cn) ^2) / ((1 + cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((((p2 `2) / |.p2.|) - cn) ^2) / ((1 + cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((((p2 `2) / |.p2.|) - cn) ^2) / ((1 + cn) ^2))) is V28() real ext-real Element of REAL
sqrt ((- ((((p2 `2) / |.p2.|) - cn) / (1 + cn))) ^2) is V28() real ext-real set
1 * (1 + cn) is V28() real ext-real Element of REAL
(1 + cn) - cn is V28() real ext-real Element of REAL
- (p2 `2) is V28() real ext-real Element of REAL
(- (p2 `2)) / |.p2.| is V28() real ext-real Element of COMPLEX
1 * |.p2.| is V28() real ext-real non negative Element of REAL
((p2 `2) ^2) - ((p2 `2) ^2) is V28() real ext-real Element of REAL
p1 `2 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `1 is V28() real ext-real Element of REAL
((p1 `2) / |.p1.|) - cn is V28() real ext-real Element of REAL
(((p1 `2) / |.p1.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p1 `2) / |.p1.|) - cn) / (1 - cn)) * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2)))) is V28() real ext-real Element of REAL
|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]| `2 is V28() real ext-real Element of REAL
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 `2 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `1 is V28() real ext-real Element of REAL
(p1 `1) ^2 is V28() real ext-real Element of REAL
(p1 `1) * (p1 `1) is V28() real ext-real set
|.p1.| ^2 is V28() real ext-real Element of REAL
|.p1.| * |.p1.| is V28() real ext-real non negative set
(p1 `2) ^2 is V28() real ext-real Element of REAL
(p1 `2) * (p1 `2) is V28() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p1 `2) ^2) is V28() real ext-real Element of REAL
((p1 `2) ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
(|.p1.| ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
(p2 `1) ^2 is V28() real ext-real Element of REAL
(p2 `1) * (p2 `1) is V28() real ext-real set
(p2 `2) ^2 is V28() real ext-real Element of REAL
(p2 `2) * (p2 `2) is V28() real ext-real set
((p2 `1) ^2) + ((p2 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p2 `2) ^2) is V28() real ext-real Element of REAL
((p2 `2) ^2) / (|.p2.| ^2) is V28() real ext-real Element of COMPLEX
(|.p2.| ^2) / (|.p2.| ^2) is V28() real ext-real Element of COMPLEX
((p2 `2) / |.p2.|) ^2 is V28() real ext-real Element of COMPLEX
((p2 `2) / |.p2.|) * ((p2 `2) / |.p2.|) is V28() real ext-real set
(- 1) - cn is V28() real ext-real Element of REAL
- (((p2 `2) / |.p2.|) - cn) is V28() real ext-real Element of REAL
- ((- 1) - cn) is V28() real ext-real Element of REAL
(- (((p2 `2) / |.p2.|) - cn)) / (1 + cn) is V28() real ext-real Element of COMPLEX
((- (((p2 `2) / |.p2.|) - cn)) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((p2 `2) / |.p2.|) - cn)) / (1 + cn)) * ((- (((p2 `2) / |.p2.|) - cn)) / (1 + cn)) is V28() real ext-real set
1 ^2 is V28() real ext-real Element of REAL
1 * 1 is V28() real ext-real non negative set
1 - (((- (((p2 `2) / |.p2.|) - cn)) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
- ((((p2 `2) / |.p2.|) - cn) / (1 + cn)) is V28() real ext-real Element of COMPLEX
(- ((((p2 `2) / |.p2.|) - cn) / (1 + cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((p2 `2) / |.p2.|) - cn) / (1 + cn))) * (- ((((p2 `2) / |.p2.|) - cn) / (1 + cn))) is V28() real ext-real set
1 - ((- ((((p2 `2) / |.p2.|) - cn) / (1 + cn))) ^2) is V28() real ext-real Element of REAL
(|[(|.p2.| * (- (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2))))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 + cn)))]| `1) ^2 is V28() real ext-real Element of REAL
(|[(|.p2.| * (- (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2))))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 + cn)))]| `1) * (|[(|.p2.| * (- (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2))))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 + cn)))]| `1) is V28() real ext-real set
(sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2))) * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real set
(|.p2.| ^2) * ((sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2))) ^2) is V28() real ext-real Element of REAL
(|.p2.| ^2) * (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
((p1 `2) / |.p1.|) - cn is V28() real ext-real Element of REAL
(((p1 `2) / |.p1.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p1 `2) / |.p1.|) - cn) / (1 + cn)) * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2)))) is V28() real ext-real Element of REAL
|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]| `2 is V28() real ext-real Element of REAL
|.|[(|.p2.| * (- (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2))))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 + cn)))]|.| is V28() real ext-real non negative Element of REAL
|.|[(|.p2.| * (- (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2))))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 + cn)))]|.| ^2 is V28() real ext-real Element of REAL
|.|[(|.p2.| * (- (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2))))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 + cn)))]|.| * |.|[(|.p2.| * (- (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2))))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 + cn)))]|.| is V28() real ext-real non negative set
(|[(|.p2.| * (- (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2))))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 + cn)))]| `2) ^2 is V28() real ext-real Element of REAL
(|[(|.p2.| * (- (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2))))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 + cn)))]| `2) * (|[(|.p2.| * (- (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2))))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 + cn)))]| `2) is V28() real ext-real set
((|[(|.p2.| * (- (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2))))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 + cn)))]| `1) ^2) + ((|[(|.p2.| * (- (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2))))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 + cn)))]| `2) ^2) is V28() real ext-real Element of REAL
sqrt (|.|[(|.p2.| * (- (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2))))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 + cn)))]|.| ^2) is V28() real ext-real Element of REAL
- (((p1 `2) / |.p1.|) - cn) is V28() real ext-real Element of REAL
(- (((p1 `2) / |.p1.|) - cn)) / (1 + cn) is V28() real ext-real Element of COMPLEX
((p1 `2) / |.p1.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `2) / |.p1.|) * ((p1 `2) / |.p1.|) is V28() real ext-real set
((- (((p1 `2) / |.p1.|) - cn)) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((p1 `2) / |.p1.|) - cn)) / (1 + cn)) * ((- (((p1 `2) / |.p1.|) - cn)) / (1 + cn)) is V28() real ext-real set
1 - (((- (((p1 `2) / |.p1.|) - cn)) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
- ((((p1 `2) / |.p1.|) - cn) / (1 + cn)) is V28() real ext-real Element of COMPLEX
(- ((((p1 `2) / |.p1.|) - cn) / (1 + cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((p1 `2) / |.p1.|) - cn) / (1 + cn))) * (- ((((p1 `2) / |.p1.|) - cn) / (1 + cn))) is V28() real ext-real set
1 - ((- ((((p1 `2) / |.p1.|) - cn) / (1 + cn))) ^2) is V28() real ext-real Element of REAL
|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]| `1 is V28() real ext-real Element of REAL
(|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]| `1) ^2 is V28() real ext-real Element of REAL
(|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]| `1) * (|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]| `1) is V28() real ext-real set
(sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))) * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real set
(|.p1.| ^2) * ((sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))) ^2) is V28() real ext-real Element of REAL
(|.p1.| ^2) * (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
|.|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]|.| is V28() real ext-real non negative Element of REAL
|.|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]|.| ^2 is V28() real ext-real Element of REAL
|.|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]|.| * |.|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]|.| is V28() real ext-real non negative set
(|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]| `2) ^2 is V28() real ext-real Element of REAL
(|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]| `2) * (|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]| `2) is V28() real ext-real set
((|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]| `1) ^2) + ((|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]| `2) ^2) is V28() real ext-real Element of REAL
sqrt (|.|[(|.p1.| * (- (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]|.| ^2) is V28() real ext-real Element of REAL
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 + cn))) / |.p1.| is V28() real ext-real Element of COMPLEX
((((p1 `2) / |.p1.|) - cn) / (1 + cn)) * (1 + cn) is V28() real ext-real Element of REAL
((p1 `2) / |.p1.|) * |.p1.| is V28() real ext-real Element of REAL
- (p1 `1) is V28() real ext-real Element of REAL
(- (p1 `1)) ^2 is V28() real ext-real Element of REAL
(- (p1 `1)) * (- (p1 `1)) is V28() real ext-real set
- (p2 `1) is V28() real ext-real Element of REAL
(- (p2 `1)) ^2 is V28() real ext-real Element of REAL
(- (p2 `1)) * (- (p2 `1)) is V28() real ext-real set
sqrt ((- (p2 `1)) ^2) is V28() real ext-real Element of REAL
- (- (p1 `1)) is V28() real ext-real Element of REAL
- (- (p2 `1)) is V28() real ext-real Element of REAL
|[(p1 `1),(p1 `2)]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() real ext-real Element of REAL
p1 `2 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
p2 `1 is V28() real ext-real Element of REAL
p2 `2 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `2) / |.p2.| is V28() real ext-real Element of COMPLEX
p2 `1 is V28() real ext-real Element of REAL
p2 `2 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `2) / |.p2.| is V28() real ext-real Element of COMPLEX
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
rng (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
q is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
dom q is functional Element of K19( the carrier of (TOP-REAL 2))
rng q is functional Element of K19( the carrier of (TOP-REAL 2))
p is set
p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() real ext-real Element of REAL
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
p1 `2 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `1 is V28() real ext-real Element of REAL
1 + cn is V28() real ext-real Element of REAL
- (1 + cn) is V28() real ext-real Element of REAL
- (- (1 + cn)) is V28() real ext-real Element of REAL
1 - cn is V28() real ext-real Element of REAL
((p1 `2) / |.p1.|) * (1 - cn) is V28() real ext-real Element of REAL
(- 1) - cn is V28() real ext-real Element of REAL
((- 1) - cn) + cn is V28() real ext-real Element of REAL
(((p1 `2) / |.p1.|) * (1 - cn)) + cn is V28() real ext-real Element of REAL
((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2 is V28() real ext-real Element of REAL
((((p1 `2) / |.p1.|) * (1 - cn)) + cn) * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn) is V28() real ext-real set
1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)) is V28() real ext-real Element of REAL
|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))) is V28() real ext-real Element of REAL
- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))) is V28() real ext-real Element of REAL
|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn) is V28() real ext-real Element of REAL
|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]| `2 is V28() real ext-real Element of REAL
|.p1.| ^2 is V28() real ext-real Element of REAL
|.p1.| * |.p1.| is V28() real ext-real non negative set
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
(p1 `1) ^2 is V28() real ext-real Element of REAL
(p1 `1) * (p1 `1) is V28() real ext-real set
(p1 `2) ^2 is V28() real ext-real Element of REAL
(p1 `2) * (p1 `2) is V28() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p1 `2) ^2) is V28() real ext-real Element of REAL
((p1 `2) ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
(|.p1.| ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
((p1 `2) / |.p1.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `2) / |.p1.|) * ((p1 `2) / |.p1.|) is V28() real ext-real set
1 * (1 - cn) is V28() real ext-real Element of REAL
((((p1 `2) / |.p1.|) * (1 - cn)) + cn) - cn is V28() real ext-real Element of REAL
1 ^2 is V28() real ext-real Element of REAL
1 * 1 is V28() real ext-real non negative set
|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]| `1 is V28() real ext-real Element of REAL
|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| is V28() real ext-real non negative Element of REAL
|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2 is V28() real ext-real Element of REAL
|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| * |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| is V28() real ext-real non negative set
(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))) ^2 is V28() real ext-real Element of REAL
(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))) * (- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))) is V28() real ext-real set
(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn)) ^2 is V28() real ext-real Element of REAL
(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn)) * (|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn)) is V28() real ext-real set
((- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))) ^2) + ((|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn)) ^2) is V28() real ext-real Element of REAL
(sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))) * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))) is V28() real ext-real set
(|.p1.| ^2) * ((sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))) ^2) is V28() real ext-real Element of REAL
(|.p1.| ^2) * (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2) is V28() real ext-real Element of REAL
((|.p1.| ^2) * ((sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))) ^2)) + ((|.p1.| ^2) * (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)) is V28() real ext-real Element of REAL
(|.p1.| ^2) * (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)) is V28() real ext-real Element of REAL
((|.p1.| ^2) * (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))) + ((|.p1.| ^2) * (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)) is V28() real ext-real Element of REAL
sqrt (|.p1.| ^2) is V28() real ext-real Element of REAL
0 + cn is V28() real ext-real Element of REAL
(|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]| `2) / |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| is V28() real ext-real Element of COMPLEX
(cn) . |[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]| `2) / |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.|) - cn is V28() real ext-real Element of REAL
(((|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]| `2) / |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
((((|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]| `2) / |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]| `2) / |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.|) - cn) / (1 - cn)) * ((((|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]| `2) / |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]| `2) / |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]| `2) / |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]| `2) / |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| * (- (sqrt (1 - (((((|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]| `2) / |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.|) - cn) / (1 - cn)) ^2)))) is V28() real ext-real Element of REAL
|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| * ((((|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]| `2) / |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
|[(|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| * (- (sqrt (1 - (((((|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]| `2) / |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.|) - cn) / (1 - cn)) ^2))))),(|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| * ((((|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]| `2) / |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.|) - cn) / (1 - cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
((p1 `1) / |.p1.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `1) / |.p1.|) * ((p1 `1) / |.p1.|) is V28() real ext-real set
sqrt (((p1 `1) / |.p1.|) ^2) is V28() real ext-real set
- (sqrt (((p1 `1) / |.p1.|) ^2)) is V28() real ext-real set
|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| * (- (sqrt (((p1 `1) / |.p1.|) ^2))) is V28() real ext-real Element of REAL
- ((p1 `1) / |.p1.|) is V28() real ext-real Element of COMPLEX
- (- ((p1 `1) / |.p1.|)) is V28() real ext-real Element of COMPLEX
|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| * (- (- ((p1 `1) / |.p1.|))) is V28() real ext-real Element of REAL
(((((p1 `2) / |.p1.|) * (1 - cn)) + cn) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
|.p1.| * ((((((p1 `2) / |.p1.|) * (1 - cn)) + cn) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
|.p1.| * ((p1 `2) / |.p1.|) is V28() real ext-real Element of REAL
(p1 `2) / |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| is V28() real ext-real Element of COMPLEX
((p1 `2) / |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `2) / |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.|) * ((p1 `2) / |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.|) is V28() real ext-real set
1 - (((p1 `2) / |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.|) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((p1 `2) / |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.|) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((p1 `2) / |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.|) ^2))) is V28() real ext-real Element of REAL
|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| * (- (sqrt (1 - (((p1 `2) / |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.|) ^2)))) is V28() real ext-real Element of REAL
((p1 `2) ^2) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2) is V28() real ext-real Element of COMPLEX
1 - (((p1 `2) ^2) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((p1 `2) ^2) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2))) is V28() real ext-real Element of REAL
- (sqrt (1 - (((p1 `2) ^2) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2)))) is V28() real ext-real Element of REAL
|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| * (- (sqrt (1 - (((p1 `2) ^2) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2))))) is V28() real ext-real Element of REAL
(|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2) is V28() real ext-real Element of COMPLEX
((|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2)) - (((p1 `2) ^2) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2)) is V28() real ext-real Element of COMPLEX
sqrt (((|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2)) - (((p1 `2) ^2) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2))) is V28() real ext-real set
- (sqrt (((|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2)) - (((p1 `2) ^2) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2)))) is V28() real ext-real set
|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| * (- (sqrt (((|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2)) - (((p1 `2) ^2) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2))))) is V28() real ext-real Element of REAL
(|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2) - ((p1 `2) ^2) is V28() real ext-real Element of REAL
((|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2) - ((p1 `2) ^2)) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2) is V28() real ext-real Element of COMPLEX
sqrt (((|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2) - ((p1 `2) ^2)) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2)) is V28() real ext-real set
- (sqrt (((|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2) - ((p1 `2) ^2)) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2))) is V28() real ext-real set
|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| * (- (sqrt (((|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2) - ((p1 `2) ^2)) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2)))) is V28() real ext-real Element of REAL
(((p1 `1) ^2) + ((p1 `2) ^2)) - ((p1 `2) ^2) is V28() real ext-real Element of REAL
((((p1 `1) ^2) + ((p1 `2) ^2)) - ((p1 `2) ^2)) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2) is V28() real ext-real Element of COMPLEX
sqrt (((((p1 `1) ^2) + ((p1 `2) ^2)) - ((p1 `2) ^2)) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2)) is V28() real ext-real set
- (sqrt (((((p1 `1) ^2) + ((p1 `2) ^2)) - ((p1 `2) ^2)) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2))) is V28() real ext-real set
|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| * (- (sqrt (((((p1 `1) ^2) + ((p1 `2) ^2)) - ((p1 `2) ^2)) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2)))) is V28() real ext-real Element of REAL
p1 `2 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `1 is V28() real ext-real Element of REAL
1 + cn is V28() real ext-real Element of REAL
((p1 `2) / |.p1.|) * (1 + cn) is V28() real ext-real Element of REAL
1 - cn is V28() real ext-real Element of REAL
(((p1 `2) / |.p1.|) * (1 + cn)) + cn is V28() real ext-real Element of REAL
(1 - cn) + cn is V28() real ext-real Element of REAL
((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2 is V28() real ext-real Element of REAL
((((p1 `2) / |.p1.|) * (1 + cn)) + cn) * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn) is V28() real ext-real set
1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)) is V28() real ext-real Element of REAL
|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))) is V28() real ext-real Element of REAL
- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))) is V28() real ext-real Element of REAL
|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn) is V28() real ext-real Element of REAL
|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]| `2 is V28() real ext-real Element of REAL
|.p1.| ^2 is V28() real ext-real Element of REAL
|.p1.| * |.p1.| is V28() real ext-real non negative set
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
(p1 `1) ^2 is V28() real ext-real Element of REAL
(p1 `1) * (p1 `1) is V28() real ext-real set
(p1 `2) ^2 is V28() real ext-real Element of REAL
(p1 `2) * (p1 `2) is V28() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p1 `2) ^2) is V28() real ext-real Element of REAL
((p1 `2) ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
(|.p1.| ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
((p1 `2) / |.p1.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `2) / |.p1.|) * ((p1 `2) / |.p1.|) is V28() real ext-real set
(- 1) * (1 + cn) is V28() real ext-real Element of REAL
(- 1) - cn is V28() real ext-real Element of REAL
((((p1 `2) / |.p1.|) * (1 + cn)) + cn) - cn is V28() real ext-real Element of REAL
1 ^2 is V28() real ext-real Element of REAL
1 * 1 is V28() real ext-real non negative set
|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]| `1 is V28() real ext-real Element of REAL
|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| is V28() real ext-real non negative Element of REAL
|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2 is V28() real ext-real Element of REAL
|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| * |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| is V28() real ext-real non negative set
(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))) ^2 is V28() real ext-real Element of REAL
(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))) * (- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))) is V28() real ext-real set
(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn)) ^2 is V28() real ext-real Element of REAL
(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn)) * (|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn)) is V28() real ext-real set
((- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))) ^2) + ((|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn)) ^2) is V28() real ext-real Element of REAL
(sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))) * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))) is V28() real ext-real set
(|.p1.| ^2) * ((sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))) ^2) is V28() real ext-real Element of REAL
(|.p1.| ^2) * (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2) is V28() real ext-real Element of REAL
((|.p1.| ^2) * ((sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))) ^2)) + ((|.p1.| ^2) * (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)) is V28() real ext-real Element of REAL
(|.p1.| ^2) * (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)) is V28() real ext-real Element of REAL
((|.p1.| ^2) * (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))) + ((|.p1.| ^2) * (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)) is V28() real ext-real Element of REAL
sqrt (|.p1.| ^2) is V28() real ext-real Element of REAL
0 + cn is V28() real ext-real Element of REAL
(|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]| `2) / |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| is V28() real ext-real Element of COMPLEX
(cn) . |[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]| `2) / |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.|) - cn is V28() real ext-real Element of REAL
(((|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]| `2) / |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
((((|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]| `2) / |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]| `2) / |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.|) - cn) / (1 + cn)) * ((((|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]| `2) / |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]| `2) / |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]| `2) / |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]| `2) / |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| * (- (sqrt (1 - (((((|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]| `2) / |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.|) - cn) / (1 + cn)) ^2)))) is V28() real ext-real Element of REAL
|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| * ((((|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]| `2) / |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
|[(|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| * (- (sqrt (1 - (((((|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]| `2) / |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.|) - cn) / (1 + cn)) ^2))))),(|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| * ((((|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]| `2) / |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.|) - cn) / (1 + cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
((p1 `1) / |.p1.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `1) / |.p1.|) * ((p1 `1) / |.p1.|) is V28() real ext-real set
sqrt (((p1 `1) / |.p1.|) ^2) is V28() real ext-real set
- (sqrt (((p1 `1) / |.p1.|) ^2)) is V28() real ext-real set
|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| * (- (sqrt (((p1 `1) / |.p1.|) ^2))) is V28() real ext-real Element of REAL
- ((p1 `1) / |.p1.|) is V28() real ext-real Element of COMPLEX
- (- ((p1 `1) / |.p1.|)) is V28() real ext-real Element of COMPLEX
|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| * (- (- ((p1 `1) / |.p1.|))) is V28() real ext-real Element of REAL
(((((p1 `2) / |.p1.|) * (1 + cn)) + cn) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
|.p1.| * ((((((p1 `2) / |.p1.|) * (1 + cn)) + cn) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
|.p1.| * ((p1 `2) / |.p1.|) is V28() real ext-real Element of REAL
(p1 `2) / |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| is V28() real ext-real Element of COMPLEX
((p1 `2) / |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `2) / |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.|) * ((p1 `2) / |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.|) is V28() real ext-real set
1 - (((p1 `2) / |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.|) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((p1 `2) / |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.|) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((p1 `2) / |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.|) ^2))) is V28() real ext-real Element of REAL
|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| * (- (sqrt (1 - (((p1 `2) / |.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.|) ^2)))) is V28() real ext-real Element of REAL
((p1 `2) ^2) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2) is V28() real ext-real Element of COMPLEX
1 - (((p1 `2) ^2) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((p1 `2) ^2) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2))) is V28() real ext-real Element of REAL
- (sqrt (1 - (((p1 `2) ^2) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2)))) is V28() real ext-real Element of REAL
|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| * (- (sqrt (1 - (((p1 `2) ^2) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2))))) is V28() real ext-real Element of REAL
(|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2) is V28() real ext-real Element of COMPLEX
((|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2)) - (((p1 `2) ^2) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2)) is V28() real ext-real Element of COMPLEX
sqrt (((|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2)) - (((p1 `2) ^2) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2))) is V28() real ext-real set
- (sqrt (((|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2)) - (((p1 `2) ^2) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2)))) is V28() real ext-real set
|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| * (- (sqrt (((|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2)) - (((p1 `2) ^2) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2))))) is V28() real ext-real Element of REAL
(|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2) - ((p1 `2) ^2) is V28() real ext-real Element of REAL
((|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2) - ((p1 `2) ^2)) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2) is V28() real ext-real Element of COMPLEX
sqrt (((|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2) - ((p1 `2) ^2)) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2)) is V28() real ext-real set
- (sqrt (((|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2) - ((p1 `2) ^2)) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2))) is V28() real ext-real set
|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| * (- (sqrt (((|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2) - ((p1 `2) ^2)) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2)))) is V28() real ext-real Element of REAL
(((p1 `1) ^2) + ((p1 `2) ^2)) - ((p1 `2) ^2) is V28() real ext-real Element of REAL
((((p1 `1) ^2) + ((p1 `2) ^2)) - ((p1 `2) ^2)) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2) is V28() real ext-real Element of COMPLEX
sqrt (((((p1 `1) ^2) + ((p1 `2) ^2)) - ((p1 `2) ^2)) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2)) is V28() real ext-real set
- (sqrt (((((p1 `1) ^2) + ((p1 `2) ^2)) - ((p1 `2) ^2)) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2))) is V28() real ext-real set
|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| * (- (sqrt (((((p1 `1) ^2) + ((p1 `2) ^2)) - ((p1 `2) ^2)) / (|.|[(- (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2)))) is V28() real ext-real Element of REAL
p1 `1 is V28() real ext-real Element of REAL
p1 `2 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
p1 `1 is V28() real ext-real Element of REAL
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
p1 `2 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
q3 is set
(cn) . q3 is Relation-like Function-like set
VV0 is set
(cn) . VV0 is Relation-like Function-like set
u2 is set
(cn) . u2 is Relation-like Function-like set
p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.p.| is V28() real ext-real non negative Element of REAL
|.p.| + 1 is non empty V28() real ext-real positive non negative Element of REAL
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.cn.| is V28() real ext-real non negative Element of REAL
|.q.| is V28() real ext-real non negative Element of REAL
p2 is Element of the carrier of (Euclid 2)
p1 is Element of the carrier of (Euclid 2)
cl_Ball (p1,(|.p.| + 1)) is Element of K19( the carrier of (Euclid 2))
q3 is Element of the carrier of (Euclid 2)
dist (p1,q3) is V28() real ext-real Element of REAL
(0. (TOP-REAL 2)) - q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
- q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K443((TOP-REAL 2),(0. (TOP-REAL 2)),(- q)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is Relation-like K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)) -defined the carrier of (TOP-REAL 2) -valued Function-like total quasi_total Element of K19(K20(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)))
K20(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) is set
K19(K20(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2))) is set
K230( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),(0. (TOP-REAL 2)),(- q)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.((0. (TOP-REAL 2)) - q).| is V28() real ext-real non negative Element of REAL
|.(- q).| is V28() real ext-real non negative Element of REAL
- cn is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.(- cn).| is V28() real ext-real non negative Element of REAL
(0. (TOP-REAL 2)) - cn is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K443((TOP-REAL 2),(0. (TOP-REAL 2)),(- cn)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K230( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),(0. (TOP-REAL 2)),(- cn)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.((0. (TOP-REAL 2)) - cn).| is V28() real ext-real non negative Element of REAL
dist (p1,p2) is V28() real ext-real Element of REAL
q is V28() real ext-real Element of REAL
(q) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(q) . p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn is Element of the carrier of (Euclid 2)
|.p.| is V28() real ext-real non negative Element of REAL
|.p.| + 1 is non empty V28() real ext-real positive non negative Element of REAL
Ball (cn,(|.p.| + 1)) is bounded Element of K19( the carrier of (Euclid 2))
p1 is functional Element of K19( the carrier of (TOP-REAL 2))
cl_Ball (cn,(|.p.| + 1)) is Element of K19( the carrier of (Euclid 2))
the carrier of (TopSpaceMetr (Euclid 2)) is set
K19( the carrier of (TopSpaceMetr (Euclid 2))) is set
p2 is functional non empty closed compact bounded Element of K19( the carrier of (TOP-REAL 2))
(q) .: p2 is functional Element of K19( the carrier of (TOP-REAL 2))
y is set
dom (q) is functional Element of K19( the carrier of (TOP-REAL 2))
q4 is set
(q) . q4 is Relation-like Function-like set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x is Element of the carrier of (Euclid 2)
dist (cn,x) is V28() real ext-real Element of REAL
(0. (TOP-REAL 2)) - y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
- y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K443((TOP-REAL 2),(0. (TOP-REAL 2)),(- y)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is Relation-like K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)) -defined the carrier of (TOP-REAL 2) -valued Function-like total quasi_total Element of K19(K20(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)))
K20(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) is set
K19(K20(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2))) is set
K230( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),(0. (TOP-REAL 2)),(- y)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.((0. (TOP-REAL 2)) - y).| is V28() real ext-real non negative Element of REAL
|.(- y).| is V28() real ext-real non negative Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
rng (q) is functional Element of K19( the carrier of (TOP-REAL 2))
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.q.| is V28() real ext-real non negative Element of REAL
- q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.(- q).| is V28() real ext-real non negative Element of REAL
(0. (TOP-REAL 2)) - q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K443((TOP-REAL 2),(0. (TOP-REAL 2)),(- q)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K230( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),(0. (TOP-REAL 2)),(- q)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.((0. (TOP-REAL 2)) - q).| is V28() real ext-real non negative Element of REAL
x is Element of the carrier of (Euclid 2)
dist (cn,x) is V28() real ext-real Element of REAL
VV0 is Element of K19( the carrier of (TopSpaceMetr (Euclid 2)))
- p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.(- p).| is V28() real ext-real non negative Element of REAL
(0. (TOP-REAL 2)) - p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K443((TOP-REAL 2),(0. (TOP-REAL 2)),(- p)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is Relation-like K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)) -defined the carrier of (TOP-REAL 2) -valued Function-like total quasi_total Element of K19(K20(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)))
K20(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) is set
K19(K20(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2))) is set
K230( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),(0. (TOP-REAL 2)),(- p)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.((0. (TOP-REAL 2)) - p).| is V28() real ext-real non negative Element of REAL
u2 is Element of the carrier of (Euclid 2)
dist (cn,u2) is V28() real ext-real Element of REAL
|.((q) . p).| is V28() real ext-real non negative Element of REAL
- ((q) . p) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.(- ((q) . p)).| is V28() real ext-real non negative Element of REAL
(0. (TOP-REAL 2)) - ((q) . p) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K443((TOP-REAL 2),(0. (TOP-REAL 2)),(- ((q) . p))) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K230( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),(0. (TOP-REAL 2)),(- ((q) . p))) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.((0. (TOP-REAL 2)) - ((q) . p)).| is V28() real ext-real non negative Element of REAL
u3 is Element of the carrier of (Euclid 2)
dist (cn,u3) is V28() real ext-real Element of REAL
y is set
q4 is Element of the carrier of (Euclid 2)
rng (q) is functional Element of K19( the carrier of (TOP-REAL 2))
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
dom (q) is functional Element of K19( the carrier of (TOP-REAL 2))
x is set
(q) . x is Relation-like Function-like set
x is Element of the carrier of (Euclid 2)
|.y.| is V28() real ext-real non negative Element of REAL
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.q.| is V28() real ext-real non negative Element of REAL
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q . p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
rng (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
p is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
1 ^2 is V28() real ext-real Element of REAL
1 * 1 is V28() real ext-real non negative set
p is V28() real ext-real Element of REAL
cn is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.cn.| is V28() real ext-real non negative Element of REAL
p / |.cn.| is V28() real ext-real Element of COMPLEX
q is V28() real ext-real Element of REAL
(p / |.cn.|) - q is V28() real ext-real Element of REAL
- ((p / |.cn.|) - q) is V28() real ext-real Element of REAL
1 - q is V28() real ext-real Element of REAL
(- ((p / |.cn.|) - q)) / (1 - q) is V28() real ext-real Element of COMPLEX
((- ((p / |.cn.|) - q)) / (1 - q)) ^2 is V28() real ext-real Element of COMPLEX
((- ((p / |.cn.|) - q)) / (1 - q)) * ((- ((p / |.cn.|) - q)) / (1 - q)) is V28() real ext-real set
1 - (((- ((p / |.cn.|) - q)) / (1 - q)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((- ((p / |.cn.|) - q)) / (1 - q)) ^2)) is V28() real ext-real Element of REAL
(- ((p / |.cn.|) - q)) ^2 is V28() real ext-real Element of REAL
(- ((p / |.cn.|) - q)) * (- ((p / |.cn.|) - q)) is V28() real ext-real set
(1 - q) ^2 is V28() real ext-real Element of REAL
(1 - q) * (1 - q) is V28() real ext-real set
((- ((p / |.cn.|) - q)) ^2) / ((1 - q) ^2) is V28() real ext-real Element of COMPLEX
1 - (((- ((p / |.cn.|) - q)) ^2) / ((1 - q) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((- ((p / |.cn.|) - q)) ^2) / ((1 - q) ^2))) is V28() real ext-real Element of REAL
((p / |.cn.|) - q) ^2 is V28() real ext-real Element of REAL
((p / |.cn.|) - q) * ((p / |.cn.|) - q) is V28() real ext-real set
(((p / |.cn.|) - q) ^2) / ((1 - q) ^2) is V28() real ext-real Element of COMPLEX
1 - ((((p / |.cn.|) - q) ^2) / ((1 - q) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - ((((p / |.cn.|) - q) ^2) / ((1 - q) ^2))) is V28() real ext-real Element of REAL
((p / |.cn.|) - q) / (1 - q) is V28() real ext-real Element of COMPLEX
(((p / |.cn.|) - q) / (1 - q)) ^2 is V28() real ext-real Element of COMPLEX
(((p / |.cn.|) - q) / (1 - q)) * (((p / |.cn.|) - q) / (1 - q)) is V28() real ext-real set
1 - ((((p / |.cn.|) - q) / (1 - q)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - ((((p / |.cn.|) - q) / (1 - q)) ^2)) is V28() real ext-real Element of REAL
- 0 is Function-like functional empty V28() real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() Element of REAL
- (sqrt (1 - ((((p / |.cn.|) - q) / (1 - q)) ^2))) is V28() real ext-real Element of REAL
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q `1 is V28() real ext-real Element of REAL
q `2 is V28() real ext-real Element of REAL
|.q.| is V28() real ext-real non negative Element of REAL
(q `2) / |.q.| is V28() real ext-real Element of COMPLEX
(cn) . q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
1 - cn is V28() real ext-real Element of REAL
p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p `1 is V28() real ext-real Element of REAL
p `2 is V28() real ext-real Element of REAL
((q `2) / |.q.|) - cn is V28() real ext-real Element of REAL
(((q `2) / |.q.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
((((q `2) / |.q.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((q `2) / |.q.|) - cn) / (1 - cn)) * ((((q `2) / |.q.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((q `2) / |.q.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.q.| * (- (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 - cn)) ^2)))) is V28() real ext-real Element of REAL
|.q.| * ((((q `2) / |.q.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
|[(|.q.| * (- (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 - cn)) ^2))))),(|.q.| * ((((q `2) / |.q.|) - cn) / (1 - cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.q.| ^2 is V28() real ext-real Element of REAL
|.q.| * |.q.| is V28() real ext-real non negative set
(q `1) ^2 is V28() real ext-real Element of REAL
(q `1) * (q `1) is V28() real ext-real set
(q `2) ^2 is V28() real ext-real Element of REAL
(q `2) * (q `2) is V28() real ext-real set
((q `1) ^2) + ((q `2) ^2) is V28() real ext-real Element of REAL
0 + ((q `2) ^2) is V28() real ext-real Element of REAL
(|.q.| ^2) / (|.q.| ^2) is V28() real ext-real Element of COMPLEX
((q `2) ^2) / (|.q.| ^2) is V28() real ext-real Element of COMPLEX
((q `2) / |.q.|) ^2 is V28() real ext-real Element of COMPLEX
((q `2) / |.q.|) * ((q `2) / |.q.|) is V28() real ext-real set
- (((q `2) / |.q.|) - cn) is V28() real ext-real Element of REAL
- (1 - cn) is V28() real ext-real Element of REAL
(- (((q `2) / |.q.|) - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
(- (1 - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
((- (((q `2) / |.q.|) - cn)) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((q `2) / |.q.|) - cn)) / (1 - cn)) * ((- (((q `2) / |.q.|) - cn)) / (1 - cn)) is V28() real ext-real set
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q `1 is V28() real ext-real Element of REAL
q `2 is V28() real ext-real Element of REAL
|.q.| is V28() real ext-real non negative Element of REAL
(q `2) / |.q.| is V28() real ext-real Element of COMPLEX
(cn) . q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
1 + cn is V28() real ext-real Element of REAL
((q `2) / |.q.|) - cn is V28() real ext-real Element of REAL
- (((q `2) / |.q.|) - cn) is V28() real ext-real Element of REAL
(- (((q `2) / |.q.|) - cn)) / (1 + cn) is V28() real ext-real Element of COMPLEX
- (1 + cn) is V28() real ext-real Element of REAL
(- (1 + cn)) / (1 + cn) is V28() real ext-real Element of COMPLEX
|.q.| ^2 is V28() real ext-real Element of REAL
|.q.| * |.q.| is V28() real ext-real non negative set
(q `1) ^2 is V28() real ext-real Element of REAL
(q `1) * (q `1) is V28() real ext-real set
(q `2) ^2 is V28() real ext-real Element of REAL
(q `2) * (q `2) is V28() real ext-real set
((q `1) ^2) + ((q `2) ^2) is V28() real ext-real Element of REAL
0 + ((q `2) ^2) is V28() real ext-real Element of REAL
(|.q.| ^2) / (|.q.| ^2) is V28() real ext-real Element of COMPLEX
((q `2) ^2) / (|.q.| ^2) is V28() real ext-real Element of COMPLEX
((q `2) / |.q.|) ^2 is V28() real ext-real Element of COMPLEX
((q `2) / |.q.|) * ((q `2) / |.q.|) is V28() real ext-real set
(- 1) - cn is V28() real ext-real Element of REAL
- (- (1 + cn)) is V28() real ext-real Element of REAL
((- (((q `2) / |.q.|) - cn)) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((q `2) / |.q.|) - cn)) / (1 + cn)) * ((- (((q `2) / |.q.|) - cn)) / (1 + cn)) is V28() real ext-real set
1 - (((- (((q `2) / |.q.|) - cn)) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((q `2) / |.q.|) - cn)) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
(- (((q `2) / |.q.|) - cn)) ^2 is V28() real ext-real Element of REAL
(- (((q `2) / |.q.|) - cn)) * (- (((q `2) / |.q.|) - cn)) is V28() real ext-real set
(1 + cn) ^2 is V28() real ext-real Element of REAL
(1 + cn) * (1 + cn) is V28() real ext-real set
((- (((q `2) / |.q.|) - cn)) ^2) / ((1 + cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((- (((q `2) / |.q.|) - cn)) ^2) / ((1 + cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((q `2) / |.q.|) - cn)) ^2) / ((1 + cn) ^2))) is V28() real ext-real Element of REAL
(((q `2) / |.q.|) - cn) ^2 is V28() real ext-real Element of REAL
(((q `2) / |.q.|) - cn) * (((q `2) / |.q.|) - cn) is V28() real ext-real set
((((q `2) / |.q.|) - cn) ^2) / ((1 + cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((((q `2) / |.q.|) - cn) ^2) / ((1 + cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((((q `2) / |.q.|) - cn) ^2) / ((1 + cn) ^2))) is V28() real ext-real Element of REAL
(((q `2) / |.q.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
((((q `2) / |.q.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((q `2) / |.q.|) - cn) / (1 + cn)) * ((((q `2) / |.q.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p `1 is V28() real ext-real Element of REAL
p `2 is V28() real ext-real Element of REAL
|.q.| * (- (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2)))) is V28() real ext-real Element of REAL
|.q.| * ((((q `2) / |.q.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
|[(|.q.| * (- (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2))))),(|.q.| * ((((q `2) / |.q.|) - cn) / (1 + cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q `1 is V28() real ext-real Element of REAL
q `2 is V28() real ext-real Element of REAL
|.q.| is V28() real ext-real non negative Element of REAL
(q `2) / |.q.| is V28() real ext-real Element of COMPLEX
p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p `1 is V28() real ext-real Element of REAL
p `2 is V28() real ext-real Element of REAL
|.p.| is V28() real ext-real non negative Element of REAL
(p `2) / |.p.| is V28() real ext-real Element of COMPLEX
(cn) . q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(cn) . p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((p `2) / |.p.|) - cn is V28() real ext-real Element of REAL
((q `2) / |.q.|) - cn is V28() real ext-real Element of REAL
1 - cn is V28() real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `2 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `2) / |.p2.| is V28() real ext-real Element of COMPLEX
p1 `2 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
(((p `2) / |.p.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
((((p `2) / |.p.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p `2) / |.p.|) - cn) / (1 - cn)) * ((((p `2) / |.p.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((p `2) / |.p.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p `2) / |.p.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((p `2) / |.p.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.p.| * (- (sqrt (1 - (((((p `2) / |.p.|) - cn) / (1 - cn)) ^2)))) is V28() real ext-real Element of REAL
|.p.| * ((((p `2) / |.p.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
|[(|.p.| * (- (sqrt (1 - (((((p `2) / |.p.|) - cn) / (1 - cn)) ^2))))),(|.p.| * ((((p `2) / |.p.|) - cn) / (1 - cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(((q `2) / |.q.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
((((q `2) / |.q.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((q `2) / |.q.|) - cn) / (1 - cn)) * ((((q `2) / |.q.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((q `2) / |.q.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.q.| * (- (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 - cn)) ^2)))) is V28() real ext-real Element of REAL
|.q.| * ((((q `2) / |.q.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
|[(|.q.| * (- (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 - cn)) ^2))))),(|.q.| * ((((q `2) / |.q.|) - cn) / (1 - cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q `1 is V28() real ext-real Element of REAL
q `2 is V28() real ext-real Element of REAL
|.q.| is V28() real ext-real non negative Element of REAL
(q `2) / |.q.| is V28() real ext-real Element of COMPLEX
p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p `1 is V28() real ext-real Element of REAL
p `2 is V28() real ext-real Element of REAL
|.p.| is V28() real ext-real non negative Element of REAL
(p `2) / |.p.| is V28() real ext-real Element of COMPLEX
(cn) . q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(cn) . p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((p `2) / |.p.|) - cn is V28() real ext-real Element of REAL
((q `2) / |.q.|) - cn is V28() real ext-real Element of REAL
1 + cn is V28() real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `2 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `2) / |.p2.| is V28() real ext-real Element of COMPLEX
p1 `2 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
(((p `2) / |.p.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
((((p `2) / |.p.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p `2) / |.p.|) - cn) / (1 + cn)) * ((((p `2) / |.p.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((p `2) / |.p.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p `2) / |.p.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((p `2) / |.p.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|.p.| * (- (sqrt (1 - (((((p `2) / |.p.|) - cn) / (1 + cn)) ^2)))) is V28() real ext-real Element of REAL
|.p.| * ((((p `2) / |.p.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
|[(|.p.| * (- (sqrt (1 - (((((p `2) / |.p.|) - cn) / (1 + cn)) ^2))))),(|.p.| * ((((p `2) / |.p.|) - cn) / (1 + cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(((q `2) / |.q.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
((((q `2) / |.q.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((q `2) / |.q.|) - cn) / (1 + cn)) * ((((q `2) / |.q.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|.q.| * (- (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2)))) is V28() real ext-real Element of REAL
|.q.| * ((((q `2) / |.q.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
|[(|.q.| * (- (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2))))),(|.q.| * ((((q `2) / |.q.|) - cn) / (1 + cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q `1 is V28() real ext-real Element of REAL
p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p `1 is V28() real ext-real Element of REAL
p `2 is V28() real ext-real Element of REAL
|.p.| is V28() real ext-real non negative Element of REAL
(p `2) / |.p.| is V28() real ext-real Element of COMPLEX
q `2 is V28() real ext-real Element of REAL
|.q.| is V28() real ext-real non negative Element of REAL
(q `2) / |.q.| is V28() real ext-real Element of COMPLEX
(cn) . q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(cn) . p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `2 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `2) / |.p2.| is V28() real ext-real Element of COMPLEX
p1 `2 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q `1 is V28() real ext-real Element of REAL
q `2 is V28() real ext-real Element of REAL
|.q.| is V28() real ext-real non negative Element of REAL
(q `2) / |.q.| is V28() real ext-real Element of COMPLEX
(cn) . q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p `1 is V28() real ext-real Element of REAL
p `2 is V28() real ext-real Element of REAL
((q `2) / |.q.|) - cn is V28() real ext-real Element of REAL
1 - cn is V28() real ext-real Element of REAL
(((q `2) / |.q.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
((((q `2) / |.q.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((q `2) / |.q.|) - cn) / (1 - cn)) * ((((q `2) / |.q.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((q `2) / |.q.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.q.| * (- (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 - cn)) ^2)))) is V28() real ext-real Element of REAL
|.q.| * ((((q `2) / |.q.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
|[(|.q.| * (- (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 - cn)) ^2))))),(|.q.| * ((((q `2) / |.q.|) - cn) / (1 - cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn is V28() real ext-real set
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(cn) . (0. (TOP-REAL 2)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn is V28() real ext-real set
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q `1 is V28() real ext-real Element of REAL
|.q.| is V28() real ext-real non negative Element of REAL
(q `1) / |.q.| is V28() real ext-real Element of COMPLEX
q `2 is V28() real ext-real Element of REAL
((q `1) / |.q.|) - cn is V28() real ext-real set
1 - cn is V28() real ext-real Element of REAL
(((q `1) / |.q.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
((((q `1) / |.q.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((q `1) / |.q.|) - cn) / (1 - cn)) * ((((q `1) / |.q.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|[((((q `1) / |.q.|) - cn) / (1 - cn)),(sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.q.| * |[((((q `1) / |.q.|) - cn) / (1 - cn)),(sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
1 + cn is V28() real ext-real Element of REAL
(((q `1) / |.q.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
((((q `1) / |.q.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((q `1) / |.q.|) - cn) / (1 + cn)) * ((((q `1) / |.q.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((q `1) / |.q.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
|[((((q `1) / |.q.|) - cn) / (1 + cn)),(sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 + cn)) ^2)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.q.| * |[((((q `1) / |.q.|) - cn) / (1 + cn)),(sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 + cn)) ^2)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn is V28() real ext-real set
cn is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn `1 is V28() real ext-real Element of REAL
|.cn.| is V28() real ext-real non negative Element of REAL
(cn `1) / |.cn.| is V28() real ext-real Element of COMPLEX
cn `2 is V28() real ext-real Element of REAL
q is V28() real ext-real set
(q) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(q) . cn is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((cn `1) / |.cn.|) - q is V28() real ext-real set
1 - q is V28() real ext-real Element of REAL
(((cn `1) / |.cn.|) - q) / (1 - q) is V28() real ext-real Element of COMPLEX
|.cn.| * ((((cn `1) / |.cn.|) - q) / (1 - q)) is V28() real ext-real Element of REAL
((((cn `1) / |.cn.|) - q) / (1 - q)) ^2 is V28() real ext-real Element of COMPLEX
((((cn `1) / |.cn.|) - q) / (1 - q)) * ((((cn `1) / |.cn.|) - q) / (1 - q)) is V28() real ext-real set
1 - (((((cn `1) / |.cn.|) - q) / (1 - q)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((cn `1) / |.cn.|) - q) / (1 - q)) ^2)) is V28() real ext-real Element of REAL
|.cn.| * (sqrt (1 - (((((cn `1) / |.cn.|) - q) / (1 - q)) ^2))) is V28() real ext-real Element of REAL
|[(|.cn.| * ((((cn `1) / |.cn.|) - q) / (1 - q))),(|.cn.| * (sqrt (1 - (((((cn `1) / |.cn.|) - q) / (1 - q)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(q,cn) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[((((cn `1) / |.cn.|) - q) / (1 - q)),(sqrt (1 - (((((cn `1) / |.cn.|) - q) / (1 - q)) ^2)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.cn.| * |[((((cn `1) / |.cn.|) - q) / (1 - q)),(sqrt (1 - (((((cn `1) / |.cn.|) - q) / (1 - q)) ^2)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn `1 is V28() real ext-real Element of REAL
|.cn.| is V28() real ext-real non negative Element of REAL
(cn `1) / |.cn.| is V28() real ext-real Element of COMPLEX
cn `2 is V28() real ext-real Element of REAL
q is V28() real ext-real Element of REAL
(q) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(q) . cn is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((cn `1) / |.cn.|) - q is V28() real ext-real Element of REAL
1 + q is V28() real ext-real Element of REAL
(((cn `1) / |.cn.|) - q) / (1 + q) is V28() real ext-real Element of COMPLEX
|.cn.| * ((((cn `1) / |.cn.|) - q) / (1 + q)) is V28() real ext-real Element of REAL
((((cn `1) / |.cn.|) - q) / (1 + q)) ^2 is V28() real ext-real Element of COMPLEX
((((cn `1) / |.cn.|) - q) / (1 + q)) * ((((cn `1) / |.cn.|) - q) / (1 + q)) is V28() real ext-real set
1 - (((((cn `1) / |.cn.|) - q) / (1 + q)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((cn `1) / |.cn.|) - q) / (1 + q)) ^2)) is V28() real ext-real Element of REAL
|.cn.| * (sqrt (1 - (((((cn `1) / |.cn.|) - q) / (1 + q)) ^2))) is V28() real ext-real Element of REAL
|[(|.cn.| * ((((cn `1) / |.cn.|) - q) / (1 + q))),(|.cn.| * (sqrt (1 - (((((cn `1) / |.cn.|) - q) / (1 + q)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(q,cn) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[((((cn `1) / |.cn.|) - q) / (1 + q)),(sqrt (1 - (((((cn `1) / |.cn.|) - q) / (1 + q)) ^2)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.cn.| * |[((((cn `1) / |.cn.|) - q) / (1 + q)),(sqrt (1 - (((((cn `1) / |.cn.|) - q) / (1 + q)) ^2)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
1 - q is V28() real ext-real Element of REAL
(((cn `1) / |.cn.|) - q) / (1 - q) is V28() real ext-real Element of COMPLEX
cn is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn `1 is V28() real ext-real Element of REAL
|.cn.| is V28() real ext-real non negative Element of REAL
(cn `1) / |.cn.| is V28() real ext-real Element of COMPLEX
cn `2 is V28() real ext-real Element of REAL
q is V28() real ext-real Element of REAL
(q) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(q) . cn is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((cn `1) / |.cn.|) - q is V28() real ext-real Element of REAL
1 - q is V28() real ext-real Element of REAL
(((cn `1) / |.cn.|) - q) / (1 - q) is V28() real ext-real Element of COMPLEX
|.cn.| * ((((cn `1) / |.cn.|) - q) / (1 - q)) is V28() real ext-real Element of REAL
((((cn `1) / |.cn.|) - q) / (1 - q)) ^2 is V28() real ext-real Element of COMPLEX
((((cn `1) / |.cn.|) - q) / (1 - q)) * ((((cn `1) / |.cn.|) - q) / (1 - q)) is V28() real ext-real set
1 - (((((cn `1) / |.cn.|) - q) / (1 - q)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((cn `1) / |.cn.|) - q) / (1 - q)) ^2)) is V28() real ext-real Element of REAL
|.cn.| * (sqrt (1 - (((((cn `1) / |.cn.|) - q) / (1 - q)) ^2))) is V28() real ext-real Element of REAL
|[(|.cn.| * ((((cn `1) / |.cn.|) - q) / (1 - q))),(|.cn.| * (sqrt (1 - (((((cn `1) / |.cn.|) - q) / (1 - q)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
1 + q is V28() real ext-real Element of REAL
(((cn `1) / |.cn.|) - q) / (1 + q) is V28() real ext-real Element of COMPLEX
|.cn.| * ((((cn `1) / |.cn.|) - q) / (1 + q)) is V28() real ext-real Element of REAL
((((cn `1) / |.cn.|) - q) / (1 + q)) ^2 is V28() real ext-real Element of COMPLEX
((((cn `1) / |.cn.|) - q) / (1 + q)) * ((((cn `1) / |.cn.|) - q) / (1 + q)) is V28() real ext-real set
1 - (((((cn `1) / |.cn.|) - q) / (1 + q)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((cn `1) / |.cn.|) - q) / (1 + q)) ^2)) is V28() real ext-real Element of REAL
|.cn.| * (sqrt (1 - (((((cn `1) / |.cn.|) - q) / (1 + q)) ^2))) is V28() real ext-real Element of REAL
|[(|.cn.| * ((((cn `1) / |.cn.|) - q) / (1 + q))),(|.cn.| * (sqrt (1 - (((((cn `1) / |.cn.|) - q) / (1 + q)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(q,cn) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[((((cn `1) / |.cn.|) - q) / (1 - q)),(sqrt (1 - (((((cn `1) / |.cn.|) - q) / (1 - q)) ^2)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.cn.| * |[((((cn `1) / |.cn.|) - q) / (1 - q)),(sqrt (1 - (((((cn `1) / |.cn.|) - q) / (1 - q)) ^2)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.cn.| ^2 is V28() real ext-real Element of REAL
|.cn.| * |.cn.| is V28() real ext-real non negative set
(cn `1) ^2 is V28() real ext-real Element of REAL
(cn `1) * (cn `1) is V28() real ext-real set
(cn `2) ^2 is V28() real ext-real Element of REAL
(cn `2) * (cn `2) is V28() real ext-real set
((cn `1) ^2) + ((cn `2) ^2) is V28() real ext-real Element of REAL
((cn `1) ^2) / (|.cn.| ^2) is V28() real ext-real Element of COMPLEX
((cn `1) / |.cn.|) ^2 is V28() real ext-real Element of COMPLEX
((cn `1) / |.cn.|) * ((cn `1) / |.cn.|) is V28() real ext-real set
sqrt (((cn `1) / |.cn.|) ^2) is V28() real ext-real set
- ((cn `1) / |.cn.|) is V28() real ext-real Element of COMPLEX
sqrt (|.cn.| ^2) is V28() real ext-real Element of REAL
1 * |.cn.| is V28() real ext-real non negative Element of REAL
((cn `1) / |.cn.|) * |.cn.| is V28() real ext-real Element of REAL
|.cn.| ^2 is V28() real ext-real Element of REAL
|.cn.| * |.cn.| is V28() real ext-real non negative set
(cn `1) ^2 is V28() real ext-real Element of REAL
(cn `1) * (cn `1) is V28() real ext-real set
(cn `2) ^2 is V28() real ext-real Element of REAL
(cn `2) * (cn `2) is V28() real ext-real set
((cn `1) ^2) + ((cn `2) ^2) is V28() real ext-real Element of REAL
- |.cn.| is V28() real ext-real non positive Element of REAL
- (1 + q) is V28() real ext-real Element of REAL
(- (1 + q)) / (1 + q) is V28() real ext-real Element of COMPLEX
- (cn `1) is V28() real ext-real Element of REAL
cn is V28() real ext-real Element of REAL
1 - cn is V28() real ext-real Element of REAL
q is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | q is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | q) is non empty set
K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1) is set
K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1)) is set
p is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
(2) | q is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of R^1))
proj1 | q is Relation-like the carrier of ((TOP-REAL 2) | q) -defined REAL -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q),REAL))
K20( the carrier of ((TOP-REAL 2) | q),REAL) is set
K19(K20( the carrier of ((TOP-REAL 2) | q),REAL)) is set
u2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
u2 is Element of the carrier of ((TOP-REAL 2) | q)
p1 . u2 is V28() real ext-real Element of the carrier of R^1
VV0 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
u2 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
dom u2 is Element of K19( the carrier of ((TOP-REAL 2) | q))
K19( the carrier of ((TOP-REAL 2) | q)) is set
dom p is Element of K19( the carrier of ((TOP-REAL 2) | q))
u3 is set
p . u3 is set
u2 . u3 is set
q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
proj1 . q4 is V28() real ext-real Element of REAL
q4 `1 is V28() real ext-real Element of REAL
(2) . q4 is V28() real ext-real Element of the carrier of R^1
|.q4.| is V28() real ext-real non negative Element of REAL
y is Element of the carrier of ((TOP-REAL 2) | q)
VV0 . y is V28() real ext-real Element of the carrier of R^1
proj1 . y is set
p1 . y is V28() real ext-real Element of the carrier of R^1
(2) . y is set
p . q4 is set
(q4 `1) / |.q4.| is V28() real ext-real Element of COMPLEX
((q4 `1) / |.q4.|) - cn is V28() real ext-real Element of REAL
(((q4 `1) / |.q4.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
|.q4.| * ((((q4 `1) / |.q4.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
cn is V28() real ext-real Element of REAL
1 + cn is V28() real ext-real Element of REAL
q is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | q is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | q) is non empty set
K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1) is set
K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1)) is set
p is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
(2) | q is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of R^1))
proj1 | q is Relation-like the carrier of ((TOP-REAL 2) | q) -defined REAL -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q),REAL))
K20( the carrier of ((TOP-REAL 2) | q),REAL) is set
K19(K20( the carrier of ((TOP-REAL 2) | q),REAL)) is set
u2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
u2 is Element of the carrier of ((TOP-REAL 2) | q)
p1 . u2 is V28() real ext-real Element of the carrier of R^1
VV0 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
u2 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
dom u2 is Element of K19( the carrier of ((TOP-REAL 2) | q))
K19( the carrier of ((TOP-REAL 2) | q)) is set
dom p is Element of K19( the carrier of ((TOP-REAL 2) | q))
u3 is set
p . u3 is set
u2 . u3 is set
q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
proj1 . q4 is V28() real ext-real Element of REAL
q4 `1 is V28() real ext-real Element of REAL
(2) . q4 is V28() real ext-real Element of the carrier of R^1
|.q4.| is V28() real ext-real non negative Element of REAL
y is Element of the carrier of ((TOP-REAL 2) | q)
VV0 . y is V28() real ext-real Element of the carrier of R^1
proj1 . y is set
p1 . y is V28() real ext-real Element of the carrier of R^1
(2) . y is set
p . q4 is set
(q4 `1) / |.q4.| is V28() real ext-real Element of COMPLEX
((q4 `1) / |.q4.|) - cn is V28() real ext-real Element of REAL
(((q4 `1) / |.q4.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
|.q4.| * ((((q4 `1) / |.q4.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
cn is V28() real ext-real Element of REAL
1 - cn is V28() real ext-real Element of REAL
q is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | q is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | q) is non empty set
K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1) is set
K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1)) is set
p is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
(2) | q is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of R^1))
proj1 | q is Relation-like the carrier of ((TOP-REAL 2) | q) -defined REAL -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q),REAL))
K20( the carrier of ((TOP-REAL 2) | q),REAL) is set
K19(K20( the carrier of ((TOP-REAL 2) | q),REAL)) is set
u2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
u2 is Element of the carrier of ((TOP-REAL 2) | q)
p1 . u2 is V28() real ext-real Element of the carrier of R^1
VV0 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
u2 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
dom u2 is Element of K19( the carrier of ((TOP-REAL 2) | q))
K19( the carrier of ((TOP-REAL 2) | q)) is set
dom p is Element of K19( the carrier of ((TOP-REAL 2) | q))
u3 is set
p . u3 is set
u2 . u3 is set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.y.| is V28() real ext-real non negative Element of REAL
|.y.| ^2 is V28() real ext-real Element of REAL
|.y.| * |.y.| is V28() real ext-real non negative set
y `1 is V28() real ext-real Element of REAL
(y `1) ^2 is V28() real ext-real Element of REAL
(y `1) * (y `1) is V28() real ext-real set
y `2 is V28() real ext-real Element of REAL
(y `2) ^2 is V28() real ext-real Element of REAL
(y `2) * (y `2) is V28() real ext-real set
((y `1) ^2) + ((y `2) ^2) is V28() real ext-real Element of REAL
(y `1) - |.y.| is V28() real ext-real Element of REAL
(y `1) + |.y.| is V28() real ext-real Element of REAL
((y `1) - |.y.|) * ((y `1) + |.y.|) is V28() real ext-real Element of REAL
- ((y `2) ^2) is V28() real ext-real Element of REAL
(y `1) / |.y.| is V28() real ext-real Element of COMPLEX
|.y.| / |.y.| is V28() real ext-real non negative Element of COMPLEX
((y `1) / |.y.|) - cn is V28() real ext-real Element of REAL
(1 - cn) ^2 is V28() real ext-real Element of REAL
(1 - cn) * (1 - cn) is V28() real ext-real set
(1 - cn) + cn is V28() real ext-real Element of REAL
0 + cn is V28() real ext-real Element of REAL
cn - ((y `1) / |.y.|) is V28() real ext-real Element of REAL
- (1 - cn) is V28() real ext-real Element of REAL
- (cn - ((y `1) / |.y.|)) is V28() real ext-real Element of REAL
(((y `1) / |.y.|) - cn) ^2 is V28() real ext-real Element of REAL
(((y `1) / |.y.|) - cn) * (((y `1) / |.y.|) - cn) is V28() real ext-real set
((((y `1) / |.y.|) - cn) ^2) / ((1 - cn) ^2) is V28() real ext-real Element of COMPLEX
((1 - cn) ^2) / ((1 - cn) ^2) is V28() real ext-real Element of COMPLEX
(((y `1) / |.y.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
((((y `1) / |.y.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((y `1) / |.y.|) - cn) / (1 - cn)) * ((((y `1) / |.y.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((y `1) / |.y.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
abs (1 - (((((y `1) / |.y.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
p . y is set
sqrt (abs (1 - (((((y `1) / |.y.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.y.| * (sqrt (abs (1 - (((((y `1) / |.y.|) - cn) / (1 - cn)) ^2)))) is V28() real ext-real Element of REAL
proj1 . y is V28() real ext-real Element of REAL
(2) . y is V28() real ext-real Element of the carrier of R^1
q4 is Element of the carrier of ((TOP-REAL 2) | q)
VV0 . q4 is V28() real ext-real Element of the carrier of R^1
proj1 . q4 is set
p1 . q4 is V28() real ext-real Element of the carrier of R^1
(2) . q4 is set
cn is V28() real ext-real Element of REAL
1 + cn is V28() real ext-real Element of REAL
q is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | q is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | q) is non empty set
K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1) is set
K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1)) is set
p is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
(2) | q is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of R^1))
proj1 | q is Relation-like the carrier of ((TOP-REAL 2) | q) -defined REAL -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q),REAL))
K20( the carrier of ((TOP-REAL 2) | q),REAL) is set
K19(K20( the carrier of ((TOP-REAL 2) | q),REAL)) is set
u2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
u2 is Element of the carrier of ((TOP-REAL 2) | q)
p1 . u2 is V28() real ext-real Element of the carrier of R^1
VV0 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
u2 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
dom u2 is Element of K19( the carrier of ((TOP-REAL 2) | q))
K19( the carrier of ((TOP-REAL 2) | q)) is set
dom p is Element of K19( the carrier of ((TOP-REAL 2) | q))
u3 is set
p . u3 is set
u2 . u3 is set
(1 + cn) ^2 is V28() real ext-real Element of REAL
(1 + cn) * (1 + cn) is V28() real ext-real set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.y.| is V28() real ext-real non negative Element of REAL
|.y.| ^2 is V28() real ext-real Element of REAL
|.y.| * |.y.| is V28() real ext-real non negative set
y `1 is V28() real ext-real Element of REAL
(y `1) ^2 is V28() real ext-real Element of REAL
(y `1) * (y `1) is V28() real ext-real set
y `2 is V28() real ext-real Element of REAL
(y `2) ^2 is V28() real ext-real Element of REAL
(y `2) * (y `2) is V28() real ext-real set
((y `1) ^2) + ((y `2) ^2) is V28() real ext-real Element of REAL
(y `1) - |.y.| is V28() real ext-real Element of REAL
(y `1) + |.y.| is V28() real ext-real Element of REAL
((y `1) - |.y.|) * ((y `1) + |.y.|) is V28() real ext-real Element of REAL
- ((y `2) ^2) is V28() real ext-real Element of REAL
- |.y.| is V28() real ext-real non positive Element of REAL
(- |.y.|) / |.y.| is V28() real ext-real non positive Element of COMPLEX
(y `1) / |.y.| is V28() real ext-real Element of COMPLEX
(- 1) - cn is V28() real ext-real Element of REAL
((y `1) / |.y.|) - cn is V28() real ext-real Element of REAL
- (1 + cn) is V28() real ext-real Element of REAL
cn - ((y `1) / |.y.|) is V28() real ext-real Element of REAL
- (cn - ((y `1) / |.y.|)) is V28() real ext-real Element of REAL
(((y `1) / |.y.|) - cn) ^2 is V28() real ext-real Element of REAL
(((y `1) / |.y.|) - cn) * (((y `1) / |.y.|) - cn) is V28() real ext-real set
((((y `1) / |.y.|) - cn) ^2) / ((1 + cn) ^2) is V28() real ext-real Element of COMPLEX
((1 + cn) ^2) / ((1 + cn) ^2) is V28() real ext-real Element of COMPLEX
(((y `1) / |.y.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
((((y `1) / |.y.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((y `1) / |.y.|) - cn) / (1 + cn)) * ((((y `1) / |.y.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((y `1) / |.y.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
abs (1 - (((((y `1) / |.y.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
p . y is set
sqrt (abs (1 - (((((y `1) / |.y.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|.y.| * (sqrt (abs (1 - (((((y `1) / |.y.|) - cn) / (1 + cn)) ^2)))) is V28() real ext-real Element of REAL
proj1 . y is V28() real ext-real Element of REAL
(2) . y is V28() real ext-real Element of the carrier of R^1
q4 is Element of the carrier of ((TOP-REAL 2) | q)
VV0 . q4 is V28() real ext-real Element of the carrier of R^1
proj1 . q4 is set
p1 . q4 is V28() real ext-real Element of the carrier of R^1
(2) . q4 is set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( 0 <= b<sub>1</sub> `2 & not b₁ = 0. (TOP-REAL 2) ) } is set
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( cn <= (b₁ `1) / |.b<sub>1</sub>.| & 0 <= b<sub>1</sub> `2 & not b₁ = 0. (TOP-REAL 2) ) } is set
q is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | q is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | q) is set
p is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | p is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | p) is set
K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p)) is set
K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p))) is set
(cn) | q is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p1 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of ((TOP-REAL 2) | p) -valued Function-like quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p)))
cn ^2 is V28() real ext-real Element of REAL
cn * cn is V28() real ext-real set
1 - (cn ^2) is V28() real ext-real Element of REAL
sqrt (1 - (cn ^2)) is V28() real ext-real Element of REAL
|[cn,(sqrt (1 - (cn ^2)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[cn,(sqrt (1 - (cn ^2)))]| `2 is V28() real ext-real Element of REAL
|[cn,(sqrt (1 - (cn ^2)))]| `1 is V28() real ext-real Element of REAL
|.|[cn,(sqrt (1 - (cn ^2)))]|.| is V28() real ext-real non negative Element of REAL
(sqrt (1 - (cn ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (cn ^2))) * (sqrt (1 - (cn ^2))) is V28() real ext-real set
((sqrt (1 - (cn ^2))) ^2) + (cn ^2) is V28() real ext-real Element of REAL
sqrt (((sqrt (1 - (cn ^2))) ^2) + (cn ^2)) is V28() real ext-real Element of REAL
(|[cn,(sqrt (1 - (cn ^2)))]| `1) / |.|[cn,(sqrt (1 - (cn ^2)))]|.| is V28() real ext-real Element of COMPLEX
VV0 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(cn) | VV0 is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
proj2 * ((cn) | VV0) is Relation-like the carrier of (TOP-REAL 2) -defined REAL -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2),REAL))
rng (proj2 * ((cn) | VV0)) is V126() V127() V128() Element of K19(REAL)
u2 is set
u3 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
u3 `1 is V28() real ext-real Element of REAL
|.u3.| is V28() real ext-real non negative Element of REAL
(u3 `1) / |.u3.| is V28() real ext-real Element of COMPLEX
u3 `2 is V28() real ext-real Element of REAL
dom ((cn) | VV0) is functional Element of K19( the carrier of (TOP-REAL 2))
proj1 * ((cn) | VV0) is Relation-like the carrier of (TOP-REAL 2) -defined REAL -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2),REAL))
dom (proj1 * ((cn) | VV0)) is functional Element of K19( the carrier of (TOP-REAL 2))
u2 is set
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
(dom (cn)) /\ VV0 is functional Element of K19( the carrier of (TOP-REAL 2))
dom proj1 is functional Element of K19( the carrier of (TOP-REAL 2))
(cn) . u2 is Relation-like Function-like set
rng (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
((cn) | VV0) . u2 is Relation-like Function-like set
rng (proj1 * ((cn) | VV0)) is V126() V127() V128() Element of K19(REAL)
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
(dom (cn)) /\ VV0 is functional Element of K19( the carrier of (TOP-REAL 2))
the carrier of (TOP-REAL 2) /\ VV0 is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | VV0 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | VV0) is non empty set
K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1) is set
K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1)) is set
u2 is Relation-like the carrier of ((TOP-REAL 2) | VV0) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1))
1 - cn is V28() real ext-real Element of REAL
u3 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
u2 . u3 is set
|.u3.| is V28() real ext-real non negative Element of REAL
u3 `1 is V28() real ext-real Element of REAL
(u3 `1) / |.u3.| is V28() real ext-real Element of COMPLEX
((u3 `1) / |.u3.|) - cn is V28() real ext-real Element of REAL
(((u3 `1) / |.u3.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
|.u3.| * ((((u3 `1) / |.u3.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
(cn) . u3 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((((u3 `1) / |.u3.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((u3 `1) / |.u3.|) - cn) / (1 - cn)) * ((((u3 `1) / |.u3.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((u3 `1) / |.u3.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((u3 `1) / |.u3.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.u3.| * (sqrt (1 - (((((u3 `1) / |.u3.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|[(|.u3.| * ((((u3 `1) / |.u3.|) - cn) / (1 - cn))),(|.u3.| * (sqrt (1 - (((((u3 `1) / |.u3.|) - cn) / (1 - cn)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `1 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `1) / |.y.| is V28() real ext-real Element of COMPLEX
y `2 is V28() real ext-real Element of REAL
((cn) | VV0) . u3 is Relation-like Function-like set
proj1 . |[(|.u3.| * ((((u3 `1) / |.u3.|) - cn) / (1 - cn))),(|.u3.| * (sqrt (1 - (((((u3 `1) / |.u3.|) - cn) / (1 - cn)) ^2))))]| is V28() real ext-real Element of REAL
|[(|.u3.| * ((((u3 `1) / |.u3.|) - cn) / (1 - cn))),(|.u3.| * (sqrt (1 - (((((u3 `1) / |.u3.|) - cn) / (1 - cn)) ^2))))]| `1 is V28() real ext-real Element of REAL
u3 is Relation-like the carrier of ((TOP-REAL 2) | VV0) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1))
dom (proj2 * ((cn) | VV0)) is functional Element of K19( the carrier of (TOP-REAL 2))
y is set
dom proj2 is functional Element of K19( the carrier of (TOP-REAL 2))
(cn) . y is Relation-like Function-like set
rng (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
((cn) | VV0) . y is Relation-like Function-like set
y is Relation-like the carrier of ((TOP-REAL 2) | VV0) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1))
q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y . q4 is set
|.q4.| is V28() real ext-real non negative Element of REAL
q4 `1 is V28() real ext-real Element of REAL
(q4 `1) / |.q4.| is V28() real ext-real Element of COMPLEX
((q4 `1) / |.q4.|) - cn is V28() real ext-real Element of REAL
(((q4 `1) / |.q4.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
((((q4 `1) / |.q4.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((q4 `1) / |.q4.|) - cn) / (1 - cn)) * ((((q4 `1) / |.q4.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((q4 `1) / |.q4.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((q4 `1) / |.q4.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.q4.| * (sqrt (1 - (((((q4 `1) / |.q4.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
(cn) . q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.q4.| * ((((q4 `1) / |.q4.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
|[(|.q4.| * ((((q4 `1) / |.q4.|) - cn) / (1 - cn))),(|.q4.| * (sqrt (1 - (((((q4 `1) / |.q4.|) - cn) / (1 - cn)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `1 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `1) / |.y.| is V28() real ext-real Element of COMPLEX
y `2 is V28() real ext-real Element of REAL
((cn) | VV0) . q4 is Relation-like Function-like set
proj2 . |[(|.q4.| * ((((q4 `1) / |.q4.|) - cn) / (1 - cn))),(|.q4.| * (sqrt (1 - (((((q4 `1) / |.q4.|) - cn) / (1 - cn)) ^2))))]| is V28() real ext-real Element of REAL
|[(|.q4.| * ((((q4 `1) / |.q4.|) - cn) / (1 - cn))),(|.q4.| * (sqrt (1 - (((((q4 `1) / |.q4.|) - cn) / (1 - cn)) ^2))))]| `2 is V28() real ext-real Element of REAL
q4 is Relation-like the carrier of ((TOP-REAL 2) | VV0) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1))
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `2 is V28() real ext-real Element of REAL
y `1 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `1) / |.y.| is V28() real ext-real Element of COMPLEX
x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x `1 is V28() real ext-real Element of REAL
|.x.| is V28() real ext-real non negative Element of REAL
(x `1) / |.x.| is V28() real ext-real Element of COMPLEX
x `2 is V28() real ext-real Element of REAL
y is V28() real ext-real set
x is V28() real ext-real set
|[y,x]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x is V28() real ext-real set
u3 . |[y,x]| is set
q is V28() real ext-real set
q4 . |[y,x]| is set
p1 . |[y,x]| is set
|[x,q]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.|[y,x]|.| is V28() real ext-real non negative Element of REAL
|[y,x]| `1 is V28() real ext-real Element of REAL
(|[y,x]| `1) / |.|[y,x]|.| is V28() real ext-real Element of COMPLEX
((|[y,x]| `1) / |.|[y,x]|.|) - cn is V28() real ext-real Element of REAL
(((|[y,x]| `1) / |.|[y,x]|.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
((((|[y,x]| `1) / |.|[y,x]|.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((|[y,x]| `1) / |.|[y,x]|.|) - cn) / (1 - cn)) * ((((|[y,x]| `1) / |.|[y,x]|.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((|[y,x]| `1) / |.|[y,x]|.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((|[y,x]| `1) / |.|[y,x]|.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.|[y,x]|.| * (sqrt (1 - (((((|[y,x]| `1) / |.|[y,x]|.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
((cn) | q) . |[y,x]| is Relation-like Function-like set
(cn) . |[y,x]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.|[y,x]|.| * ((((|[y,x]| `1) / |.|[y,x]|.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
|[(|.|[y,x]|.| * ((((|[y,x]| `1) / |.|[y,x]|.|) - cn) / (1 - cn))),(|.|[y,x]|.| * (sqrt (1 - (((((|[y,x]| `1) / |.|[y,x]|.|) - cn) / (1 - cn)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K111 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K111 `1 is V28() real ext-real Element of REAL
|.K111.| is V28() real ext-real non negative Element of REAL
(K111 `1) / |.K111.| is V28() real ext-real Element of COMPLEX
K111 `2 is V28() real ext-real Element of REAL
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `2 is V28() real ext-real Element of REAL
x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x `1 is V28() real ext-real Element of REAL
|.x.| is V28() real ext-real non negative Element of REAL
(x `1) / |.x.| is V28() real ext-real Element of COMPLEX
x `2 is V28() real ext-real Element of REAL
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( (b₁ `1) / |.b<sub>1</sub>.| <= cn & 0 <= b<sub>1</sub> `2 & not b₁ = 0. (TOP-REAL 2) ) } is set
q is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | q is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | q) is set
p is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | p is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | p) is set
K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p)) is set
K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p))) is set
(cn) | q is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p1 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of ((TOP-REAL 2) | p) -valued Function-like quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p)))
cn ^2 is V28() real ext-real Element of REAL
cn * cn is V28() real ext-real set
1 - (cn ^2) is V28() real ext-real Element of REAL
sqrt (1 - (cn ^2)) is V28() real ext-real Element of REAL
|[cn,(sqrt (1 - (cn ^2)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[cn,(sqrt (1 - (cn ^2)))]| `2 is V28() real ext-real Element of REAL
|[cn,(sqrt (1 - (cn ^2)))]| `1 is V28() real ext-real Element of REAL
|.|[cn,(sqrt (1 - (cn ^2)))]|.| is V28() real ext-real non negative Element of REAL
(sqrt (1 - (cn ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (cn ^2))) * (sqrt (1 - (cn ^2))) is V28() real ext-real set
((sqrt (1 - (cn ^2))) ^2) + (cn ^2) is V28() real ext-real Element of REAL
sqrt (((sqrt (1 - (cn ^2))) ^2) + (cn ^2)) is V28() real ext-real Element of REAL
(|[cn,(sqrt (1 - (cn ^2)))]| `1) / |.|[cn,(sqrt (1 - (cn ^2)))]|.| is V28() real ext-real Element of COMPLEX
VV0 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(cn) | VV0 is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
proj2 * ((cn) | VV0) is Relation-like the carrier of (TOP-REAL 2) -defined REAL -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2),REAL))
rng (proj2 * ((cn) | VV0)) is V126() V127() V128() Element of K19(REAL)
u2 is set
u3 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
u3 `1 is V28() real ext-real Element of REAL
|.u3.| is V28() real ext-real non negative Element of REAL
(u3 `1) / |.u3.| is V28() real ext-real Element of COMPLEX
u3 `2 is V28() real ext-real Element of REAL
dom ((cn) | VV0) is functional Element of K19( the carrier of (TOP-REAL 2))
proj1 * ((cn) | VV0) is Relation-like the carrier of (TOP-REAL 2) -defined REAL -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2),REAL))
dom (proj1 * ((cn) | VV0)) is functional Element of K19( the carrier of (TOP-REAL 2))
u2 is set
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
(dom (cn)) /\ VV0 is functional Element of K19( the carrier of (TOP-REAL 2))
dom proj1 is functional Element of K19( the carrier of (TOP-REAL 2))
(cn) . u2 is Relation-like Function-like set
rng (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
((cn) | VV0) . u2 is Relation-like Function-like set
rng (proj1 * ((cn) | VV0)) is V126() V127() V128() Element of K19(REAL)
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
(dom (cn)) /\ VV0 is functional Element of K19( the carrier of (TOP-REAL 2))
the carrier of (TOP-REAL 2) /\ VV0 is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | VV0 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | VV0) is non empty set
K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1) is set
K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1)) is set
u2 is Relation-like the carrier of ((TOP-REAL 2) | VV0) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1))
1 + cn is V28() real ext-real Element of REAL
u3 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
u2 . u3 is set
|.u3.| is V28() real ext-real non negative Element of REAL
u3 `1 is V28() real ext-real Element of REAL
(u3 `1) / |.u3.| is V28() real ext-real Element of COMPLEX
((u3 `1) / |.u3.|) - cn is V28() real ext-real Element of REAL
(((u3 `1) / |.u3.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
|.u3.| * ((((u3 `1) / |.u3.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
(cn) . u3 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((((u3 `1) / |.u3.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((u3 `1) / |.u3.|) - cn) / (1 + cn)) * ((((u3 `1) / |.u3.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((u3 `1) / |.u3.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((u3 `1) / |.u3.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
|.u3.| * (sqrt (1 - (((((u3 `1) / |.u3.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|[(|.u3.| * ((((u3 `1) / |.u3.|) - cn) / (1 + cn))),(|.u3.| * (sqrt (1 - (((((u3 `1) / |.u3.|) - cn) / (1 + cn)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `1 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `1) / |.y.| is V28() real ext-real Element of COMPLEX
y `2 is V28() real ext-real Element of REAL
((cn) | VV0) . u3 is Relation-like Function-like set
proj1 . |[(|.u3.| * ((((u3 `1) / |.u3.|) - cn) / (1 + cn))),(|.u3.| * (sqrt (1 - (((((u3 `1) / |.u3.|) - cn) / (1 + cn)) ^2))))]| is V28() real ext-real Element of REAL
|[(|.u3.| * ((((u3 `1) / |.u3.|) - cn) / (1 + cn))),(|.u3.| * (sqrt (1 - (((((u3 `1) / |.u3.|) - cn) / (1 + cn)) ^2))))]| `1 is V28() real ext-real Element of REAL
u3 is Relation-like the carrier of ((TOP-REAL 2) | VV0) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1))
dom (proj2 * ((cn) | VV0)) is functional Element of K19( the carrier of (TOP-REAL 2))
y is set
dom proj2 is functional Element of K19( the carrier of (TOP-REAL 2))
(cn) . y is Relation-like Function-like set
rng (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
((cn) | VV0) . y is Relation-like Function-like set
y is Relation-like the carrier of ((TOP-REAL 2) | VV0) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1))
q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y . q4 is set
|.q4.| is V28() real ext-real non negative Element of REAL
q4 `1 is V28() real ext-real Element of REAL
(q4 `1) / |.q4.| is V28() real ext-real Element of COMPLEX
((q4 `1) / |.q4.|) - cn is V28() real ext-real Element of REAL
(((q4 `1) / |.q4.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
((((q4 `1) / |.q4.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((q4 `1) / |.q4.|) - cn) / (1 + cn)) * ((((q4 `1) / |.q4.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((q4 `1) / |.q4.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((q4 `1) / |.q4.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
|.q4.| * (sqrt (1 - (((((q4 `1) / |.q4.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
(cn) . q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.q4.| * ((((q4 `1) / |.q4.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
|[(|.q4.| * ((((q4 `1) / |.q4.|) - cn) / (1 + cn))),(|.q4.| * (sqrt (1 - (((((q4 `1) / |.q4.|) - cn) / (1 + cn)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `1 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `1) / |.y.| is V28() real ext-real Element of COMPLEX
y `2 is V28() real ext-real Element of REAL
((cn) | VV0) . q4 is Relation-like Function-like set
proj2 . |[(|.q4.| * ((((q4 `1) / |.q4.|) - cn) / (1 + cn))),(|.q4.| * (sqrt (1 - (((((q4 `1) / |.q4.|) - cn) / (1 + cn)) ^2))))]| is V28() real ext-real Element of REAL
|[(|.q4.| * ((((q4 `1) / |.q4.|) - cn) / (1 + cn))),(|.q4.| * (sqrt (1 - (((((q4 `1) / |.q4.|) - cn) / (1 + cn)) ^2))))]| `2 is V28() real ext-real Element of REAL
q4 is Relation-like the carrier of ((TOP-REAL 2) | VV0) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1))
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `2 is V28() real ext-real Element of REAL
y `1 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `1) / |.y.| is V28() real ext-real Element of COMPLEX
x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x `1 is V28() real ext-real Element of REAL
|.x.| is V28() real ext-real non negative Element of REAL
(x `1) / |.x.| is V28() real ext-real Element of COMPLEX
x `2 is V28() real ext-real Element of REAL
y is V28() real ext-real set
x is V28() real ext-real set
|[y,x]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x is V28() real ext-real set
u3 . |[y,x]| is set
q is V28() real ext-real set
q4 . |[y,x]| is set
p1 . |[y,x]| is set
|[x,q]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.|[y,x]|.| is V28() real ext-real non negative Element of REAL
|[y,x]| `1 is V28() real ext-real Element of REAL
(|[y,x]| `1) / |.|[y,x]|.| is V28() real ext-real Element of COMPLEX
((|[y,x]| `1) / |.|[y,x]|.|) - cn is V28() real ext-real Element of REAL
(((|[y,x]| `1) / |.|[y,x]|.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
((((|[y,x]| `1) / |.|[y,x]|.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((|[y,x]| `1) / |.|[y,x]|.|) - cn) / (1 + cn)) * ((((|[y,x]| `1) / |.|[y,x]|.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((|[y,x]| `1) / |.|[y,x]|.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((|[y,x]| `1) / |.|[y,x]|.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
|.|[y,x]|.| * (sqrt (1 - (((((|[y,x]| `1) / |.|[y,x]|.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
((cn) | q) . |[y,x]| is Relation-like Function-like set
(cn) . |[y,x]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.|[y,x]|.| * ((((|[y,x]| `1) / |.|[y,x]|.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
|[(|.|[y,x]|.| * ((((|[y,x]| `1) / |.|[y,x]|.|) - cn) / (1 + cn))),(|.|[y,x]|.| * (sqrt (1 - (((((|[y,x]| `1) / |.|[y,x]|.|) - cn) / (1 + cn)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K111 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K111 `1 is V28() real ext-real Element of REAL
|.K111.| is V28() real ext-real non negative Element of REAL
(K111 `1) / |.K111.| is V28() real ext-real Element of COMPLEX
K111 `2 is V28() real ext-real Element of REAL
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `2 is V28() real ext-real Element of REAL
x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x `1 is V28() real ext-real Element of REAL
|.x.| is V28() real ext-real non negative Element of REAL
(x `1) / |.x.| is V28() real ext-real Element of COMPLEX
x `2 is V28() real ext-real Element of REAL
cn is V28() real ext-real Element of REAL
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( cn * |.b₁.| <= b₁ `1 & 0 <= b<sub>1</sub> `2 ) } is set
q is functional Element of K19( the carrier of (TOP-REAL 2))
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₁[b₁] } is set
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₂[b₁] } is set
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( S₂[b₁] & S₁[b₁] ) } is set
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₂[b₁] } /\ { b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₁[b₁] } is set
p1 is functional Element of K19( the carrier of (TOP-REAL 2))
p is functional Element of K19( the carrier of (TOP-REAL 2))
cn is V28() real ext-real Element of REAL
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( b₁ `1 <= cn * |.b<sub>1</sub>.| & 0 <= b<sub>1</sub> `2 ) } is set
q is functional Element of K19( the carrier of (TOP-REAL 2))
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₁[b₁] } is set
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₂[b₁] } is set
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( S₂[b₁] & S₁[b₁] ) } is set
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₂[b₁] } /\ { b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₁[b₁] } is set
p1 is functional Element of K19( the carrier of (TOP-REAL 2))
p is functional Element of K19( the carrier of (TOP-REAL 2))
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | q is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | q) is set
p is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | p is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | p) is set
K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p)) is set
K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p))) is set
(cn) | q is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p1 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of ((TOP-REAL 2) | p) -valued Function-like quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p)))
cn ^2 is V28() real ext-real Element of REAL
cn * cn is V28() real ext-real set
1 - (cn ^2) is V28() real ext-real Element of REAL
sqrt (1 - (cn ^2)) is V28() real ext-real Element of REAL
|[cn,(sqrt (1 - (cn ^2)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[cn,(sqrt (1 - (cn ^2)))]| `2 is V28() real ext-real Element of REAL
VV0 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | VV0 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | VV0) is non empty set
|[cn,(sqrt (1 - (cn ^2)))]| `1 is V28() real ext-real Element of REAL
|.|[cn,(sqrt (1 - (cn ^2)))]|.| is V28() real ext-real non negative Element of REAL
(sqrt (1 - (cn ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (cn ^2))) * (sqrt (1 - (cn ^2))) is V28() real ext-real set
((sqrt (1 - (cn ^2))) ^2) + (cn ^2) is V28() real ext-real Element of REAL
sqrt (((sqrt (1 - (cn ^2))) ^2) + (cn ^2)) is V28() real ext-real Element of REAL
u2 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(|[cn,(sqrt (1 - (cn ^2)))]| `1) / |.|[cn,(sqrt (1 - (cn ^2)))]|.| is V28() real ext-real Element of COMPLEX
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( cn <= (b<sub>1</sub> `1) / |.b₁.| & 0 <= b₁ `2 & not b<sub>1</sub> = 0. (TOP-REAL 2) ) } is set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( (b<sub>1</sub> `1) / |.b₁.| <= cn & 0 <= b₁ `2 & not b<sub>1</sub> = 0. (TOP-REAL 2) ) } is set
u3 is set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `1 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `1) / |.y.| is V28() real ext-real Element of COMPLEX
y `2 is V28() real ext-real Element of REAL
u3 is set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `1 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `1) / |.y.| is V28() real ext-real Element of COMPLEX
y `2 is V28() real ext-real Element of REAL
K19( the carrier of ((TOP-REAL 2) | VV0)) is set
(TOP-REAL 2) | u2 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | u2) is non empty set
u3 is non empty Element of K19( the carrier of ((TOP-REAL 2) | VV0))
p1 | u3 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of ((TOP-REAL 2) | p) -valued Function-like Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p)))
rng (p1 | u3) is Element of K19( the carrier of ((TOP-REAL 2) | p))
K19( the carrier of ((TOP-REAL 2) | p)) is set
y is non empty Element of K19( the carrier of ((TOP-REAL 2) | VV0))
p1 | y is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of ((TOP-REAL 2) | p) -valued Function-like Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p)))
rng (p1 | y) is Element of K19( the carrier of ((TOP-REAL 2) | p))
dom p1 is Element of K19( the carrier of ((TOP-REAL 2) | q))
K19( the carrier of ((TOP-REAL 2) | q)) is set
dom (p1 | u3) is Element of K19( the carrier of ((TOP-REAL 2) | q))
((TOP-REAL 2) | VV0) | u3 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of (TOP-REAL 2) | VV0
the carrier of (((TOP-REAL 2) | VV0) | u3) is non empty set
K20( the carrier of (((TOP-REAL 2) | VV0) | u3), the carrier of ((TOP-REAL 2) | u2)) is set
K19(K20( the carrier of (((TOP-REAL 2) | VV0) | u3), the carrier of ((TOP-REAL 2) | u2))) is set
dom (p1 | y) is Element of K19( the carrier of ((TOP-REAL 2) | q))
((TOP-REAL 2) | VV0) | y is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of (TOP-REAL 2) | VV0
the carrier of (((TOP-REAL 2) | VV0) | y) is non empty set
K20( the carrier of (((TOP-REAL 2) | VV0) | y), the carrier of ((TOP-REAL 2) | u2)) is set
K19(K20( the carrier of (((TOP-REAL 2) | VV0) | y), the carrier of ((TOP-REAL 2) | u2))) is set
y is Relation-like the carrier of (((TOP-REAL 2) | VV0) | y) -defined the carrier of ((TOP-REAL 2) | u2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (((TOP-REAL 2) | VV0) | y), the carrier of ((TOP-REAL 2) | u2)))
dom y is Element of K19( the carrier of (((TOP-REAL 2) | VV0) | y))
K19( the carrier of (((TOP-REAL 2) | VV0) | y)) is set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S<sub>1</sub>[b<sub>1</sub>] } is set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S<sub>2</sub>[b<sub>1</sub>] } is set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( cn * |.b<sub>1</sub>.| <= b<sub>1</sub> `1 & 0 <= b₁ `2 ) } is set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S<sub>3</sub>[b<sub>1</sub>] } is set
x is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(cn) | x is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
rng ((cn) | x) is functional Element of K19( the carrier of (TOP-REAL 2))
q is set
dom ((cn) | x) is functional Element of K19( the carrier of (TOP-REAL 2))
K004 is set
((cn) | x) . K004 is Relation-like Function-like set
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
K111 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(cn) . K111 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(dom (cn)) /\ x is functional Element of K19( the carrier of (TOP-REAL 2))
the carrier of (TOP-REAL 2) /\ x is functional Element of K19( the carrier of (TOP-REAL 2))
K111 `1 is V28() real ext-real Element of REAL
|.K111.| is V28() real ext-real non negative Element of REAL
(K111 `1) / |.K111.| is V28() real ext-real Element of COMPLEX
((K111 `1) / |.K111.|) - cn is V28() real ext-real Element of REAL
f4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
f4 `1 is V28() real ext-real Element of REAL
|.f4.| is V28() real ext-real non negative Element of REAL
(f4 `1) / |.f4.| is V28() real ext-real Element of COMPLEX
f4 `2 is V28() real ext-real Element of REAL
f4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
f4 `1 is V28() real ext-real Element of REAL
|.f4.| is V28() real ext-real non negative Element of REAL
(f4 `1) / |.f4.| is V28() real ext-real Element of COMPLEX
f4 `2 is V28() real ext-real Element of REAL
|.K111.| ^2 is V28() real ext-real Element of REAL
|.K111.| * |.K111.| is V28() real ext-real non negative set
0 ^2 is V28() real ext-real Element of REAL
0 * 0 is Function-like functional empty V28() real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() set
1 - cn is V28() real ext-real Element of REAL
(((K111 `1) / |.K111.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
|.K111.| * ((((K111 `1) / |.K111.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((K111 `1) / |.K111.|) - cn) / (1 - cn)) * ((((K111 `1) / |.K111.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.K111.| * (sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|[(|.K111.| * ((((K111 `1) / |.K111.|) - cn) / (1 - cn))),(|.K111.| * (sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.K111.| * ((((K111 `1) / |.K111.|) - cn) / (1 - cn))),(|.K111.| * (sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2))))]| `1 is V28() real ext-real Element of REAL
K111 `2 is V28() real ext-real Element of REAL
(K111 `2) ^2 is V28() real ext-real Element of REAL
(K111 `2) * (K111 `2) is V28() real ext-real set
(K111 `1) ^2 is V28() real ext-real Element of REAL
(K111 `1) * (K111 `1) is V28() real ext-real set
0 + ((K111 `1) ^2) is V28() real ext-real Element of REAL
((K111 `1) ^2) + ((K111 `2) ^2) is V28() real ext-real Element of REAL
((K111 `1) ^2) / (|.K111.| ^2) is V28() real ext-real Element of COMPLEX
(|.K111.| ^2) / (|.K111.| ^2) is V28() real ext-real Element of COMPLEX
((K111 `1) / |.K111.|) ^2 is V28() real ext-real Element of COMPLEX
((K111 `1) / |.K111.|) * ((K111 `1) / |.K111.|) is V28() real ext-real set
- (1 - cn) is V28() real ext-real Element of REAL
- (((K111 `1) / |.K111.|) - cn) is V28() real ext-real Element of REAL
(- (1 - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
(- (((K111 `1) / |.K111.|) - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
((- (((K111 `1) / |.K111.|) - cn)) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((K111 `1) / |.K111.|) - cn)) / (1 - cn)) * ((- (((K111 `1) / |.K111.|) - cn)) / (1 - cn)) is V28() real ext-real set
1 - (((- (((K111 `1) / |.K111.|) - cn)) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
- ((((K111 `1) / |.K111.|) - cn) / (1 - cn)) is V28() real ext-real Element of COMPLEX
(- ((((K111 `1) / |.K111.|) - cn) / (1 - cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((K111 `1) / |.K111.|) - cn) / (1 - cn))) * (- ((((K111 `1) / |.K111.|) - cn) / (1 - cn))) is V28() real ext-real set
1 - ((- ((((K111 `1) / |.K111.|) - cn) / (1 - cn))) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((K111 `1) / |.K111.|) - cn)) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
(- (((K111 `1) / |.K111.|) - cn)) ^2 is V28() real ext-real Element of REAL
(- (((K111 `1) / |.K111.|) - cn)) * (- (((K111 `1) / |.K111.|) - cn)) is V28() real ext-real set
(1 - cn) ^2 is V28() real ext-real Element of REAL
(1 - cn) * (1 - cn) is V28() real ext-real set
((- (((K111 `1) / |.K111.|) - cn)) ^2) / ((1 - cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((- (((K111 `1) / |.K111.|) - cn)) ^2) / ((1 - cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((K111 `1) / |.K111.|) - cn)) ^2) / ((1 - cn) ^2))) is V28() real ext-real Element of REAL
(((K111 `1) / |.K111.|) - cn) ^2 is V28() real ext-real Element of REAL
(((K111 `1) / |.K111.|) - cn) * (((K111 `1) / |.K111.|) - cn) is V28() real ext-real set
((((K111 `1) / |.K111.|) - cn) ^2) / ((1 - cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((((K111 `1) / |.K111.|) - cn) ^2) / ((1 - cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((((K111 `1) / |.K111.|) - cn) ^2) / ((1 - cn) ^2))) is V28() real ext-real Element of REAL
|[(|.K111.| * ((((K111 `1) / |.K111.|) - cn) / (1 - cn))),(|.K111.| * (sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2))))]| `2 is V28() real ext-real Element of REAL
(|[(|.K111.| * ((((K111 `1) / |.K111.|) - cn) / (1 - cn))),(|.K111.| * (sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2))))]| `2) ^2 is V28() real ext-real Element of REAL
(|[(|.K111.| * ((((K111 `1) / |.K111.|) - cn) / (1 - cn))),(|.K111.| * (sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2))))]| `2) * (|[(|.K111.| * ((((K111 `1) / |.K111.|) - cn) / (1 - cn))),(|.K111.| * (sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2))))]| `2) is V28() real ext-real set
(sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2))) * (sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real set
(|.K111.| ^2) * ((sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2))) ^2) is V28() real ext-real Element of REAL
(|.K111.| ^2) * (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.|[(|.K111.| * ((((K111 `1) / |.K111.|) - cn) / (1 - cn))),(|.K111.| * (sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2))))]|.| is V28() real ext-real non negative Element of REAL
|.|[(|.K111.| * ((((K111 `1) / |.K111.|) - cn) / (1 - cn))),(|.K111.| * (sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2))))]|.| ^2 is V28() real ext-real Element of REAL
|.|[(|.K111.| * ((((K111 `1) / |.K111.|) - cn) / (1 - cn))),(|.K111.| * (sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2))))]|.| * |.|[(|.K111.| * ((((K111 `1) / |.K111.|) - cn) / (1 - cn))),(|.K111.| * (sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2))))]|.| is V28() real ext-real non negative set
(|[(|.K111.| * ((((K111 `1) / |.K111.|) - cn) / (1 - cn))),(|.K111.| * (sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2))))]| `1) ^2 is V28() real ext-real Element of REAL
(|[(|.K111.| * ((((K111 `1) / |.K111.|) - cn) / (1 - cn))),(|.K111.| * (sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2))))]| `1) * (|[(|.K111.| * ((((K111 `1) / |.K111.|) - cn) / (1 - cn))),(|.K111.| * (sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2))))]| `1) is V28() real ext-real set
((|[(|.K111.| * ((((K111 `1) / |.K111.|) - cn) / (1 - cn))),(|.K111.| * (sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2))))]| `1) ^2) + ((|[(|.K111.| * ((((K111 `1) / |.K111.|) - cn) / (1 - cn))),(|.K111.| * (sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2))))]| `2) ^2) is V28() real ext-real Element of REAL
T1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
T1 `1 is V28() real ext-real Element of REAL
|.T1.| is V28() real ext-real non negative Element of REAL
(T1 `1) / |.T1.| is V28() real ext-real Element of COMPLEX
T1 `2 is V28() real ext-real Element of REAL
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
dom ((cn) | x) is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | x is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | x) is non empty set
K20( the carrier of ((TOP-REAL 2) | x), the carrier of ((TOP-REAL 2) | VV0)) is set
K19(K20( the carrier of ((TOP-REAL 2) | x), the carrier of ((TOP-REAL 2) | VV0))) is set
x is functional Element of K19( the carrier of (TOP-REAL 2))
K004 is set
K111 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K111 `2 is V28() real ext-real Element of REAL
VV0 \/ u2 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
K004 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(cn) | K004 is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
rng ((cn) | K004) is functional Element of K19( the carrier of (TOP-REAL 2))
K111 is set
dom ((cn) | K004) is functional Element of K19( the carrier of (TOP-REAL 2))
f4 is set
((cn) | K004) . f4 is Relation-like Function-like set
T1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(cn) . T1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(dom (cn)) /\ K004 is functional Element of K19( the carrier of (TOP-REAL 2))
the carrier of (TOP-REAL 2) /\ K004 is functional Element of K19( the carrier of (TOP-REAL 2))
T1 `1 is V28() real ext-real Element of REAL
|.T1.| is V28() real ext-real non negative Element of REAL
(T1 `1) / |.T1.| is V28() real ext-real Element of COMPLEX
((T1 `1) / |.T1.|) - cn is V28() real ext-real Element of REAL
T2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
T2 `1 is V28() real ext-real Element of REAL
|.T2.| is V28() real ext-real non negative Element of REAL
(T2 `1) / |.T2.| is V28() real ext-real Element of COMPLEX
T2 `2 is V28() real ext-real Element of REAL
T2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
T2 `1 is V28() real ext-real Element of REAL
|.T2.| is V28() real ext-real non negative Element of REAL
(T2 `1) / |.T2.| is V28() real ext-real Element of COMPLEX
T2 `2 is V28() real ext-real Element of REAL
|.T1.| ^2 is V28() real ext-real Element of REAL
|.T1.| * |.T1.| is V28() real ext-real non negative set
0 ^2 is V28() real ext-real Element of REAL
0 * 0 is Function-like functional empty V28() real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() set
1 + cn is V28() real ext-real Element of REAL
(((T1 `1) / |.T1.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
|.T1.| * ((((T1 `1) / |.T1.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
((((T1 `1) / |.T1.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((T1 `1) / |.T1.|) - cn) / (1 + cn)) * ((((T1 `1) / |.T1.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((T1 `1) / |.T1.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((T1 `1) / |.T1.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
|.T1.| * (sqrt (1 - (((((T1 `1) / |.T1.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|[(|.T1.| * ((((T1 `1) / |.T1.|) - cn) / (1 + cn))),(|.T1.| * (sqrt (1 - (((((T1 `1) / |.T1.|) - cn) / (1 + cn)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.T1.| * ((((T1 `1) / |.T1.|) - cn) / (1 + cn))),(|.T1.| * (sqrt (1 - (((((T1 `1) / |.T1.|) - cn) / (1 + cn)) ^2))))]| `1 is V28() real ext-real Element of REAL
T1 `2 is V28() real ext-real Element of REAL
(T1 `2) ^2 is V28() real ext-real Element of REAL
(T1 `2) * (T1 `2) is V28() real ext-real set
(T1 `1) ^2 is V28() real ext-real Element of REAL
(T1 `1) * (T1 `1) is V28() real ext-real set
((T1 `1) ^2) + ((T1 `2) ^2) is V28() real ext-real Element of REAL
0 + ((T1 `1) ^2) is V28() real ext-real Element of REAL
((T1 `1) ^2) / (|.T1.| ^2) is V28() real ext-real Element of COMPLEX
(|.T1.| ^2) / (|.T1.| ^2) is V28() real ext-real Element of COMPLEX
((T1 `1) / |.T1.|) ^2 is V28() real ext-real Element of COMPLEX
((T1 `1) / |.T1.|) * ((T1 `1) / |.T1.|) is V28() real ext-real set
(- 1) - cn is V28() real ext-real Element of REAL
- (1 + cn) is V28() real ext-real Element of REAL
(- (1 + cn)) / (1 + cn) is V28() real ext-real Element of COMPLEX
- ((((T1 `1) / |.T1.|) - cn) / (1 + cn)) is V28() real ext-real Element of COMPLEX
(- ((((T1 `1) / |.T1.|) - cn) / (1 + cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((T1 `1) / |.T1.|) - cn) / (1 + cn))) * (- ((((T1 `1) / |.T1.|) - cn) / (1 + cn))) is V28() real ext-real set
1 - ((- ((((T1 `1) / |.T1.|) - cn) / (1 + cn))) ^2) is V28() real ext-real Element of REAL
- (((T1 `1) / |.T1.|) - cn) is V28() real ext-real Element of REAL
(- (((T1 `1) / |.T1.|) - cn)) / (1 + cn) is V28() real ext-real Element of COMPLEX
((- (((T1 `1) / |.T1.|) - cn)) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((T1 `1) / |.T1.|) - cn)) / (1 + cn)) * ((- (((T1 `1) / |.T1.|) - cn)) / (1 + cn)) is V28() real ext-real set
1 - (((- (((T1 `1) / |.T1.|) - cn)) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((T1 `1) / |.T1.|) - cn)) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
(- (((T1 `1) / |.T1.|) - cn)) ^2 is V28() real ext-real Element of REAL
(- (((T1 `1) / |.T1.|) - cn)) * (- (((T1 `1) / |.T1.|) - cn)) is V28() real ext-real set
(1 + cn) ^2 is V28() real ext-real Element of REAL
(1 + cn) * (1 + cn) is V28() real ext-real set
((- (((T1 `1) / |.T1.|) - cn)) ^2) / ((1 + cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((- (((T1 `1) / |.T1.|) - cn)) ^2) / ((1 + cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((T1 `1) / |.T1.|) - cn)) ^2) / ((1 + cn) ^2))) is V28() real ext-real Element of REAL
(((T1 `1) / |.T1.|) - cn) ^2 is V28() real ext-real Element of REAL
(((T1 `1) / |.T1.|) - cn) * (((T1 `1) / |.T1.|) - cn) is V28() real ext-real set
((((T1 `1) / |.T1.|) - cn) ^2) / ((1 + cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((((T1 `1) / |.T1.|) - cn) ^2) / ((1 + cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((((T1 `1) / |.T1.|) - cn) ^2) / ((1 + cn) ^2))) is V28() real ext-real Element of REAL
|[(|.T1.| * ((((T1 `1) / |.T1.|) - cn) / (1 + cn))),(|.T1.| * (sqrt (1 - (((((T1 `1) / |.T1.|) - cn) / (1 + cn)) ^2))))]| `2 is V28() real ext-real Element of REAL
(|[(|.T1.| * ((((T1 `1) / |.T1.|) - cn) / (1 + cn))),(|.T1.| * (sqrt (1 - (((((T1 `1) / |.T1.|) - cn) / (1 + cn)) ^2))))]| `2) ^2 is V28() real ext-real Element of REAL
(|[(|.T1.| * ((((T1 `1) / |.T1.|) - cn) / (1 + cn))),(|.T1.| * (sqrt (1 - (((((T1 `1) / |.T1.|) - cn) / (1 + cn)) ^2))))]| `2) * (|[(|.T1.| * ((((T1 `1) / |.T1.|) - cn) / (1 + cn))),(|.T1.| * (sqrt (1 - (((((T1 `1) / |.T1.|) - cn) / (1 + cn)) ^2))))]| `2) is V28() real ext-real set
(sqrt (1 - (((((T1 `1) / |.T1.|) - cn) / (1 + cn)) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((T1 `1) / |.T1.|) - cn) / (1 + cn)) ^2))) * (sqrt (1 - (((((T1 `1) / |.T1.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real set
(|.T1.| ^2) * ((sqrt (1 - (((((T1 `1) / |.T1.|) - cn) / (1 + cn)) ^2))) ^2) is V28() real ext-real Element of REAL
(|.T1.| ^2) * (1 - (((((T1 `1) / |.T1.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
|.|[(|.T1.| * ((((T1 `1) / |.T1.|) - cn) / (1 + cn))),(|.T1.| * (sqrt (1 - (((((T1 `1) / |.T1.|) - cn) / (1 + cn)) ^2))))]|.| is V28() real ext-real non negative Element of REAL
|.|[(|.T1.| * ((((T1 `1) / |.T1.|) - cn) / (1 + cn))),(|.T1.| * (sqrt (1 - (((((T1 `1) / |.T1.|) - cn) / (1 + cn)) ^2))))]|.| ^2 is V28() real ext-real Element of REAL
|.|[(|.T1.| * ((((T1 `1) / |.T1.|) - cn) / (1 + cn))),(|.T1.| * (sqrt (1 - (((((T1 `1) / |.T1.|) - cn) / (1 + cn)) ^2))))]|.| * |.|[(|.T1.| * ((((T1 `1) / |.T1.|) - cn) / (1 + cn))),(|.T1.| * (sqrt (1 - (((((T1 `1) / |.T1.|) - cn) / (1 + cn)) ^2))))]|.| is V28() real ext-real non negative set
(|[(|.T1.| * ((((T1 `1) / |.T1.|) - cn) / (1 + cn))),(|.T1.| * (sqrt (1 - (((((T1 `1) / |.T1.|) - cn) / (1 + cn)) ^2))))]| `1) ^2 is V28() real ext-real Element of REAL
(|[(|.T1.| * ((((T1 `1) / |.T1.|) - cn) / (1 + cn))),(|.T1.| * (sqrt (1 - (((((T1 `1) / |.T1.|) - cn) / (1 + cn)) ^2))))]| `1) * (|[(|.T1.| * ((((T1 `1) / |.T1.|) - cn) / (1 + cn))),(|.T1.| * (sqrt (1 - (((((T1 `1) / |.T1.|) - cn) / (1 + cn)) ^2))))]| `1) is V28() real ext-real set
((|[(|.T1.| * ((((T1 `1) / |.T1.|) - cn) / (1 + cn))),(|.T1.| * (sqrt (1 - (((((T1 `1) / |.T1.|) - cn) / (1 + cn)) ^2))))]| `1) ^2) + ((|[(|.T1.| * ((((T1 `1) / |.T1.|) - cn) / (1 + cn))),(|.T1.| * (sqrt (1 - (((((T1 `1) / |.T1.|) - cn) / (1 + cn)) ^2))))]| `2) ^2) is V28() real ext-real Element of REAL
h is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
h `1 is V28() real ext-real Element of REAL
|.h.| is V28() real ext-real non negative Element of REAL
(h `1) / |.h.| is V28() real ext-real Element of COMPLEX
h `2 is V28() real ext-real Element of REAL
dom ((cn) | K004) is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | K004 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | K004) is non empty set
K20( the carrier of ((TOP-REAL 2) | K004), the carrier of ((TOP-REAL 2) | VV0)) is set
K19(K20( the carrier of ((TOP-REAL 2) | K004), the carrier of ((TOP-REAL 2) | VV0))) is set
K111 is Relation-like the carrier of ((TOP-REAL 2) | K004) -defined the carrier of ((TOP-REAL 2) | VV0) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | K004), the carrier of ((TOP-REAL 2) | VV0)))
[#] (((TOP-REAL 2) | VV0) | y) is non empty non proper closed Element of K19( the carrier of (((TOP-REAL 2) | VV0) | y))
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₄[b₁] } is set
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( b₁ `1 <= cn * |.b<sub>1</sub>.| & 0 <= b<sub>1</sub> `2 ) } is set
T2 is functional Element of K19( the carrier of (TOP-REAL 2))
T2 /\ VV0 is functional Element of K19( the carrier of (TOP-REAL 2))
h is set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `1 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
cn * |.y.| is V28() real ext-real Element of REAL
y `2 is V28() real ext-real Element of REAL
(y `1) / |.y.| is V28() real ext-real Element of COMPLEX
(cn * |.y.|) / |.y.| is V28() real ext-real Element of COMPLEX
c<sub>23</sub> is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
c<sub>23</sub> `2 is V28() real ext-real Element of REAL
c₂₃ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
c₂₃ `2 is V28() real ext-real Element of REAL
q4 is Relation-like the carrier of (((TOP-REAL 2) | VV0) | u3) -defined the carrier of ((TOP-REAL 2) | u2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (((TOP-REAL 2) | VV0) | u3), the carrier of ((TOP-REAL 2) | u2)))
q is Relation-like the carrier of ((TOP-REAL 2) | x) -defined the carrier of ((TOP-REAL 2) | VV0) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | x), the carrier of ((TOP-REAL 2) | VV0)))
[#] ((TOP-REAL 2) | VV0) is non empty non proper closed Element of K19( the carrier of ((TOP-REAL 2) | VV0))
h is set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `1 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `1) / |.y.| is V28() real ext-real Element of COMPLEX
y `2 is V28() real ext-real Element of REAL
((y `1) / |.y.|) * |.y.| is V28() real ext-real Element of REAL
cn * |.y.| is V28() real ext-real Element of REAL
T2 /\ ([#] ((TOP-REAL 2) | VV0)) is Element of K19( the carrier of ((TOP-REAL 2) | VV0))
x /\ VV0 is functional Element of K19( the carrier of (TOP-REAL 2))
h is set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.y.| is V28() real ext-real non negative Element of REAL
cn * |.y.| is V28() real ext-real Element of REAL
y `1 is V28() real ext-real Element of REAL
y `2 is V28() real ext-real Element of REAL
(cn * |.y.|) / |.y.| is V28() real ext-real Element of COMPLEX
(y `1) / |.y.| is V28() real ext-real Element of COMPLEX
c₂₃ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
c₂₃ `2 is V28() real ext-real Element of REAL
c<sub>23</sub> is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
c<sub>23</sub> `2 is V28() real ext-real Element of REAL
h is set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `1 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `1) / |.y.| is V28() real ext-real Element of COMPLEX
y `2 is V28() real ext-real Element of REAL
cn * |.y.| is V28() real ext-real Element of REAL
((y `1) / |.y.|) * |.y.| is V28() real ext-real Element of REAL
x /\ ([#] ((TOP-REAL 2) | VV0)) is Element of K19( the carrier of ((TOP-REAL 2) | VV0))
[#] (((TOP-REAL 2) | VV0) | u3) is non empty non proper closed Element of K19( the carrier of (((TOP-REAL 2) | VV0) | u3))
K19( the carrier of (((TOP-REAL 2) | VV0) | u3)) is set
([#] (((TOP-REAL 2) | VV0) | u3)) /\ ([#] (((TOP-REAL 2) | VV0) | y)) is Element of K19( the carrier of (((TOP-REAL 2) | VV0) | y))
h is set
q4 . h is set
y . h is set
p1 . h is set
u3 \/ y is non empty Element of K19( the carrier of ((TOP-REAL 2) | VV0))
h is set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `2 is V28() real ext-real Element of REAL
y `1 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `1) / |.y.| is V28() real ext-real Element of COMPLEX
y `1 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `1) / |.y.| is V28() real ext-real Element of COMPLEX
y `1 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `1) / |.y.| is V28() real ext-real Element of COMPLEX
([#] (((TOP-REAL 2) | VV0) | u3)) \/ ([#] (((TOP-REAL 2) | VV0) | y)) is non empty set
K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of ((TOP-REAL 2) | u2)) is set
K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of ((TOP-REAL 2) | u2))) is set
q4 +* y is Relation-like Function-like set
h is Relation-like the carrier of ((TOP-REAL 2) | VV0) -defined the carrier of ((TOP-REAL 2) | u2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of ((TOP-REAL 2) | u2)))
dom h is Element of K19( the carrier of ((TOP-REAL 2) | VV0))
dom q4 is Element of K19( the carrier of (((TOP-REAL 2) | VV0) | u3))
y is set
h . y is set
p1 . y is set
(dom q4) \/ (dom y) is set
q4 . y is set
(dom q4) \/ (dom y) is set
y . y is set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( b<sub>1</sub> `2 <= 0 & not b₁ = 0. (TOP-REAL 2) ) } is set
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | q is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | q) is set
p is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | p is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | p) is set
K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p)) is set
K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p))) is set
(cn) | q is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p1 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of ((TOP-REAL 2) | p) -valued Function-like quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p)))
cn ^2 is V28() real ext-real Element of REAL
cn * cn is V28() real ext-real set
1 - (cn ^2) is V28() real ext-real Element of REAL
sqrt (1 - (cn ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (cn ^2))) is V28() real ext-real Element of REAL
|[cn,(- (sqrt (1 - (cn ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[cn,(- (sqrt (1 - (cn ^2))))]| `2 is V28() real ext-real Element of REAL
- (- (sqrt (1 - (cn ^2)))) is V28() real ext-real Element of REAL
VV0 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
u2 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
u3 is set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `2 is V28() real ext-real Element of REAL
(TOP-REAL 2) | VV0 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | VV0) is non empty set
(TOP-REAL 2) | u2 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | u2) is non empty set
K19( the carrier of ((TOP-REAL 2) | u2)) is set
K19( the carrier of ((TOP-REAL 2) | VV0)) is set
u3 is Element of the carrier of ((TOP-REAL 2) | VV0)
p1 . u3 is set
y is Element of K19( the carrier of ((TOP-REAL 2) | u2))
[#] ((TOP-REAL 2) | u2) is non empty non proper closed Element of K19( the carrier of ((TOP-REAL 2) | u2))
q4 is functional Element of K19( the carrier of (TOP-REAL 2))
q4 /\ ([#] ((TOP-REAL 2) | u2)) is Element of K19( the carrier of ((TOP-REAL 2) | u2))
[#] ((TOP-REAL 2) | VV0) is non empty non proper closed Element of K19( the carrier of ((TOP-REAL 2) | VV0))
q4 /\ ([#] ((TOP-REAL 2) | VV0)) is Element of K19( the carrier of ((TOP-REAL 2) | VV0))
(cn) . u3 is Relation-like Function-like set
y is Element of K19( the carrier of ((TOP-REAL 2) | VV0))
p1 .: y is Element of K19( the carrier of ((TOP-REAL 2) | p))
K19( the carrier of ((TOP-REAL 2) | p)) is set
x is set
dom p1 is Element of K19( the carrier of ((TOP-REAL 2) | q))
K19( the carrier of ((TOP-REAL 2) | q)) is set
x is set
p1 . x is set
K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of ((TOP-REAL 2) | u2)) is set
K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of ((TOP-REAL 2) | u2))) is set
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q `2 is V28() real ext-real Element of REAL
p1 . q is set
(cn) . q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x `2 is V28() real ext-real Element of REAL
(cn) . x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( S<sub>1</sub>[b<sub>1</sub>] & not b<sub>1</sub> = 0. (TOP-REAL 2) ) } is set
p is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | p is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | p) is set
K19( the carrier of ((TOP-REAL 2) | p)) is set
p1 is Element of K19( the carrier of ((TOP-REAL 2) | p))
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S<sub>1</sub>[b<sub>1</sub>] } is set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S<sub>1</sub>[b<sub>1</sub>] } /\ (NonZero (TOP-REAL 2)) is functional Element of K19( the carrier of (TOP-REAL 2))
p2 is functional Element of K19( the carrier of (TOP-REAL 2))
[#] ((TOP-REAL 2) | p) is non proper closed Element of K19( the carrier of ((TOP-REAL 2) | p))
p2 /\ ([#] ((TOP-REAL 2) | p)) is Element of K19( the carrier of ((TOP-REAL 2) | p))
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( S<sub>1</sub>[b<sub>1</sub>] & not b<sub>1</sub> = 0. (TOP-REAL 2) ) } is set
p is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | p is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | p) is set
K19( the carrier of ((TOP-REAL 2) | p)) is set
p1 is Element of K19( the carrier of ((TOP-REAL 2) | p))
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S<sub>1</sub>[b<sub>1</sub>] } is set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S<sub>1</sub>[b<sub>1</sub>] } /\ (NonZero (TOP-REAL 2)) is functional Element of K19( the carrier of (TOP-REAL 2))
p2 is functional Element of K19( the carrier of (TOP-REAL 2))
[#] ((TOP-REAL 2) | p) is non proper closed Element of K19( the carrier of ((TOP-REAL 2) | p))
p2 /\ ([#] ((TOP-REAL 2) | p)) is Element of K19( the carrier of ((TOP-REAL 2) | p))
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | q is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | q) is set
K19( the carrier of ((TOP-REAL 2) | q)) is set
p is Element of K19( the carrier of ((TOP-REAL 2) | q))
((TOP-REAL 2) | q) | p is strict TopSpace-like T_0 T_1 T_2 SubSpace of (TOP-REAL 2) | q
the carrier of (((TOP-REAL 2) | q) | p) is set
K20( the carrier of (((TOP-REAL 2) | q) | p), the carrier of ((TOP-REAL 2) | q)) is set
K19(K20( the carrier of (((TOP-REAL 2) | q) | p), the carrier of ((TOP-REAL 2) | q))) is set
(cn) | p is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p1 is Relation-like the carrier of (((TOP-REAL 2) | q) | p) -defined the carrier of ((TOP-REAL 2) | q) -valued Function-like quasi_total Element of K19(K20( the carrier of (((TOP-REAL 2) | q) | p), the carrier of ((TOP-REAL 2) | q)))
q3 is set
VV0 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
VV0 `2 is V28() real ext-real Element of REAL
VV0 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
VV0 `2 is V28() real ext-real Element of REAL
p2 is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | p2 is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | q is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | q) is set
K19( the carrier of ((TOP-REAL 2) | q)) is set
p is Element of K19( the carrier of ((TOP-REAL 2) | q))
((TOP-REAL 2) | q) | p is strict TopSpace-like T_0 T_1 T_2 SubSpace of (TOP-REAL 2) | q
the carrier of (((TOP-REAL 2) | q) | p) is set
K20( the carrier of (((TOP-REAL 2) | q) | p), the carrier of ((TOP-REAL 2) | q)) is set
K19(K20( the carrier of (((TOP-REAL 2) | q) | p), the carrier of ((TOP-REAL 2) | q))) is set
(cn) | p is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p1 is Relation-like the carrier of (((TOP-REAL 2) | q) | p) -defined the carrier of ((TOP-REAL 2) | q) -valued Function-like quasi_total Element of K19(K20( the carrier of (((TOP-REAL 2) | q) | p), the carrier of ((TOP-REAL 2) | q)))
q3 is set
VV0 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
VV0 `2 is V28() real ext-real Element of REAL
VV0 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
VV0 `2 is V28() real ext-real Element of REAL
p2 is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | p2 is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(cn) . q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.((cn) . q).| is V28() real ext-real non negative Element of REAL
|.q.| is V28() real ext-real non negative Element of REAL
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `1 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `1) / |.p2.| is V28() real ext-real Element of COMPLEX
p2 `2 is V28() real ext-real Element of REAL
(cn) . p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((p2 `1) / |.p2.|) - cn is V28() real ext-real Element of REAL
1 - cn is V28() real ext-real Element of REAL
(((p2 `1) / |.p2.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p2 `1) / |.p2.|) - cn) / (1 - cn)) * ((((p2 `1) / |.p2.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 - cn))),(|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q3 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q3 `2 is V28() real ext-real Element of REAL
q3 `1 is V28() real ext-real Element of REAL
|.p2.| ^2 is V28() real ext-real Element of REAL
|.p2.| * |.p2.| is V28() real ext-real non negative set
(p2 `1) ^2 is V28() real ext-real Element of REAL
(p2 `1) * (p2 `1) is V28() real ext-real set
(p2 `2) ^2 is V28() real ext-real Element of REAL
(p2 `2) * (p2 `2) is V28() real ext-real set
((p2 `1) ^2) + ((p2 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p2 `1) ^2) is V28() real ext-real Element of REAL
((p2 `1) ^2) / (|.p2.| ^2) is V28() real ext-real Element of COMPLEX
(|.p2.| ^2) / (|.p2.| ^2) is V28() real ext-real Element of COMPLEX
((p2 `1) / |.p2.|) ^2 is V28() real ext-real Element of COMPLEX
((p2 `1) / |.p2.|) * ((p2 `1) / |.p2.|) is V28() real ext-real set
(1 - cn) " is V28() real ext-real Element of REAL
(((p2 `1) / |.p2.|) - cn) * ((1 - cn) ") is V28() real ext-real Element of REAL
(((p2 `1) / |.p2.|) - cn) * 0 is V28() real ext-real Element of REAL
|.p2.| * 0 is Function-like functional empty V28() real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() Element of REAL
|.p2.| * 1 is V28() real ext-real non negative Element of REAL
|[(|.p2.| * 0),(|.p2.| * 1)]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[0,|.p2.|]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((cn) . p2) `2 is V28() real ext-real Element of REAL
((cn) . p2) `1 is V28() real ext-real Element of REAL
0 ^2 is V28() real ext-real Element of REAL
0 * 0 is Function-like functional empty V28() real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() set
(|.p2.| ^2) + (0 ^2) is V28() real ext-real Element of REAL
sqrt ((|.p2.| ^2) + (0 ^2)) is V28() real ext-real Element of REAL
- (1 - cn) is V28() real ext-real Element of REAL
- (((p2 `1) / |.p2.|) - cn) is V28() real ext-real Element of REAL
(- (1 - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
(- (((p2 `1) / |.p2.|) - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
((- (((p2 `1) / |.p2.|) - cn)) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((p2 `1) / |.p2.|) - cn)) / (1 - cn)) * ((- (((p2 `1) / |.p2.|) - cn)) / (1 - cn)) is V28() real ext-real set
1 - (((- (((p2 `1) / |.p2.|) - cn)) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
- ((((p2 `1) / |.p2.|) - cn) / (1 - cn)) is V28() real ext-real Element of COMPLEX
(- ((((p2 `1) / |.p2.|) - cn) / (1 - cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((p2 `1) / |.p2.|) - cn) / (1 - cn))) * (- ((((p2 `1) / |.p2.|) - cn) / (1 - cn))) is V28() real ext-real set
1 - ((- ((((p2 `1) / |.p2.|) - cn) / (1 - cn))) ^2) is V28() real ext-real Element of REAL
(q3 `2) ^2 is V28() real ext-real Element of REAL
(q3 `2) * (q3 `2) is V28() real ext-real set
(sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2))) * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real set
(|.p2.| ^2) * ((sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2))) ^2) is V28() real ext-real Element of REAL
(|.p2.| ^2) * (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.q3.| is V28() real ext-real non negative Element of REAL
|.q3.| ^2 is V28() real ext-real Element of REAL
|.q3.| * |.q3.| is V28() real ext-real non negative set
(q3 `1) ^2 is V28() real ext-real Element of REAL
(q3 `1) * (q3 `1) is V28() real ext-real set
((q3 `1) ^2) + ((q3 `2) ^2) is V28() real ext-real Element of REAL
sqrt (|.q3.| ^2) is V28() real ext-real Element of REAL
(p2 `1) / |.q.| is V28() real ext-real Element of COMPLEX
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `1 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `1) / |.p2.| is V28() real ext-real Element of COMPLEX
p2 `2 is V28() real ext-real Element of REAL
|.p2.| ^2 is V28() real ext-real Element of REAL
|.p2.| * |.p2.| is V28() real ext-real non negative set
((p2 `1) / |.p2.|) - cn is V28() real ext-real Element of REAL
(p2 `1) ^2 is V28() real ext-real Element of REAL
(p2 `1) * (p2 `1) is V28() real ext-real set
(p2 `2) ^2 is V28() real ext-real Element of REAL
(p2 `2) * (p2 `2) is V28() real ext-real set
((p2 `1) ^2) + ((p2 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p2 `1) ^2) is V28() real ext-real Element of REAL
((p2 `1) ^2) / (|.p2.| ^2) is V28() real ext-real Element of COMPLEX
(|.p2.| ^2) / (|.p2.| ^2) is V28() real ext-real Element of COMPLEX
((p2 `1) / |.p2.|) ^2 is V28() real ext-real Element of COMPLEX
((p2 `1) / |.p2.|) * ((p2 `1) / |.p2.|) is V28() real ext-real set
(- 1) - cn is V28() real ext-real Element of REAL
(cn) . p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
1 + cn is V28() real ext-real Element of REAL
(((p2 `1) / |.p2.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p2 `1) / |.p2.|) - cn) / (1 + cn)) * ((((p2 `1) / |.p2.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 + cn))),(|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q3 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q3 `2 is V28() real ext-real Element of REAL
q3 `1 is V28() real ext-real Element of REAL
(1 + cn) " is V28() real ext-real Element of REAL
(((p2 `1) / |.p2.|) - cn) * ((1 + cn) ") is V28() real ext-real Element of REAL
(((p2 `1) / |.p2.|) - cn) * 0 is V28() real ext-real Element of REAL
((cn) . p2) `2 is V28() real ext-real Element of REAL
((cn) . p2) `1 is V28() real ext-real Element of REAL
0 ^2 is V28() real ext-real Element of REAL
0 * 0 is Function-like functional empty V28() real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() set
(|.p2.| ^2) + (0 ^2) is V28() real ext-real Element of REAL
sqrt ((|.p2.| ^2) + (0 ^2)) is V28() real ext-real Element of REAL
- (1 + cn) is V28() real ext-real Element of REAL
(- (1 + cn)) / (1 + cn) is V28() real ext-real Element of COMPLEX
(q3 `2) ^2 is V28() real ext-real Element of REAL
(q3 `2) * (q3 `2) is V28() real ext-real set
(sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2))) * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real set
(|.p2.| ^2) * ((sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2))) ^2) is V28() real ext-real Element of REAL
(|.p2.| ^2) * (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
|.q3.| is V28() real ext-real non negative Element of REAL
|.q3.| ^2 is V28() real ext-real Element of REAL
|.q3.| * |.q3.| is V28() real ext-real non negative set
(q3 `1) ^2 is V28() real ext-real Element of REAL
(q3 `1) * (q3 `1) is V28() real ext-real set
((q3 `1) ^2) + ((q3 `2) ^2) is V28() real ext-real Element of REAL
sqrt (|.q3.| ^2) is V28() real ext-real Element of REAL
(p2 `1) / |.q.| is V28() real ext-real Element of COMPLEX
- (1 + cn) is V28() real ext-real Element of REAL
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `2 is V28() real ext-real Element of REAL
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `1 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `1) / |.p2.| is V28() real ext-real Element of COMPLEX
p2 `2 is V28() real ext-real Element of REAL
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is set
p is set
(cn) . q is Relation-like Function-like set
p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 `2 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
|.p1.| ^2 is V28() real ext-real Element of REAL
|.p1.| * |.p1.| is V28() real ext-real non negative set
p1 `1 is V28() real ext-real Element of REAL
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((p1 `1) / |.p1.|) - cn is V28() real ext-real Element of REAL
1 + cn is V28() real ext-real Element of REAL
(((p1 `1) / |.p1.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p1 `1) / |.p1.|) - cn) / (1 + cn)) * ((((p1 `1) / |.p1.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn))),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `2 is V28() real ext-real Element of REAL
(p1 `1) ^2 is V28() real ext-real Element of REAL
(p1 `1) * (p1 `1) is V28() real ext-real set
(p1 `2) ^2 is V28() real ext-real Element of REAL
(p1 `2) * (p1 `2) is V28() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p1 `1) ^2) is V28() real ext-real Element of REAL
(|.p1.| ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
((p1 `1) ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
((p1 `1) / |.p1.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `1) / |.p1.|) * ((p1 `1) / |.p1.|) is V28() real ext-real set
(- 1) - cn is V28() real ext-real Element of REAL
(- 1) * (1 + cn) is V28() real ext-real Element of REAL
((- 1) * (1 + cn)) / (1 + cn) is V28() real ext-real Element of COMPLEX
p1 `1 is V28() real ext-real Element of REAL
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((p1 `1) / |.p1.|) - cn is V28() real ext-real Element of REAL
1 - cn is V28() real ext-real Element of REAL
(((p1 `1) / |.p1.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p1 `1) / |.p1.|) - cn) / (1 - cn)) * ((((p1 `1) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn))),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `2 is V28() real ext-real Element of REAL
(p1 `1) ^2 is V28() real ext-real Element of REAL
(p1 `1) * (p1 `1) is V28() real ext-real set
(p1 `2) ^2 is V28() real ext-real Element of REAL
(p1 `2) * (p1 `2) is V28() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p1 `1) ^2) is V28() real ext-real Element of REAL
(|.p1.| ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
((p1 `1) ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
((p1 `1) / |.p1.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `1) / |.p1.|) * ((p1 `1) / |.p1.|) is V28() real ext-real set
(1 - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
- (1 - cn) is V28() real ext-real Element of REAL
cn - cn is V28() real ext-real Element of REAL
(- 1) * (1 - cn) is V28() real ext-real Element of REAL
((- 1) * (1 - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
p1 `1 is V28() real ext-real Element of REAL
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is set
p is set
(cn) . q is Relation-like Function-like set
p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 `2 is V28() real ext-real Element of REAL
|[0,1]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[0,1]| `2 is V28() real ext-real Element of REAL
|[0,(- 1)]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p is V28() real ext-real Element of REAL
(p) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p1 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
p1 ` is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | p1 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | p1) is non empty set
K20( the carrier of ((TOP-REAL 2) | p1), the carrier of ((TOP-REAL 2) | p1)) is set
K19(K20( the carrier of ((TOP-REAL 2) | p1), the carrier of ((TOP-REAL 2) | p1))) is set
(p) | p1 is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is functional Element of K19( the carrier of (TOP-REAL 2))
q ` is functional Element of K19( the carrier of (TOP-REAL 2))
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( S₁[b₁] & not b₁ = 0. (TOP-REAL 2) ) } is set
K19( the carrier of ((TOP-REAL 2) | p1)) is set
p2 is non empty Element of K19( the carrier of ((TOP-REAL 2) | p1))
((TOP-REAL 2) | p1) | p2 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of (TOP-REAL 2) | p1
the carrier of (((TOP-REAL 2) | p1) | p2) is non empty set
(p) | p2 is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
rng ((p) | p2) is functional Element of K19( the carrier of (TOP-REAL 2))
q3 is set
dom ((p) | p2) is functional Element of K19( the carrier of (TOP-REAL 2))
VV0 is set
((p) | p2) . VV0 is Relation-like Function-like set
dom (p) is functional Element of K19( the carrier of (TOP-REAL 2))
(dom (p)) /\ p2 is Element of K19( the carrier of ((TOP-REAL 2) | p1))
u2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(p) . u2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q3 is set
VV0 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
VV0 `2 is V28() real ext-real Element of REAL
|[0,(- 1)]| `2 is V28() real ext-real Element of REAL
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( S₂[b₁] & not b₁ = 0. (TOP-REAL 2) ) } is set
q3 is non empty Element of K19( the carrier of ((TOP-REAL 2) | p1))
dom ((p) | p2) is functional Element of K19( the carrier of (TOP-REAL 2))
dom (p) is functional Element of K19( the carrier of (TOP-REAL 2))
(dom (p)) /\ p2 is Element of K19( the carrier of ((TOP-REAL 2) | p1))
the carrier of (TOP-REAL 2) /\ p2 is Element of K19( the carrier of ((TOP-REAL 2) | p1))
K20( the carrier of (((TOP-REAL 2) | p1) | p2), the carrier of ((TOP-REAL 2) | p1)) is set
K19(K20( the carrier of (((TOP-REAL 2) | p1) | p2), the carrier of ((TOP-REAL 2) | p1))) is set
((TOP-REAL 2) | p1) | q3 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of (TOP-REAL 2) | p1
the carrier of (((TOP-REAL 2) | p1) | q3) is non empty set
(p) | q3 is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
rng ((p) | q3) is functional Element of K19( the carrier of (TOP-REAL 2))
u2 is set
dom ((p) | q3) is functional Element of K19( the carrier of (TOP-REAL 2))
u3 is set
((p) | q3) . u3 is Relation-like Function-like set
(dom (p)) /\ q3 is Element of K19( the carrier of ((TOP-REAL 2) | p1))
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(p) . y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
u2 is set
u3 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
u3 `2 is V28() real ext-real Element of REAL
dom ((p) | q3) is functional Element of K19( the carrier of (TOP-REAL 2))
(dom (p)) /\ q3 is Element of K19( the carrier of ((TOP-REAL 2) | p1))
the carrier of (TOP-REAL 2) /\ q3 is Element of K19( the carrier of ((TOP-REAL 2) | p1))
K20( the carrier of (((TOP-REAL 2) | p1) | q3), the carrier of ((TOP-REAL 2) | p1)) is set
K19(K20( the carrier of (((TOP-REAL 2) | p1) | q3), the carrier of ((TOP-REAL 2) | p1))) is set
[#] (((TOP-REAL 2) | p1) | q3) is non empty non proper closed Element of K19( the carrier of (((TOP-REAL 2) | p1) | q3))
K19( the carrier of (((TOP-REAL 2) | p1) | q3)) is set
p2 \/ q3 is non empty Element of K19( the carrier of ((TOP-REAL 2) | p1))
u3 is set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `2 is V28() real ext-real Element of REAL
VV0 is Relation-like the carrier of (((TOP-REAL 2) | p1) | p2) -defined the carrier of ((TOP-REAL 2) | p1) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (((TOP-REAL 2) | p1) | p2), the carrier of ((TOP-REAL 2) | p1)))
dom VV0 is Element of K19( the carrier of (((TOP-REAL 2) | p1) | p2))
K19( the carrier of (((TOP-REAL 2) | p1) | p2)) is set
[#] (((TOP-REAL 2) | p1) | p2) is non empty non proper closed Element of K19( the carrier of (((TOP-REAL 2) | p1) | p2))
([#] (((TOP-REAL 2) | p1) | p2)) /\ ([#] (((TOP-REAL 2) | p1) | q3)) is Element of K19( the carrier of (((TOP-REAL 2) | p1) | q3))
u2 is Relation-like the carrier of (((TOP-REAL 2) | p1) | q3) -defined the carrier of ((TOP-REAL 2) | p1) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (((TOP-REAL 2) | p1) | q3), the carrier of ((TOP-REAL 2) | p1)))
u3 is set
VV0 . u3 is set
u2 . u3 is set
(p) . u3 is Relation-like Function-like set
[#] ((TOP-REAL 2) | p1) is non empty non proper closed Element of K19( the carrier of ((TOP-REAL 2) | p1))
([#] (((TOP-REAL 2) | p1) | p2)) \/ ([#] (((TOP-REAL 2) | p1) | q3)) is non empty set
VV0 +* u2 is Relation-like Function-like set
u3 is Relation-like the carrier of ((TOP-REAL 2) | p1) -defined the carrier of ((TOP-REAL 2) | p1) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | p1), the carrier of ((TOP-REAL 2) | p1)))
dom u3 is Element of K19( the carrier of ((TOP-REAL 2) | p1))
dom u2 is Element of K19( the carrier of (((TOP-REAL 2) | p1) | q3))
y is set
u3 . y is set
((p) | p1) . y is Relation-like Function-like set
(p1 `) ` is functional Element of K19( the carrier of (TOP-REAL 2))
q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((p) | p1) . q4 is Relation-like Function-like set
(p) . q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
VV0 . q4 is set
u3 . q4 is set
u2 +* VV0 is Relation-like Function-like set
(u2 +* VV0) . q4 is set
q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q4 `2 is V28() real ext-real Element of REAL
((p) | p1) . q4 is Relation-like Function-like set
(p) . q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
u2 . q4 is set
dom ((p) | p1) is functional Element of K19( the carrier of (TOP-REAL 2))
the carrier of (TOP-REAL 2) /\ p1 is functional Element of K19( the carrier of (TOP-REAL 2))
q is V28() real ext-real Element of REAL
(q) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p . (0. (TOP-REAL 2)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | cn is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | cn) is non empty set
p1 is Element of the carrier of ((TOP-REAL 2) | cn)
p . p1 is Relation-like Function-like set
[#] ((TOP-REAL 2) | cn) is non empty non proper closed Element of K19( the carrier of ((TOP-REAL 2) | cn))
K19( the carrier of ((TOP-REAL 2) | cn)) is set
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `1 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `1) / |.p2.| is V28() real ext-real Element of COMPLEX
p2 `2 is V28() real ext-real Element of REAL
((p2 `1) / |.p2.|) - q is V28() real ext-real Element of REAL
1 - q is V28() real ext-real Element of REAL
(((p2 `1) / |.p2.|) - q) / (1 - q) is V28() real ext-real Element of COMPLEX
|.p2.| * ((((p2 `1) / |.p2.|) - q) / (1 - q)) is V28() real ext-real Element of REAL
((((p2 `1) / |.p2.|) - q) / (1 - q)) ^2 is V28() real ext-real Element of COMPLEX
((((p2 `1) / |.p2.|) - q) / (1 - q)) * ((((p2 `1) / |.p2.|) - q) / (1 - q)) is V28() real ext-real set
1 - (((((p2 `1) / |.p2.|) - q) / (1 - q)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p2 `1) / |.p2.|) - q) / (1 - q)) ^2)) is V28() real ext-real Element of REAL
|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - q) / (1 - q)) ^2))) is V28() real ext-real Element of REAL
|[(|.p2.| * ((((p2 `1) / |.p2.|) - q) / (1 - q))),(|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - q) / (1 - q)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p2.| * ((((p2 `1) / |.p2.|) - q) / (1 - q))),(|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - q) / (1 - q)) ^2))))]| `1 is V28() real ext-real Element of REAL
0 ^2 is V28() real ext-real Element of REAL
0 * 0 is Function-like functional empty V28() real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() set
1 - 0 is non empty V28() real ext-real positive non negative Element of REAL
sqrt (1 - 0) is V28() real ext-real Element of REAL
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `1 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `1) / |.p2.| is V28() real ext-real Element of COMPLEX
p2 `2 is V28() real ext-real Element of REAL
((p2 `1) / |.p2.|) - q is V28() real ext-real Element of REAL
1 + q is V28() real ext-real Element of REAL
(((p2 `1) / |.p2.|) - q) / (1 + q) is V28() real ext-real Element of COMPLEX
|.p2.| * ((((p2 `1) / |.p2.|) - q) / (1 + q)) is V28() real ext-real Element of REAL
((((p2 `1) / |.p2.|) - q) / (1 + q)) ^2 is V28() real ext-real Element of COMPLEX
((((p2 `1) / |.p2.|) - q) / (1 + q)) * ((((p2 `1) / |.p2.|) - q) / (1 + q)) is V28() real ext-real set
1 - (((((p2 `1) / |.p2.|) - q) / (1 + q)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p2 `1) / |.p2.|) - q) / (1 + q)) ^2)) is V28() real ext-real Element of REAL
|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - q) / (1 + q)) ^2))) is V28() real ext-real Element of REAL
|[(|.p2.| * ((((p2 `1) / |.p2.|) - q) / (1 + q))),(|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - q) / (1 + q)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p2.| * ((((p2 `1) / |.p2.|) - q) / (1 + q))),(|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - q) / (1 + q)) ^2))))]| `1 is V28() real ext-real Element of REAL
0 ^2 is V28() real ext-real Element of REAL
0 * 0 is Function-like functional empty V28() real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() set
1 - 0 is non empty V28() real ext-real positive non negative Element of REAL
sqrt (1 - 0) is V28() real ext-real Element of REAL
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `2 is V28() real ext-real Element of REAL
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `1 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `1) / |.p2.| is V28() real ext-real Element of COMPLEX
p2 `2 is V28() real ext-real Element of REAL
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `1 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `1) / |.p2.| is V28() real ext-real Element of COMPLEX
p2 `2 is V28() real ext-real Element of REAL
p2 is functional Element of K19( the carrier of (TOP-REAL 2))
the carrier of (TopSpaceMetr (Euclid 2)) is set
K19( the carrier of (TopSpaceMetr (Euclid 2))) is set
q3 is Element of K19( the carrier of (TopSpaceMetr (Euclid 2)))
p1 is Element of the carrier of (Euclid 2)
VV0 is V28() real ext-real set
Ball (p1,VV0) is bounded Element of K19( the carrier of (Euclid 2))
u2 is V28() real ext-real Element of REAL
Ball (p1,u2) is bounded Element of K19( the carrier of (Euclid 2))
u3 is functional Element of K19( the carrier of (TOP-REAL 2))
p .: u3 is functional Element of K19( the carrier of (TOP-REAL 2))
y is set
dom p is functional Element of K19( the carrier of (TOP-REAL 2))
q4 is set
p . q4 is Relation-like Function-like set
rng p is functional Element of K19( the carrier of (TOP-REAL 2))
x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x is Element of the carrier of (Euclid 2)
dist (p1,x) is V28() real ext-real Element of REAL
(0. (TOP-REAL 2)) - x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
- x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K443((TOP-REAL 2),(0. (TOP-REAL 2)),(- x)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is Relation-like K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)) -defined the carrier of (TOP-REAL 2) -valued Function-like total quasi_total Element of K19(K20(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)))
K20(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) is set
K19(K20(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2))) is set
K230( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),(0. (TOP-REAL 2)),(- x)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.((0. (TOP-REAL 2)) - x).| is V28() real ext-real non negative Element of REAL
x `2 is V28() real ext-real Element of REAL
x `1 is V28() real ext-real Element of REAL
|.x.| is V28() real ext-real non negative Element of REAL
(x `1) / |.x.| is V28() real ext-real Element of COMPLEX
x `2 is V28() real ext-real Element of REAL
((x `1) / |.x.|) - q is V28() real ext-real Element of REAL
(x `2) ^2 is V28() real ext-real Element of REAL
(x `2) * (x `2) is V28() real ext-real set
|.x.| ^2 is V28() real ext-real Element of REAL
|.x.| * |.x.| is V28() real ext-real non negative set
(x `1) ^2 is V28() real ext-real Element of REAL
(x `1) * (x `1) is V28() real ext-real set
((x `1) ^2) + ((x `2) ^2) is V28() real ext-real Element of REAL
0 + ((x `1) ^2) is V28() real ext-real Element of REAL
((x `1) ^2) / (|.x.| ^2) is V28() real ext-real Element of COMPLEX
(|.x.| ^2) / (|.x.| ^2) is V28() real ext-real Element of COMPLEX
1 - q is V28() real ext-real Element of REAL
((x `1) / |.x.|) ^2 is V28() real ext-real Element of COMPLEX
((x `1) / |.x.|) * ((x `1) / |.x.|) is V28() real ext-real set
- (1 - q) is V28() real ext-real Element of REAL
- (((x `1) / |.x.|) - q) is V28() real ext-real Element of REAL
(- (1 - q)) / (1 - q) is V28() real ext-real Element of COMPLEX
(- (((x `1) / |.x.|) - q)) / (1 - q) is V28() real ext-real Element of COMPLEX
((- (((x `1) / |.x.|) - q)) / (1 - q)) ^2 is V28() real ext-real Element of COMPLEX
((- (((x `1) / |.x.|) - q)) / (1 - q)) * ((- (((x `1) / |.x.|) - q)) / (1 - q)) is V28() real ext-real set
1 - (((- (((x `1) / |.x.|) - q)) / (1 - q)) ^2) is V28() real ext-real Element of REAL
(((x `1) / |.x.|) - q) / (1 - q) is V28() real ext-real Element of COMPLEX
- ((((x `1) / |.x.|) - q) / (1 - q)) is V28() real ext-real Element of COMPLEX
(- ((((x `1) / |.x.|) - q) / (1 - q))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((x `1) / |.x.|) - q) / (1 - q))) * (- ((((x `1) / |.x.|) - q) / (1 - q))) is V28() real ext-real set
1 - ((- ((((x `1) / |.x.|) - q) / (1 - q))) ^2) is V28() real ext-real Element of REAL
(q) . x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.x.| * ((((x `1) / |.x.|) - q) / (1 - q)) is V28() real ext-real Element of REAL
((((x `1) / |.x.|) - q) / (1 - q)) ^2 is V28() real ext-real Element of COMPLEX
((((x `1) / |.x.|) - q) / (1 - q)) * ((((x `1) / |.x.|) - q) / (1 - q)) is V28() real ext-real set
1 - (((((x `1) / |.x.|) - q) / (1 - q)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((x `1) / |.x.|) - q) / (1 - q)) ^2)) is V28() real ext-real Element of REAL
|.x.| * (sqrt (1 - (((((x `1) / |.x.|) - q) / (1 - q)) ^2))) is V28() real ext-real Element of REAL
|[(|.x.| * ((((x `1) / |.x.|) - q) / (1 - q))),(|.x.| * (sqrt (1 - (((((x `1) / |.x.|) - q) / (1 - q)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `1 is V28() real ext-real Element of REAL
y `2 is V28() real ext-real Element of REAL
(y `2) ^2 is V28() real ext-real Element of REAL
(y `2) * (y `2) is V28() real ext-real set
(sqrt (1 - (((((x `1) / |.x.|) - q) / (1 - q)) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((x `1) / |.x.|) - q) / (1 - q)) ^2))) * (sqrt (1 - (((((x `1) / |.x.|) - q) / (1 - q)) ^2))) is V28() real ext-real set
(|.x.| ^2) * ((sqrt (1 - (((((x `1) / |.x.|) - q) / (1 - q)) ^2))) ^2) is V28() real ext-real Element of REAL
(|.x.| ^2) * (1 - (((((x `1) / |.x.|) - q) / (1 - q)) ^2)) is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
|.y.| ^2 is V28() real ext-real Element of REAL
|.y.| * |.y.| is V28() real ext-real non negative set
(y `1) ^2 is V28() real ext-real Element of REAL
(y `1) * (y `1) is V28() real ext-real set
((y `1) ^2) + ((y `2) ^2) is V28() real ext-real Element of REAL
sqrt (|.y.| ^2) is V28() real ext-real Element of REAL
|.(- x).| is V28() real ext-real non negative Element of REAL
- y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.(- y).| is V28() real ext-real non negative Element of REAL
(0. (TOP-REAL 2)) - y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K443((TOP-REAL 2),(0. (TOP-REAL 2)),(- y)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K230( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),(0. (TOP-REAL 2)),(- y)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.((0. (TOP-REAL 2)) - y).| is V28() real ext-real non negative Element of REAL
q is Element of the carrier of (Euclid 2)
dist (p1,q) is V28() real ext-real Element of REAL
x `1 is V28() real ext-real Element of REAL
|.x.| is V28() real ext-real non negative Element of REAL
(x `1) / |.x.| is V28() real ext-real Element of COMPLEX
x `2 is V28() real ext-real Element of REAL
(x `2) ^2 is V28() real ext-real Element of REAL
(x `2) * (x `2) is V28() real ext-real set
|.x.| ^2 is V28() real ext-real Element of REAL
|.x.| * |.x.| is V28() real ext-real non negative set
(x `1) ^2 is V28() real ext-real Element of REAL
(x `1) * (x `1) is V28() real ext-real set
((x `1) ^2) + ((x `2) ^2) is V28() real ext-real Element of REAL
0 + ((x `1) ^2) is V28() real ext-real Element of REAL
((x `1) ^2) / (|.x.| ^2) is V28() real ext-real Element of COMPLEX
(|.x.| ^2) / (|.x.| ^2) is V28() real ext-real Element of COMPLEX
1 + q is V28() real ext-real Element of REAL
((x `1) / |.x.|) ^2 is V28() real ext-real Element of COMPLEX
((x `1) / |.x.|) * ((x `1) / |.x.|) is V28() real ext-real set
- ((x `1) / |.x.|) is V28() real ext-real Element of COMPLEX
- (- 1) is V28() real ext-real non negative Element of REAL
(- ((x `1) / |.x.|)) + q is V28() real ext-real Element of REAL
((x `1) / |.x.|) - q is V28() real ext-real Element of REAL
- (((x `1) / |.x.|) - q) is V28() real ext-real Element of REAL
(- (((x `1) / |.x.|) - q)) / (1 + q) is V28() real ext-real Element of COMPLEX
q - ((x `1) / |.x.|) is V28() real ext-real Element of REAL
((- (((x `1) / |.x.|) - q)) / (1 + q)) ^2 is V28() real ext-real Element of COMPLEX
((- (((x `1) / |.x.|) - q)) / (1 + q)) * ((- (((x `1) / |.x.|) - q)) / (1 + q)) is V28() real ext-real set
1 - (((- (((x `1) / |.x.|) - q)) / (1 + q)) ^2) is V28() real ext-real Element of REAL
(((x `1) / |.x.|) - q) / (1 + q) is V28() real ext-real Element of COMPLEX
- ((((x `1) / |.x.|) - q) / (1 + q)) is V28() real ext-real Element of COMPLEX
(- ((((x `1) / |.x.|) - q) / (1 + q))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((x `1) / |.x.|) - q) / (1 + q))) * (- ((((x `1) / |.x.|) - q) / (1 + q))) is V28() real ext-real set
1 - ((- ((((x `1) / |.x.|) - q) / (1 + q))) ^2) is V28() real ext-real Element of REAL
(q) . x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.x.| * ((((x `1) / |.x.|) - q) / (1 + q)) is V28() real ext-real Element of REAL
((((x `1) / |.x.|) - q) / (1 + q)) ^2 is V28() real ext-real Element of COMPLEX
((((x `1) / |.x.|) - q) / (1 + q)) * ((((x `1) / |.x.|) - q) / (1 + q)) is V28() real ext-real set
1 - (((((x `1) / |.x.|) - q) / (1 + q)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((x `1) / |.x.|) - q) / (1 + q)) ^2)) is V28() real ext-real Element of REAL
|.x.| * (sqrt (1 - (((((x `1) / |.x.|) - q) / (1 + q)) ^2))) is V28() real ext-real Element of REAL
|[(|.x.| * ((((x `1) / |.x.|) - q) / (1 + q))),(|.x.| * (sqrt (1 - (((((x `1) / |.x.|) - q) / (1 + q)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `1 is V28() real ext-real Element of REAL
y `2 is V28() real ext-real Element of REAL
(y `2) ^2 is V28() real ext-real Element of REAL
(y `2) * (y `2) is V28() real ext-real set
(sqrt (1 - (((((x `1) / |.x.|) - q) / (1 + q)) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((x `1) / |.x.|) - q) / (1 + q)) ^2))) * (sqrt (1 - (((((x `1) / |.x.|) - q) / (1 + q)) ^2))) is V28() real ext-real set
(|.x.| ^2) * ((sqrt (1 - (((((x `1) / |.x.|) - q) / (1 + q)) ^2))) ^2) is V28() real ext-real Element of REAL
(|.x.| ^2) * (1 - (((((x `1) / |.x.|) - q) / (1 + q)) ^2)) is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
|.y.| ^2 is V28() real ext-real Element of REAL
|.y.| * |.y.| is V28() real ext-real non negative set
(y `1) ^2 is V28() real ext-real Element of REAL
(y `1) * (y `1) is V28() real ext-real set
((y `1) ^2) + ((y `2) ^2) is V28() real ext-real Element of REAL
sqrt (|.y.| ^2) is V28() real ext-real Element of REAL
|.(- x).| is V28() real ext-real non negative Element of REAL
- y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.(- y).| is V28() real ext-real non negative Element of REAL
(0. (TOP-REAL 2)) - y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K443((TOP-REAL 2),(0. (TOP-REAL 2)),(- y)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K230( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),(0. (TOP-REAL 2)),(- y)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.((0. (TOP-REAL 2)) - y).| is V28() real ext-real non negative Element of REAL
q is Element of the carrier of (Euclid 2)
dist (p1,q) is V28() real ext-real Element of REAL
x `2 is V28() real ext-real Element of REAL
x `1 is V28() real ext-real Element of REAL
|.x.| is V28() real ext-real non negative Element of REAL
(x `1) / |.x.| is V28() real ext-real Element of COMPLEX
x `2 is V28() real ext-real Element of REAL
x `1 is V28() real ext-real Element of REAL
|.x.| is V28() real ext-real non negative Element of REAL
(x `1) / |.x.| is V28() real ext-real Element of COMPLEX
cn ` is functional Element of K19( the carrier of (TOP-REAL 2))
K20( the carrier of ((TOP-REAL 2) | cn), the carrier of ((TOP-REAL 2) | cn)) is set
K19(K20( the carrier of ((TOP-REAL 2) | cn), the carrier of ((TOP-REAL 2) | cn))) is set
(q) | cn is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p1 is Relation-like the carrier of ((TOP-REAL 2) | cn) -defined the carrier of ((TOP-REAL 2) | cn) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | cn), the carrier of ((TOP-REAL 2) | cn)))
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
q is set
p is set
(cn) . q is Relation-like Function-like set
(cn) . p is Relation-like Function-like set
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
1 - cn is V28() real ext-real Element of REAL
p2 `2 is V28() real ext-real Element of REAL
(cn) . p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 `2 is V28() real ext-real Element of REAL
p1 `1 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `2 is V28() real ext-real Element of REAL
((p1 `1) / |.p1.|) - cn is V28() real ext-real Element of REAL
(((p1 `1) / |.p1.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p1 `1) / |.p1.|) - cn) / (1 - cn)) * ((((p1 `1) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn))),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.p1.| ^2 is V28() real ext-real Element of REAL
|.p1.| * |.p1.| is V28() real ext-real non negative set
(p1 `1) ^2 is V28() real ext-real Element of REAL
(p1 `1) * (p1 `1) is V28() real ext-real set
(p1 `2) ^2 is V28() real ext-real Element of REAL
(p1 `2) * (p1 `2) is V28() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p1 `1) ^2) is V28() real ext-real Element of REAL
((p1 `1) ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
(|.p1.| ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
((p1 `1) / |.p1.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `1) / |.p1.|) * ((p1 `1) / |.p1.|) is V28() real ext-real set
- (1 - cn) is V28() real ext-real Element of REAL
- (((p1 `1) / |.p1.|) - cn) is V28() real ext-real Element of REAL
(- (1 - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
(- (((p1 `1) / |.p1.|) - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((- (((p1 `1) / |.p1.|) - cn)) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((p1 `1) / |.p1.|) - cn)) / (1 - cn)) * ((- (((p1 `1) / |.p1.|) - cn)) / (1 - cn)) is V28() real ext-real set
1 - (((- (((p1 `1) / |.p1.|) - cn)) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((p1 `1) / |.p1.|) - cn)) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
(- (((p1 `1) / |.p1.|) - cn)) ^2 is V28() real ext-real Element of REAL
(- (((p1 `1) / |.p1.|) - cn)) * (- (((p1 `1) / |.p1.|) - cn)) is V28() real ext-real set
(1 - cn) ^2 is V28() real ext-real Element of REAL
(1 - cn) * (1 - cn) is V28() real ext-real set
((- (((p1 `1) / |.p1.|) - cn)) ^2) / ((1 - cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((- (((p1 `1) / |.p1.|) - cn)) ^2) / ((1 - cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((p1 `1) / |.p1.|) - cn)) ^2) / ((1 - cn) ^2))) is V28() real ext-real Element of REAL
(((p1 `1) / |.p1.|) - cn) ^2 is V28() real ext-real Element of REAL
(((p1 `1) / |.p1.|) - cn) * (((p1 `1) / |.p1.|) - cn) is V28() real ext-real set
((((p1 `1) / |.p1.|) - cn) ^2) / ((1 - cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((((p1 `1) / |.p1.|) - cn) ^2) / ((1 - cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `1) / |.p1.|) - cn) ^2) / ((1 - cn) ^2))) is V28() real ext-real Element of REAL
|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn))),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2))))]| `2 is V28() real ext-real Element of REAL
- ((((p1 `1) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real Element of COMPLEX
(- ((((p1 `1) / |.p1.|) - cn) / (1 - cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((p1 `1) / |.p1.|) - cn) / (1 - cn))) * (- ((((p1 `1) / |.p1.|) - cn) / (1 - cn))) is V28() real ext-real set
1 - ((- ((((p1 `1) / |.p1.|) - cn) / (1 - cn))) ^2) is V28() real ext-real Element of REAL
1 * (1 - cn) is V28() real ext-real Element of REAL
1 * |.p1.| is V28() real ext-real non negative Element of REAL
p1 `1 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `2 is V28() real ext-real Element of REAL
|.p1.| ^2 is V28() real ext-real Element of REAL
|.p1.| * |.p1.| is V28() real ext-real non negative set
((p1 `1) / |.p1.|) - cn is V28() real ext-real Element of REAL
1 + cn is V28() real ext-real Element of REAL
(((p1 `1) / |.p1.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p1 `1) / |.p1.|) - cn) / (1 + cn)) * ((((p1 `1) / |.p1.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn))),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(p1 `1) ^2 is V28() real ext-real Element of REAL
(p1 `1) * (p1 `1) is V28() real ext-real set
(p1 `2) ^2 is V28() real ext-real Element of REAL
(p1 `2) * (p1 `2) is V28() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V28() real ext-real Element of REAL
- (((p1 `1) / |.p1.|) - cn) is V28() real ext-real Element of REAL
(- (((p1 `1) / |.p1.|) - cn)) / (1 + cn) is V28() real ext-real Element of COMPLEX
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
0 + ((p1 `1) ^2) is V28() real ext-real Element of REAL
((p1 `1) ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
(|.p1.| ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
((p1 `1) / |.p1.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `1) / |.p1.|) * ((p1 `1) / |.p1.|) is V28() real ext-real set
- ((p1 `1) / |.p1.|) is V28() real ext-real Element of COMPLEX
(- ((p1 `1) / |.p1.|)) ^2 is V28() real ext-real Element of COMPLEX
(- ((p1 `1) / |.p1.|)) * (- ((p1 `1) / |.p1.|)) is V28() real ext-real set
(- ((p1 `1) / |.p1.|)) + cn is V28() real ext-real Element of REAL
((- (((p1 `1) / |.p1.|) - cn)) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((p1 `1) / |.p1.|) - cn)) / (1 + cn)) * ((- (((p1 `1) / |.p1.|) - cn)) / (1 + cn)) is V28() real ext-real set
1 - (((- (((p1 `1) / |.p1.|) - cn)) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((p1 `1) / |.p1.|) - cn)) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
(- (((p1 `1) / |.p1.|) - cn)) ^2 is V28() real ext-real Element of REAL
(- (((p1 `1) / |.p1.|) - cn)) * (- (((p1 `1) / |.p1.|) - cn)) is V28() real ext-real set
(1 + cn) ^2 is V28() real ext-real Element of REAL
(1 + cn) * (1 + cn) is V28() real ext-real set
((- (((p1 `1) / |.p1.|) - cn)) ^2) / ((1 + cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((- (((p1 `1) / |.p1.|) - cn)) ^2) / ((1 + cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((p1 `1) / |.p1.|) - cn)) ^2) / ((1 + cn) ^2))) is V28() real ext-real Element of REAL
(((p1 `1) / |.p1.|) - cn) ^2 is V28() real ext-real Element of REAL
(((p1 `1) / |.p1.|) - cn) * (((p1 `1) / |.p1.|) - cn) is V28() real ext-real set
((((p1 `1) / |.p1.|) - cn) ^2) / ((1 + cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((((p1 `1) / |.p1.|) - cn) ^2) / ((1 + cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `1) / |.p1.|) - cn) ^2) / ((1 + cn) ^2))) is V28() real ext-real Element of REAL
|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn))),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2))))]| `2 is V28() real ext-real Element of REAL
- ((((p1 `1) / |.p1.|) - cn) / (1 + cn)) is V28() real ext-real Element of COMPLEX
(- ((((p1 `1) / |.p1.|) - cn) / (1 + cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((p1 `1) / |.p1.|) - cn) / (1 + cn))) * (- ((((p1 `1) / |.p1.|) - cn) / (1 + cn))) is V28() real ext-real set
1 - ((- ((((p1 `1) / |.p1.|) - cn) / (1 + cn))) ^2) is V28() real ext-real Element of REAL
sqrt ((- ((((p1 `1) / |.p1.|) - cn) / (1 + cn))) ^2) is V28() real ext-real set
1 * (1 + cn) is V28() real ext-real Element of REAL
(1 + cn) - cn is V28() real ext-real Element of REAL
- (p1 `1) is V28() real ext-real Element of REAL
(- (p1 `1)) / |.p1.| is V28() real ext-real Element of COMPLEX
1 * |.p1.| is V28() real ext-real non negative Element of REAL
((p1 `1) ^2) - ((p1 `1) ^2) is V28() real ext-real Element of REAL
p1 `2 is V28() real ext-real Element of REAL
p1 `1 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `2 is V28() real ext-real Element of REAL
p1 `1 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
p2 `1 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `1) / |.p2.| is V28() real ext-real Element of COMPLEX
p2 `2 is V28() real ext-real Element of REAL
|.p2.| ^2 is V28() real ext-real Element of REAL
|.p2.| * |.p2.| is V28() real ext-real non negative set
((p2 `1) / |.p2.|) - cn is V28() real ext-real Element of REAL
(((p2 `1) / |.p2.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p2 `1) / |.p2.|) - cn) / (1 - cn)) * ((((p2 `1) / |.p2.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 - cn))),(|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 - cn))),(|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2))))]| `1 is V28() real ext-real Element of REAL
(cn) . p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 - cn))),(|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2))))]| `2 is V28() real ext-real Element of REAL
p1 `2 is V28() real ext-real Element of REAL
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(p2 `1) ^2 is V28() real ext-real Element of REAL
(p2 `1) * (p2 `1) is V28() real ext-real set
(p2 `2) ^2 is V28() real ext-real Element of REAL
(p2 `2) * (p2 `2) is V28() real ext-real set
((p2 `1) ^2) + ((p2 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p2 `1) ^2) is V28() real ext-real Element of REAL
((p2 `1) ^2) / (|.p2.| ^2) is V28() real ext-real Element of COMPLEX
(|.p2.| ^2) / (|.p2.| ^2) is V28() real ext-real Element of COMPLEX
((p2 `1) / |.p2.|) ^2 is V28() real ext-real Element of COMPLEX
((p2 `1) / |.p2.|) * ((p2 `1) / |.p2.|) is V28() real ext-real set
- (1 - cn) is V28() real ext-real Element of REAL
- (((p2 `1) / |.p2.|) - cn) is V28() real ext-real Element of REAL
(- (1 - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
(- (((p2 `1) / |.p2.|) - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
((- (((p2 `1) / |.p2.|) - cn)) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((p2 `1) / |.p2.|) - cn)) / (1 - cn)) * ((- (((p2 `1) / |.p2.|) - cn)) / (1 - cn)) is V28() real ext-real set
1 - (((- (((p2 `1) / |.p2.|) - cn)) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((p2 `1) / |.p2.|) - cn)) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
(- (((p2 `1) / |.p2.|) - cn)) ^2 is V28() real ext-real Element of REAL
(- (((p2 `1) / |.p2.|) - cn)) * (- (((p2 `1) / |.p2.|) - cn)) is V28() real ext-real set
(1 - cn) ^2 is V28() real ext-real Element of REAL
(1 - cn) * (1 - cn) is V28() real ext-real set
((- (((p2 `1) / |.p2.|) - cn)) ^2) / ((1 - cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((- (((p2 `1) / |.p2.|) - cn)) ^2) / ((1 - cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((p2 `1) / |.p2.|) - cn)) ^2) / ((1 - cn) ^2))) is V28() real ext-real Element of REAL
(((p2 `1) / |.p2.|) - cn) ^2 is V28() real ext-real Element of REAL
(((p2 `1) / |.p2.|) - cn) * (((p2 `1) / |.p2.|) - cn) is V28() real ext-real set
((((p2 `1) / |.p2.|) - cn) ^2) / ((1 - cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((((p2 `1) / |.p2.|) - cn) ^2) / ((1 - cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((((p2 `1) / |.p2.|) - cn) ^2) / ((1 - cn) ^2))) is V28() real ext-real Element of REAL
- ((((p2 `1) / |.p2.|) - cn) / (1 - cn)) is V28() real ext-real Element of COMPLEX
(- ((((p2 `1) / |.p2.|) - cn) / (1 - cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((p2 `1) / |.p2.|) - cn) / (1 - cn))) * (- ((((p2 `1) / |.p2.|) - cn) / (1 - cn))) is V28() real ext-real set
1 - ((- ((((p2 `1) / |.p2.|) - cn) / (1 - cn))) ^2) is V28() real ext-real Element of REAL
1 * (1 - cn) is V28() real ext-real Element of REAL
1 * |.p2.| is V28() real ext-real non negative Element of REAL
p1 `1 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `2 is V28() real ext-real Element of REAL
(p2 `2) ^2 is V28() real ext-real Element of REAL
(p2 `2) * (p2 `2) is V28() real ext-real set
(p2 `1) ^2 is V28() real ext-real Element of REAL
(p2 `1) * (p2 `1) is V28() real ext-real set
((p2 `1) ^2) + ((p2 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p2 `1) ^2) is V28() real ext-real Element of REAL
((p2 `1) ^2) / (|.p2.| ^2) is V28() real ext-real Element of COMPLEX
(|.p2.| ^2) / (|.p2.| ^2) is V28() real ext-real Element of COMPLEX
((p2 `1) / |.p2.|) ^2 is V28() real ext-real Element of COMPLEX
((p2 `1) / |.p2.|) * ((p2 `1) / |.p2.|) is V28() real ext-real set
- (1 - cn) is V28() real ext-real Element of REAL
- (((p2 `1) / |.p2.|) - cn) is V28() real ext-real Element of REAL
(- (1 - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
(- (((p2 `1) / |.p2.|) - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
((- (((p2 `1) / |.p2.|) - cn)) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((p2 `1) / |.p2.|) - cn)) / (1 - cn)) * ((- (((p2 `1) / |.p2.|) - cn)) / (1 - cn)) is V28() real ext-real set
1 - (((- (((p2 `1) / |.p2.|) - cn)) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
- ((((p2 `1) / |.p2.|) - cn) / (1 - cn)) is V28() real ext-real Element of COMPLEX
(- ((((p2 `1) / |.p2.|) - cn) / (1 - cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((p2 `1) / |.p2.|) - cn) / (1 - cn))) * (- ((((p2 `1) / |.p2.|) - cn) / (1 - cn))) is V28() real ext-real set
1 - ((- ((((p2 `1) / |.p2.|) - cn) / (1 - cn))) ^2) is V28() real ext-real Element of REAL
(|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 - cn))),(|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2))))]| `2) ^2 is V28() real ext-real Element of REAL
(|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 - cn))),(|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2))))]| `2) * (|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 - cn))),(|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2))))]| `2) is V28() real ext-real set
(sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2))) * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real set
(|.p2.| ^2) * ((sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2))) ^2) is V28() real ext-real Element of REAL
(|.p2.| ^2) * (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 - cn))),(|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2))))]|.| is V28() real ext-real non negative Element of REAL
|.|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 - cn))),(|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2))))]|.| ^2 is V28() real ext-real Element of REAL
|.|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 - cn))),(|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2))))]|.| * |.|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 - cn))),(|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2))))]|.| is V28() real ext-real non negative set
(|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 - cn))),(|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2))))]| `1) ^2 is V28() real ext-real Element of REAL
(|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 - cn))),(|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2))))]| `1) * (|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 - cn))),(|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2))))]| `1) is V28() real ext-real set
((|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 - cn))),(|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2))))]| `1) ^2) + ((|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 - cn))),(|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2))))]| `2) ^2) is V28() real ext-real Element of REAL
sqrt (|.|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 - cn))),(|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2))))]|.| ^2) is V28() real ext-real Element of REAL
(p1 `2) ^2 is V28() real ext-real Element of REAL
(p1 `2) * (p1 `2) is V28() real ext-real set
|.p1.| ^2 is V28() real ext-real Element of REAL
|.p1.| * |.p1.| is V28() real ext-real non negative set
(p1 `1) ^2 is V28() real ext-real Element of REAL
(p1 `1) * (p1 `1) is V28() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p1 `1) ^2) is V28() real ext-real Element of REAL
((p1 `1) ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
(|.p1.| ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
((p1 `1) / |.p1.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `1) / |.p1.|) * ((p1 `1) / |.p1.|) is V28() real ext-real set
((p1 `1) / |.p1.|) - cn is V28() real ext-real Element of REAL
- (((p1 `1) / |.p1.|) - cn) is V28() real ext-real Element of REAL
(- (((p1 `1) / |.p1.|) - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
((- (((p1 `1) / |.p1.|) - cn)) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((p1 `1) / |.p1.|) - cn)) / (1 - cn)) * ((- (((p1 `1) / |.p1.|) - cn)) / (1 - cn)) is V28() real ext-real set
1 - (((- (((p1 `1) / |.p1.|) - cn)) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
(((p1 `1) / |.p1.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
- ((((p1 `1) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real Element of COMPLEX
(- ((((p1 `1) / |.p1.|) - cn) / (1 - cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((p1 `1) / |.p1.|) - cn) / (1 - cn))) * (- ((((p1 `1) / |.p1.|) - cn) / (1 - cn))) is V28() real ext-real set
1 - ((- ((((p1 `1) / |.p1.|) - cn) / (1 - cn))) ^2) is V28() real ext-real Element of REAL
|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p1 `1) / |.p1.|) - cn) / (1 - cn)) * ((((p1 `1) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn))),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn))),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2))))]| `1 is V28() real ext-real Element of REAL
|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn))),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2))))]| `2 is V28() real ext-real Element of REAL
(|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn))),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2))))]| `2) ^2 is V28() real ext-real Element of REAL
(|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn))),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2))))]| `2) * (|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn))),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2))))]| `2) is V28() real ext-real set
(sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2))) * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real set
(|.p1.| ^2) * ((sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2))) ^2) is V28() real ext-real Element of REAL
(|.p1.| ^2) * (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn))),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2))))]|.| is V28() real ext-real non negative Element of REAL
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn))),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2))))]|.| ^2 is V28() real ext-real Element of REAL
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn))),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2))))]|.| * |.|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn))),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2))))]|.| is V28() real ext-real non negative set
(|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn))),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2))))]| `1) ^2 is V28() real ext-real Element of REAL
(|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn))),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2))))]| `1) * (|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn))),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2))))]| `1) is V28() real ext-real set
((|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn))),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2))))]| `1) ^2) + ((|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn))),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2))))]| `2) ^2) is V28() real ext-real Element of REAL
sqrt (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn))),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2))))]|.| ^2) is V28() real ext-real Element of REAL
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 - cn))) / |.p1.| is V28() real ext-real Element of COMPLEX
((((p1 `1) / |.p1.|) - cn) / (1 - cn)) * (1 - cn) is V28() real ext-real Element of REAL
((p1 `1) / |.p1.|) * |.p1.| is V28() real ext-real Element of REAL
|[(p1 `1),(p1 `2)]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
sqrt ((p2 `2) ^2) is V28() real ext-real Element of REAL
p1 `1 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `2 is V28() real ext-real Element of REAL
((p1 `1) / |.p1.|) - cn is V28() real ext-real Element of REAL
1 + cn is V28() real ext-real Element of REAL
(((p1 `1) / |.p1.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p1 `1) / |.p1.|) - cn) / (1 + cn)) * ((((p1 `1) / |.p1.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn))),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn))),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2))))]| `1 is V28() real ext-real Element of REAL
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 `2 is V28() real ext-real Element of REAL
p1 `1 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `2 is V28() real ext-real Element of REAL
p1 `1 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
p2 `1 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `1) / |.p2.| is V28() real ext-real Element of COMPLEX
p2 `2 is V28() real ext-real Element of REAL
|.p2.| ^2 is V28() real ext-real Element of REAL
|.p2.| * |.p2.| is V28() real ext-real non negative set
((p2 `1) / |.p2.|) - cn is V28() real ext-real Element of REAL
1 + cn is V28() real ext-real Element of REAL
(((p2 `1) / |.p2.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p2 `1) / |.p2.|) - cn) / (1 + cn)) * ((((p2 `1) / |.p2.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 + cn))),(|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 + cn))),(|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2))))]| `1 is V28() real ext-real Element of REAL
(cn) . p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 + cn))),(|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2))))]| `2 is V28() real ext-real Element of REAL
p1 `2 is V28() real ext-real Element of REAL
(p2 `1) ^2 is V28() real ext-real Element of REAL
(p2 `1) * (p2 `1) is V28() real ext-real set
(p2 `2) ^2 is V28() real ext-real Element of REAL
(p2 `2) * (p2 `2) is V28() real ext-real set
((p2 `1) ^2) + ((p2 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p2 `1) ^2) is V28() real ext-real Element of REAL
((p2 `1) ^2) / (|.p2.| ^2) is V28() real ext-real Element of COMPLEX
(|.p2.| ^2) / (|.p2.| ^2) is V28() real ext-real Element of COMPLEX
((p2 `1) / |.p2.|) ^2 is V28() real ext-real Element of COMPLEX
((p2 `1) / |.p2.|) * ((p2 `1) / |.p2.|) is V28() real ext-real set
- ((p2 `1) / |.p2.|) is V28() real ext-real Element of COMPLEX
(- ((p2 `1) / |.p2.|)) ^2 is V28() real ext-real Element of COMPLEX
(- ((p2 `1) / |.p2.|)) * (- ((p2 `1) / |.p2.|)) is V28() real ext-real set
(- ((p2 `1) / |.p2.|)) + cn is V28() real ext-real Element of REAL
- (((p2 `1) / |.p2.|) - cn) is V28() real ext-real Element of REAL
(- (((p2 `1) / |.p2.|) - cn)) / (1 + cn) is V28() real ext-real Element of COMPLEX
((- (((p2 `1) / |.p2.|) - cn)) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((p2 `1) / |.p2.|) - cn)) / (1 + cn)) * ((- (((p2 `1) / |.p2.|) - cn)) / (1 + cn)) is V28() real ext-real set
1 - (((- (((p2 `1) / |.p2.|) - cn)) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
- ((((p2 `1) / |.p2.|) - cn) / (1 + cn)) is V28() real ext-real Element of COMPLEX
(- ((((p2 `1) / |.p2.|) - cn) / (1 + cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((p2 `1) / |.p2.|) - cn) / (1 + cn))) * (- ((((p2 `1) / |.p2.|) - cn) / (1 + cn))) is V28() real ext-real set
1 - ((- ((((p2 `1) / |.p2.|) - cn) / (1 + cn))) ^2) is V28() real ext-real Element of REAL
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
sqrt (1 - (((- (((p2 `1) / |.p2.|) - cn)) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
(- (((p2 `1) / |.p2.|) - cn)) ^2 is V28() real ext-real Element of REAL
(- (((p2 `1) / |.p2.|) - cn)) * (- (((p2 `1) / |.p2.|) - cn)) is V28() real ext-real set
(1 + cn) ^2 is V28() real ext-real Element of REAL
(1 + cn) * (1 + cn) is V28() real ext-real set
((- (((p2 `1) / |.p2.|) - cn)) ^2) / ((1 + cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((- (((p2 `1) / |.p2.|) - cn)) ^2) / ((1 + cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((p2 `1) / |.p2.|) - cn)) ^2) / ((1 + cn) ^2))) is V28() real ext-real Element of REAL
(((p2 `1) / |.p2.|) - cn) ^2 is V28() real ext-real Element of REAL
(((p2 `1) / |.p2.|) - cn) * (((p2 `1) / |.p2.|) - cn) is V28() real ext-real set
((((p2 `1) / |.p2.|) - cn) ^2) / ((1 + cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((((p2 `1) / |.p2.|) - cn) ^2) / ((1 + cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((((p2 `1) / |.p2.|) - cn) ^2) / ((1 + cn) ^2))) is V28() real ext-real Element of REAL
sqrt ((- ((((p2 `1) / |.p2.|) - cn) / (1 + cn))) ^2) is V28() real ext-real set
1 * (1 + cn) is V28() real ext-real Element of REAL
(1 + cn) - cn is V28() real ext-real Element of REAL
- (p2 `1) is V28() real ext-real Element of REAL
(- (p2 `1)) / |.p2.| is V28() real ext-real Element of COMPLEX
1 * |.p2.| is V28() real ext-real non negative Element of REAL
((p2 `1) ^2) - ((p2 `1) ^2) is V28() real ext-real Element of REAL
p1 `1 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `2 is V28() real ext-real Element of REAL
((p1 `1) / |.p1.|) - cn is V28() real ext-real Element of REAL
(((p1 `1) / |.p1.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p1 `1) / |.p1.|) - cn) / (1 - cn)) * ((((p1 `1) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn))),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn))),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2))))]| `1 is V28() real ext-real Element of REAL
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `2 is V28() real ext-real Element of REAL
(p1 `2) ^2 is V28() real ext-real Element of REAL
(p1 `2) * (p1 `2) is V28() real ext-real set
|.p1.| ^2 is V28() real ext-real Element of REAL
|.p1.| * |.p1.| is V28() real ext-real non negative set
(p1 `1) ^2 is V28() real ext-real Element of REAL
(p1 `1) * (p1 `1) is V28() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p1 `1) ^2) is V28() real ext-real Element of REAL
((p1 `1) ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
(|.p1.| ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
(p2 `2) ^2 is V28() real ext-real Element of REAL
(p2 `2) * (p2 `2) is V28() real ext-real set
(p2 `1) ^2 is V28() real ext-real Element of REAL
(p2 `1) * (p2 `1) is V28() real ext-real set
((p2 `1) ^2) + ((p2 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p2 `1) ^2) is V28() real ext-real Element of REAL
((p2 `1) ^2) / (|.p2.| ^2) is V28() real ext-real Element of COMPLEX
(|.p2.| ^2) / (|.p2.| ^2) is V28() real ext-real Element of COMPLEX
((p2 `1) / |.p2.|) ^2 is V28() real ext-real Element of COMPLEX
((p2 `1) / |.p2.|) * ((p2 `1) / |.p2.|) is V28() real ext-real set
(- 1) - cn is V28() real ext-real Element of REAL
- (((p2 `1) / |.p2.|) - cn) is V28() real ext-real Element of REAL
- ((- 1) - cn) is V28() real ext-real Element of REAL
(- (((p2 `1) / |.p2.|) - cn)) / (1 + cn) is V28() real ext-real Element of COMPLEX
((- (((p2 `1) / |.p2.|) - cn)) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((p2 `1) / |.p2.|) - cn)) / (1 + cn)) * ((- (((p2 `1) / |.p2.|) - cn)) / (1 + cn)) is V28() real ext-real set
1 - (((- (((p2 `1) / |.p2.|) - cn)) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
- ((((p2 `1) / |.p2.|) - cn) / (1 + cn)) is V28() real ext-real Element of COMPLEX
(- ((((p2 `1) / |.p2.|) - cn) / (1 + cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((p2 `1) / |.p2.|) - cn) / (1 + cn))) * (- ((((p2 `1) / |.p2.|) - cn) / (1 + cn))) is V28() real ext-real set
1 - ((- ((((p2 `1) / |.p2.|) - cn) / (1 + cn))) ^2) is V28() real ext-real Element of REAL
(|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 + cn))),(|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2))))]| `2) ^2 is V28() real ext-real Element of REAL
(|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 + cn))),(|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2))))]| `2) * (|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 + cn))),(|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2))))]| `2) is V28() real ext-real set
(sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2))) * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real set
(|.p2.| ^2) * ((sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2))) ^2) is V28() real ext-real Element of REAL
(|.p2.| ^2) * (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
((p1 `1) / |.p1.|) - cn is V28() real ext-real Element of REAL
(((p1 `1) / |.p1.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p1 `1) / |.p1.|) - cn) / (1 + cn)) * ((((p1 `1) / |.p1.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn))),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn))),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2))))]| `1 is V28() real ext-real Element of REAL
((p1 `1) / |.p1.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `1) / |.p1.|) * ((p1 `1) / |.p1.|) is V28() real ext-real set
- (((p1 `1) / |.p1.|) - cn) is V28() real ext-real Element of REAL
(- (((p1 `1) / |.p1.|) - cn)) / (1 + cn) is V28() real ext-real Element of COMPLEX
((- (((p1 `1) / |.p1.|) - cn)) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((p1 `1) / |.p1.|) - cn)) / (1 + cn)) * ((- (((p1 `1) / |.p1.|) - cn)) / (1 + cn)) is V28() real ext-real set
1 - (((- (((p1 `1) / |.p1.|) - cn)) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
- ((((p1 `1) / |.p1.|) - cn) / (1 + cn)) is V28() real ext-real Element of COMPLEX
(- ((((p1 `1) / |.p1.|) - cn) / (1 + cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((p1 `1) / |.p1.|) - cn) / (1 + cn))) * (- ((((p1 `1) / |.p1.|) - cn) / (1 + cn))) is V28() real ext-real set
1 - ((- ((((p1 `1) / |.p1.|) - cn) / (1 + cn))) ^2) is V28() real ext-real Element of REAL
|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn))),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2))))]| `2 is V28() real ext-real Element of REAL
(|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn))),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2))))]| `2) ^2 is V28() real ext-real Element of REAL
(|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn))),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2))))]| `2) * (|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn))),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2))))]| `2) is V28() real ext-real set
(sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2))) * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real set
(|.p1.| ^2) * ((sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2))) ^2) is V28() real ext-real Element of REAL
(|.p1.| ^2) * (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn))),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2))))]|.| is V28() real ext-real non negative Element of REAL
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn))),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2))))]|.| ^2 is V28() real ext-real Element of REAL
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn))),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2))))]|.| * |.|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn))),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2))))]|.| is V28() real ext-real non negative set
(|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn))),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2))))]| `1) ^2 is V28() real ext-real Element of REAL
(|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn))),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2))))]| `1) * (|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn))),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2))))]| `1) is V28() real ext-real set
((|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn))),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2))))]| `1) ^2) + ((|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn))),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2))))]| `2) ^2) is V28() real ext-real Element of REAL
sqrt (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn))),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2))))]|.| ^2) is V28() real ext-real Element of REAL
|.|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 + cn))),(|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2))))]|.| is V28() real ext-real non negative Element of REAL
|.|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 + cn))),(|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2))))]|.| ^2 is V28() real ext-real Element of REAL
|.|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 + cn))),(|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2))))]|.| * |.|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 + cn))),(|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2))))]|.| is V28() real ext-real non negative set
(|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 + cn))),(|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2))))]| `1) ^2 is V28() real ext-real Element of REAL
(|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 + cn))),(|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2))))]| `1) * (|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 + cn))),(|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2))))]| `1) is V28() real ext-real set
((|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 + cn))),(|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2))))]| `1) ^2) + ((|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 + cn))),(|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2))))]| `2) ^2) is V28() real ext-real Element of REAL
sqrt (|.|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 + cn))),(|.p2.| * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2))))]|.| ^2) is V28() real ext-real Element of REAL
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 + cn))) / |.p1.| is V28() real ext-real Element of COMPLEX
((((p1 `1) / |.p1.|) - cn) / (1 + cn)) * (1 + cn) is V28() real ext-real Element of REAL
((p1 `1) / |.p1.|) * |.p1.| is V28() real ext-real Element of REAL
|[(p1 `1),(p1 `2)]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
sqrt ((p2 `2) ^2) is V28() real ext-real Element of REAL
p1 `2 is V28() real ext-real Element of REAL
p1 `1 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `2 is V28() real ext-real Element of REAL
p1 `1 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
p2 `2 is V28() real ext-real Element of REAL
p2 `1 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `1) / |.p2.| is V28() real ext-real Element of COMPLEX
p2 `2 is V28() real ext-real Element of REAL
p2 `1 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `1) / |.p2.| is V28() real ext-real Element of COMPLEX
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
rng (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
q is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
dom q is functional Element of K19( the carrier of (TOP-REAL 2))
rng q is functional Element of K19( the carrier of (TOP-REAL 2))
p is set
p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 `2 is V28() real ext-real Element of REAL
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
p1 `1 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `2 is V28() real ext-real Element of REAL
1 + cn is V28() real ext-real Element of REAL
- (1 + cn) is V28() real ext-real Element of REAL
- (- (1 + cn)) is V28() real ext-real Element of REAL
(- 1) - cn is V28() real ext-real Element of REAL
- ((- 1) - cn) is V28() real ext-real Element of REAL
1 - cn is V28() real ext-real Element of REAL
((p1 `1) / |.p1.|) * (1 - cn) is V28() real ext-real Element of REAL
((- 1) - cn) + cn is V28() real ext-real Element of REAL
(((p1 `1) / |.p1.|) * (1 - cn)) + cn is V28() real ext-real Element of REAL
|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn) is V28() real ext-real Element of REAL
((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2 is V28() real ext-real Element of REAL
((((p1 `1) / |.p1.|) * (1 - cn)) + cn) * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn) is V28() real ext-real set
1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)) is V28() real ext-real Element of REAL
|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))) is V28() real ext-real Element of REAL
|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]| `1 is V28() real ext-real Element of REAL
|.p1.| ^2 is V28() real ext-real Element of REAL
|.p1.| * |.p1.| is V28() real ext-real non negative set
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
(p1 `2) ^2 is V28() real ext-real Element of REAL
(p1 `2) * (p1 `2) is V28() real ext-real set
(p1 `1) ^2 is V28() real ext-real Element of REAL
(p1 `1) * (p1 `1) is V28() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p1 `1) ^2) is V28() real ext-real Element of REAL
((p1 `1) ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
(|.p1.| ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
((p1 `1) / |.p1.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `1) / |.p1.|) * ((p1 `1) / |.p1.|) is V28() real ext-real set
1 * (1 - cn) is V28() real ext-real Element of REAL
((((p1 `1) / |.p1.|) * (1 - cn)) + cn) - cn is V28() real ext-real Element of REAL
|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]| `2 is V28() real ext-real Element of REAL
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.| is V28() real ext-real non negative Element of REAL
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.| ^2 is V28() real ext-real Element of REAL
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.| * |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.| is V28() real ext-real non negative set
(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))) ^2 is V28() real ext-real Element of REAL
(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))) * (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))) is V28() real ext-real set
(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)) ^2 is V28() real ext-real Element of REAL
(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)) * (|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)) is V28() real ext-real set
((|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))) ^2) + ((|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)) ^2) is V28() real ext-real Element of REAL
(sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))) * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))) is V28() real ext-real set
(|.p1.| ^2) * ((sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))) ^2) is V28() real ext-real Element of REAL
(|.p1.| ^2) * (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2) is V28() real ext-real Element of REAL
((|.p1.| ^2) * ((sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))) ^2)) + ((|.p1.| ^2) * (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)) is V28() real ext-real Element of REAL
(|.p1.| ^2) * (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)) is V28() real ext-real Element of REAL
((|.p1.| ^2) * (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))) + ((|.p1.| ^2) * (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)) is V28() real ext-real Element of REAL
sqrt (|.p1.| ^2) is V28() real ext-real Element of REAL
0 + cn is V28() real ext-real Element of REAL
(|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.| is V28() real ext-real Element of COMPLEX
(cn) . |[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.|) - cn is V28() real ext-real Element of REAL
(((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.| * ((((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
((((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.|) - cn) / (1 - cn)) * ((((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.| * (sqrt (1 - (((((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|[(|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.| * ((((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.|) - cn) / (1 - cn))),(|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.| * (sqrt (1 - (((((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.|) - cn) / (1 - cn)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
((p1 `2) / |.p1.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `2) / |.p1.|) * ((p1 `2) / |.p1.|) is V28() real ext-real set
sqrt (((p1 `2) / |.p1.|) ^2) is V28() real ext-real set
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.| * (sqrt (((p1 `2) / |.p1.|) ^2)) is V28() real ext-real Element of REAL
|.p1.| * ((p1 `2) / |.p1.|) is V28() real ext-real Element of REAL
(((((p1 `1) / |.p1.|) * (1 - cn)) + cn) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
|.p1.| * ((((((p1 `1) / |.p1.|) * (1 - cn)) + cn) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
|.p1.| * ((p1 `1) / |.p1.|) is V28() real ext-real Element of REAL
(p1 `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.| is V28() real ext-real Element of COMPLEX
((p1 `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.|) * ((p1 `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.|) is V28() real ext-real set
1 - (((p1 `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.|) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((p1 `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.|) ^2)) is V28() real ext-real Element of REAL
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.| * (sqrt (1 - (((p1 `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.|) ^2))) is V28() real ext-real Element of REAL
((p1 `1) ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.| ^2) is V28() real ext-real Element of COMPLEX
1 - (((p1 `1) ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.| ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((p1 `1) ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.| ^2))) is V28() real ext-real Element of REAL
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.| * (sqrt (1 - (((p1 `1) ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.| ^2)))) is V28() real ext-real Element of REAL
(|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.| ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.| ^2) is V28() real ext-real Element of COMPLEX
((|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.| ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.| ^2)) - (((p1 `1) ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.| ^2)) is V28() real ext-real Element of COMPLEX
sqrt (((|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.| ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.| ^2)) - (((p1 `1) ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.| ^2))) is V28() real ext-real set
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.| * (sqrt (((|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.| ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.| ^2)) - (((p1 `1) ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.| ^2)))) is V28() real ext-real Element of REAL
(|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.| ^2) - ((p1 `1) ^2) is V28() real ext-real Element of REAL
((|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.| ^2) - ((p1 `1) ^2)) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.| ^2) is V28() real ext-real Element of COMPLEX
sqrt (((|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.| ^2) - ((p1 `1) ^2)) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.| ^2)) is V28() real ext-real set
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.| * (sqrt (((|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.| ^2) - ((p1 `1) ^2)) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.| ^2))) is V28() real ext-real Element of REAL
(((p1 `1) ^2) + ((p1 `2) ^2)) - ((p1 `1) ^2) is V28() real ext-real Element of REAL
((((p1 `1) ^2) + ((p1 `2) ^2)) - ((p1 `1) ^2)) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.| ^2) is V28() real ext-real Element of COMPLEX
sqrt (((((p1 `1) ^2) + ((p1 `2) ^2)) - ((p1 `1) ^2)) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.| ^2)) is V28() real ext-real set
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.| * (sqrt (((((p1 `1) ^2) + ((p1 `2) ^2)) - ((p1 `1) ^2)) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))))]|.| ^2))) is V28() real ext-real Element of REAL
p1 `1 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `2 is V28() real ext-real Element of REAL
1 + cn is V28() real ext-real Element of REAL
1 - cn is V28() real ext-real Element of REAL
((p1 `1) / |.p1.|) * (1 + cn) is V28() real ext-real Element of REAL
(((p1 `1) / |.p1.|) * (1 + cn)) + cn is V28() real ext-real Element of REAL
(1 - cn) + cn is V28() real ext-real Element of REAL
|.p1.| ^2 is V28() real ext-real Element of REAL
|.p1.| * |.p1.| is V28() real ext-real non negative set
(p1 `2) ^2 is V28() real ext-real Element of REAL
(p1 `2) * (p1 `2) is V28() real ext-real set
(p1 `1) ^2 is V28() real ext-real Element of REAL
(p1 `1) * (p1 `1) is V28() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p1 `1) ^2) is V28() real ext-real Element of REAL
((p1 `1) ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
(|.p1.| ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
((p1 `1) / |.p1.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `1) / |.p1.|) * ((p1 `1) / |.p1.|) is V28() real ext-real set
(- 1) * (1 + cn) is V28() real ext-real Element of REAL
(- 1) - cn is V28() real ext-real Element of REAL
((((p1 `1) / |.p1.|) * (1 + cn)) + cn) - cn is V28() real ext-real Element of REAL
((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2 is V28() real ext-real Element of REAL
((((p1 `1) / |.p1.|) * (1 + cn)) + cn) * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn) is V28() real ext-real set
1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)) is V28() real ext-real Element of REAL
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn) is V28() real ext-real Element of REAL
|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))) is V28() real ext-real Element of REAL
|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]| `1 is V28() real ext-real Element of REAL
|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]| `2 is V28() real ext-real Element of REAL
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.| is V28() real ext-real non negative Element of REAL
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.| ^2 is V28() real ext-real Element of REAL
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.| * |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.| is V28() real ext-real non negative set
(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))) ^2 is V28() real ext-real Element of REAL
(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))) * (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))) is V28() real ext-real set
(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)) ^2 is V28() real ext-real Element of REAL
(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)) * (|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)) is V28() real ext-real set
((|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))) ^2) + ((|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)) ^2) is V28() real ext-real Element of REAL
(sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))) * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))) is V28() real ext-real set
(|.p1.| ^2) * ((sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))) ^2) is V28() real ext-real Element of REAL
(|.p1.| ^2) * (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2) is V28() real ext-real Element of REAL
((|.p1.| ^2) * ((sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))) ^2)) + ((|.p1.| ^2) * (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)) is V28() real ext-real Element of REAL
(|.p1.| ^2) * (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)) is V28() real ext-real Element of REAL
((|.p1.| ^2) * (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))) + ((|.p1.| ^2) * (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)) is V28() real ext-real Element of REAL
sqrt (|.p1.| ^2) is V28() real ext-real Element of REAL
0 + cn is V28() real ext-real Element of REAL
(|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.| is V28() real ext-real Element of COMPLEX
(cn) . |[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.|) - cn is V28() real ext-real Element of REAL
(((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.| * ((((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
((((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.|) - cn) / (1 + cn)) * ((((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.| * (sqrt (1 - (((((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|[(|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.| * ((((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.|) - cn) / (1 + cn))),(|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.| * (sqrt (1 - (((((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.|) - cn) / (1 + cn)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
((p1 `2) / |.p1.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `2) / |.p1.|) * ((p1 `2) / |.p1.|) is V28() real ext-real set
sqrt (((p1 `2) / |.p1.|) ^2) is V28() real ext-real set
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.| * (sqrt (((p1 `2) / |.p1.|) ^2)) is V28() real ext-real Element of REAL
|.p1.| * ((p1 `2) / |.p1.|) is V28() real ext-real Element of REAL
(((((p1 `1) / |.p1.|) * (1 + cn)) + cn) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
|.p1.| * ((((((p1 `1) / |.p1.|) * (1 + cn)) + cn) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
|.p1.| * ((p1 `1) / |.p1.|) is V28() real ext-real Element of REAL
(p1 `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.| is V28() real ext-real Element of COMPLEX
((p1 `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.|) * ((p1 `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.|) is V28() real ext-real set
1 - (((p1 `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.|) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((p1 `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.|) ^2)) is V28() real ext-real Element of REAL
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.| * (sqrt (1 - (((p1 `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.|) ^2))) is V28() real ext-real Element of REAL
((p1 `1) ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.| ^2) is V28() real ext-real Element of COMPLEX
1 - (((p1 `1) ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.| ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((p1 `1) ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.| ^2))) is V28() real ext-real Element of REAL
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.| * (sqrt (1 - (((p1 `1) ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.| ^2)))) is V28() real ext-real Element of REAL
(|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.| ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.| ^2) is V28() real ext-real Element of COMPLEX
((|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.| ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.| ^2)) - (((p1 `1) ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.| ^2)) is V28() real ext-real Element of COMPLEX
sqrt (((|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.| ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.| ^2)) - (((p1 `1) ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.| ^2))) is V28() real ext-real set
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.| * (sqrt (((|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.| ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.| ^2)) - (((p1 `1) ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.| ^2)))) is V28() real ext-real Element of REAL
(|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.| ^2) - ((p1 `1) ^2) is V28() real ext-real Element of REAL
((|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.| ^2) - ((p1 `1) ^2)) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.| ^2) is V28() real ext-real Element of COMPLEX
sqrt (((|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.| ^2) - ((p1 `1) ^2)) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.| ^2)) is V28() real ext-real set
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.| * (sqrt (((|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.| ^2) - ((p1 `1) ^2)) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.| ^2))) is V28() real ext-real Element of REAL
(((p1 `1) ^2) + ((p1 `2) ^2)) - ((p1 `1) ^2) is V28() real ext-real Element of REAL
((((p1 `1) ^2) + ((p1 `2) ^2)) - ((p1 `1) ^2)) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.| ^2) is V28() real ext-real Element of COMPLEX
sqrt (((((p1 `1) ^2) + ((p1 `2) ^2)) - ((p1 `1) ^2)) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.| ^2)) is V28() real ext-real set
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.| * (sqrt (((((p1 `1) ^2) + ((p1 `2) ^2)) - ((p1 `1) ^2)) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))]|.| ^2))) is V28() real ext-real Element of REAL
p1 `2 is V28() real ext-real Element of REAL
p1 `1 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
p1 `2 is V28() real ext-real Element of REAL
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
p1 `1 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
q3 is set
(cn) . q3 is Relation-like Function-like set
VV0 is set
(cn) . VV0 is Relation-like Function-like set
u2 is set
(cn) . u2 is Relation-like Function-like set
q is V28() real ext-real Element of REAL
(q) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(q) . p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn is Element of the carrier of (Euclid 2)
|.p.| is V28() real ext-real non negative Element of REAL
|.p.| + 1 is non empty V28() real ext-real positive non negative Element of REAL
Ball (cn,(|.p.| + 1)) is bounded Element of K19( the carrier of (Euclid 2))
p1 is functional Element of K19( the carrier of (TOP-REAL 2))
cl_Ball (cn,(|.p.| + 1)) is Element of K19( the carrier of (Euclid 2))
the carrier of (TopSpaceMetr (Euclid 2)) is set
K19( the carrier of (TopSpaceMetr (Euclid 2))) is set
p2 is functional non empty closed compact bounded Element of K19( the carrier of (TOP-REAL 2))
(q) .: p2 is functional Element of K19( the carrier of (TOP-REAL 2))
y is set
dom (q) is functional Element of K19( the carrier of (TOP-REAL 2))
q4 is set
(q) . q4 is Relation-like Function-like set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x is Element of the carrier of (Euclid 2)
dist (cn,x) is V28() real ext-real Element of REAL
(0. (TOP-REAL 2)) - y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
- y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K443((TOP-REAL 2),(0. (TOP-REAL 2)),(- y)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is Relation-like K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)) -defined the carrier of (TOP-REAL 2) -valued Function-like total quasi_total Element of K19(K20(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)))
K20(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) is set
K19(K20(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2))) is set
K230( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),(0. (TOP-REAL 2)),(- y)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.((0. (TOP-REAL 2)) - y).| is V28() real ext-real non negative Element of REAL
|.(- y).| is V28() real ext-real non negative Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
rng (q) is functional Element of K19( the carrier of (TOP-REAL 2))
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.q.| is V28() real ext-real non negative Element of REAL
- q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.(- q).| is V28() real ext-real non negative Element of REAL
(0. (TOP-REAL 2)) - q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K443((TOP-REAL 2),(0. (TOP-REAL 2)),(- q)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K230( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),(0. (TOP-REAL 2)),(- q)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.((0. (TOP-REAL 2)) - q).| is V28() real ext-real non negative Element of REAL
x is Element of the carrier of (Euclid 2)
dist (cn,x) is V28() real ext-real Element of REAL
VV0 is Element of K19( the carrier of (TopSpaceMetr (Euclid 2)))
- p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.(- p).| is V28() real ext-real non negative Element of REAL
(0. (TOP-REAL 2)) - p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K443((TOP-REAL 2),(0. (TOP-REAL 2)),(- p)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is Relation-like K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)) -defined the carrier of (TOP-REAL 2) -valued Function-like total quasi_total Element of K19(K20(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)))
K20(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) is set
K19(K20(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2))) is set
K230( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),(0. (TOP-REAL 2)),(- p)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.((0. (TOP-REAL 2)) - p).| is V28() real ext-real non negative Element of REAL
u2 is Element of the carrier of (Euclid 2)
dist (cn,u2) is V28() real ext-real Element of REAL
|.((q) . p).| is V28() real ext-real non negative Element of REAL
- ((q) . p) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.(- ((q) . p)).| is V28() real ext-real non negative Element of REAL
(0. (TOP-REAL 2)) - ((q) . p) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K443((TOP-REAL 2),(0. (TOP-REAL 2)),(- ((q) . p))) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K230( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),(0. (TOP-REAL 2)),(- ((q) . p))) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.((0. (TOP-REAL 2)) - ((q) . p)).| is V28() real ext-real non negative Element of REAL
u3 is Element of the carrier of (Euclid 2)
dist (cn,u3) is V28() real ext-real Element of REAL
y is set
rng (q) is functional Element of K19( the carrier of (TOP-REAL 2))
q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
dom (q) is functional Element of K19( the carrier of (TOP-REAL 2))
y is Element of the carrier of (Euclid 2)
x is set
(q) . x is Relation-like Function-like set
x is Element of the carrier of (Euclid 2)
|.q4.| is V28() real ext-real non negative Element of REAL
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.q.| is V28() real ext-real non negative Element of REAL
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q . p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
rng (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
p is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q `2 is V28() real ext-real Element of REAL
q `1 is V28() real ext-real Element of REAL
|.q.| is V28() real ext-real non negative Element of REAL
(q `1) / |.q.| is V28() real ext-real Element of COMPLEX
(cn) . q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((q `1) / |.q.|) - cn is V28() real ext-real Element of REAL
p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p `2 is V28() real ext-real Element of REAL
p `1 is V28() real ext-real Element of REAL
1 - cn is V28() real ext-real Element of REAL
|.q.| ^2 is V28() real ext-real Element of REAL
|.q.| * |.q.| is V28() real ext-real non negative set
(q `1) ^2 is V28() real ext-real Element of REAL
(q `1) * (q `1) is V28() real ext-real set
(q `2) ^2 is V28() real ext-real Element of REAL
(q `2) * (q `2) is V28() real ext-real set
((q `1) ^2) + ((q `2) ^2) is V28() real ext-real Element of REAL
0 + ((q `1) ^2) is V28() real ext-real Element of REAL
(|.q.| ^2) / (|.q.| ^2) is V28() real ext-real Element of COMPLEX
((q `1) ^2) / (|.q.| ^2) is V28() real ext-real Element of COMPLEX
((q `1) / |.q.|) ^2 is V28() real ext-real Element of COMPLEX
((q `1) / |.q.|) * ((q `1) / |.q.|) is V28() real ext-real set
- (((q `1) / |.q.|) - cn) is V28() real ext-real Element of REAL
- (1 - cn) is V28() real ext-real Element of REAL
(- (((q `1) / |.q.|) - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
(- (1 - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
((- (((q `1) / |.q.|) - cn)) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((q `1) / |.q.|) - cn)) / (1 - cn)) * ((- (((q `1) / |.q.|) - cn)) / (1 - cn)) is V28() real ext-real set
1 - (((- (((q `1) / |.q.|) - cn)) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((q `1) / |.q.|) - cn)) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
(- (((q `1) / |.q.|) - cn)) ^2 is V28() real ext-real Element of REAL
(- (((q `1) / |.q.|) - cn)) * (- (((q `1) / |.q.|) - cn)) is V28() real ext-real set
(1 - cn) ^2 is V28() real ext-real Element of REAL
(1 - cn) * (1 - cn) is V28() real ext-real set
((- (((q `1) / |.q.|) - cn)) ^2) / ((1 - cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((- (((q `1) / |.q.|) - cn)) ^2) / ((1 - cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((q `1) / |.q.|) - cn)) ^2) / ((1 - cn) ^2))) is V28() real ext-real Element of REAL
(((q `1) / |.q.|) - cn) ^2 is V28() real ext-real Element of REAL
(((q `1) / |.q.|) - cn) * (((q `1) / |.q.|) - cn) is V28() real ext-real set
((((q `1) / |.q.|) - cn) ^2) / ((1 - cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((((q `1) / |.q.|) - cn) ^2) / ((1 - cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((((q `1) / |.q.|) - cn) ^2) / ((1 - cn) ^2))) is V28() real ext-real Element of REAL
(((q `1) / |.q.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
((((q `1) / |.q.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((q `1) / |.q.|) - cn) / (1 - cn)) * ((((q `1) / |.q.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.q.| * ((((q `1) / |.q.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
|.q.| * (sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|[(|.q.| * ((((q `1) / |.q.|) - cn) / (1 - cn))),(|.q.| * (sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q `2 is V28() real ext-real Element of REAL
q `1 is V28() real ext-real Element of REAL
|.q.| is V28() real ext-real non negative Element of REAL
(q `1) / |.q.| is V28() real ext-real Element of COMPLEX
(cn) . q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
1 + cn is V28() real ext-real Element of REAL
p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p `2 is V28() real ext-real Element of REAL
p `1 is V28() real ext-real Element of REAL
((q `1) / |.q.|) - cn is V28() real ext-real Element of REAL
(((q `1) / |.q.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
|.q.| * ((((q `1) / |.q.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
((((q `1) / |.q.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((q `1) / |.q.|) - cn) / (1 + cn)) * ((((q `1) / |.q.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((q `1) / |.q.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
|.q.| * (sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|[(|.q.| * ((((q `1) / |.q.|) - cn) / (1 + cn))),(|.q.| * (sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 + cn)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.q.| ^2 is V28() real ext-real Element of REAL
|.q.| * |.q.| is V28() real ext-real non negative set
- (((q `1) / |.q.|) - cn) is V28() real ext-real Element of REAL
(- (((q `1) / |.q.|) - cn)) / (1 + cn) is V28() real ext-real Element of COMPLEX
- (1 + cn) is V28() real ext-real Element of REAL
(- (1 + cn)) / (1 + cn) is V28() real ext-real Element of COMPLEX
(q `1) ^2 is V28() real ext-real Element of REAL
(q `1) * (q `1) is V28() real ext-real set
(q `2) ^2 is V28() real ext-real Element of REAL
(q `2) * (q `2) is V28() real ext-real set
((q `1) ^2) + ((q `2) ^2) is V28() real ext-real Element of REAL
0 + ((q `1) ^2) is V28() real ext-real Element of REAL
(|.q.| ^2) / (|.q.| ^2) is V28() real ext-real Element of COMPLEX
((q `1) ^2) / (|.q.| ^2) is V28() real ext-real Element of COMPLEX
((q `1) / |.q.|) ^2 is V28() real ext-real Element of COMPLEX
((q `1) / |.q.|) * ((q `1) / |.q.|) is V28() real ext-real set
(- 1) - cn is V28() real ext-real Element of REAL
- (- (1 + cn)) is V28() real ext-real Element of REAL
((- (((q `1) / |.q.|) - cn)) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((q `1) / |.q.|) - cn)) / (1 + cn)) * ((- (((q `1) / |.q.|) - cn)) / (1 + cn)) is V28() real ext-real set
1 - (((- (((q `1) / |.q.|) - cn)) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((q `1) / |.q.|) - cn)) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
(- (((q `1) / |.q.|) - cn)) ^2 is V28() real ext-real Element of REAL
(- (((q `1) / |.q.|) - cn)) * (- (((q `1) / |.q.|) - cn)) is V28() real ext-real set
(1 + cn) ^2 is V28() real ext-real Element of REAL
(1 + cn) * (1 + cn) is V28() real ext-real set
((- (((q `1) / |.q.|) - cn)) ^2) / ((1 + cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((- (((q `1) / |.q.|) - cn)) ^2) / ((1 + cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((q `1) / |.q.|) - cn)) ^2) / ((1 + cn) ^2))) is V28() real ext-real Element of REAL
(((q `1) / |.q.|) - cn) ^2 is V28() real ext-real Element of REAL
(((q `1) / |.q.|) - cn) * (((q `1) / |.q.|) - cn) is V28() real ext-real set
((((q `1) / |.q.|) - cn) ^2) / ((1 + cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((((q `1) / |.q.|) - cn) ^2) / ((1 + cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((((q `1) / |.q.|) - cn) ^2) / ((1 + cn) ^2))) is V28() real ext-real Element of REAL
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q `2 is V28() real ext-real Element of REAL
q `1 is V28() real ext-real Element of REAL
|.q.| is V28() real ext-real non negative Element of REAL
(q `1) / |.q.| is V28() real ext-real Element of COMPLEX
p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p `2 is V28() real ext-real Element of REAL
p `1 is V28() real ext-real Element of REAL
|.p.| is V28() real ext-real non negative Element of REAL
(p `1) / |.p.| is V28() real ext-real Element of COMPLEX
(cn) . q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(cn) . p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((p `1) / |.p.|) - cn is V28() real ext-real Element of REAL
((q `1) / |.q.|) - cn is V28() real ext-real Element of REAL
1 - cn is V28() real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `1 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `1) / |.p2.| is V28() real ext-real Element of COMPLEX
p1 `1 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
(((p `1) / |.p.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
|.p.| * ((((p `1) / |.p.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
((((p `1) / |.p.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p `1) / |.p.|) - cn) / (1 - cn)) * ((((p `1) / |.p.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((p `1) / |.p.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p `1) / |.p.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.p.| * (sqrt (1 - (((((p `1) / |.p.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|[(|.p.| * ((((p `1) / |.p.|) - cn) / (1 - cn))),(|.p.| * (sqrt (1 - (((((p `1) / |.p.|) - cn) / (1 - cn)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(((q `1) / |.q.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
|.q.| * ((((q `1) / |.q.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
((((q `1) / |.q.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((q `1) / |.q.|) - cn) / (1 - cn)) * ((((q `1) / |.q.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.q.| * (sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|[(|.q.| * ((((q `1) / |.q.|) - cn) / (1 - cn))),(|.q.| * (sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q `2 is V28() real ext-real Element of REAL
q `1 is V28() real ext-real Element of REAL
|.q.| is V28() real ext-real non negative Element of REAL
(q `1) / |.q.| is V28() real ext-real Element of COMPLEX
p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p `2 is V28() real ext-real Element of REAL
p `1 is V28() real ext-real Element of REAL
|.p.| is V28() real ext-real non negative Element of REAL
(p `1) / |.p.| is V28() real ext-real Element of COMPLEX
(cn) . q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(cn) . p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((p `1) / |.p.|) - cn is V28() real ext-real Element of REAL
((q `1) / |.q.|) - cn is V28() real ext-real Element of REAL
1 + cn is V28() real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `1 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `1) / |.p2.| is V28() real ext-real Element of COMPLEX
p1 `1 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
(((p `1) / |.p.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
|.p.| * ((((p `1) / |.p.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
((((p `1) / |.p.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p `1) / |.p.|) - cn) / (1 + cn)) * ((((p `1) / |.p.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((p `1) / |.p.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p `1) / |.p.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
|.p.| * (sqrt (1 - (((((p `1) / |.p.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|[(|.p.| * ((((p `1) / |.p.|) - cn) / (1 + cn))),(|.p.| * (sqrt (1 - (((((p `1) / |.p.|) - cn) / (1 + cn)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(((q `1) / |.q.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
|.q.| * ((((q `1) / |.q.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
((((q `1) / |.q.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((q `1) / |.q.|) - cn) / (1 + cn)) * ((((q `1) / |.q.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((q `1) / |.q.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
|.q.| * (sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|[(|.q.| * ((((q `1) / |.q.|) - cn) / (1 + cn))),(|.q.| * (sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 + cn)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q `2 is V28() real ext-real Element of REAL
p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p `2 is V28() real ext-real Element of REAL
p `1 is V28() real ext-real Element of REAL
|.p.| is V28() real ext-real non negative Element of REAL
(p `1) / |.p.| is V28() real ext-real Element of COMPLEX
q `1 is V28() real ext-real Element of REAL
|.q.| is V28() real ext-real non negative Element of REAL
(q `1) / |.q.| is V28() real ext-real Element of COMPLEX
(cn) . q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(cn) . p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `1 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `1) / |.p2.| is V28() real ext-real Element of COMPLEX
p1 `1 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q `2 is V28() real ext-real Element of REAL
q `1 is V28() real ext-real Element of REAL
|.q.| is V28() real ext-real non negative Element of REAL
(q `1) / |.q.| is V28() real ext-real Element of COMPLEX
(cn) . q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((q `1) / |.q.|) - cn is V28() real ext-real Element of REAL
- (((q `1) / |.q.|) - cn) is V28() real ext-real Element of REAL
1 - cn is V28() real ext-real Element of REAL
(- (((q `1) / |.q.|) - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
((- (((q `1) / |.q.|) - cn)) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((q `1) / |.q.|) - cn)) / (1 - cn)) * ((- (((q `1) / |.q.|) - cn)) / (1 - cn)) is V28() real ext-real set
1 - (((- (((q `1) / |.q.|) - cn)) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((q `1) / |.q.|) - cn)) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p `2 is V28() real ext-real Element of REAL
p `1 is V28() real ext-real Element of REAL
(((q `1) / |.q.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
|.q.| * ((((q `1) / |.q.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
((((q `1) / |.q.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((q `1) / |.q.|) - cn) / (1 - cn)) * ((((q `1) / |.q.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.q.| * (sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|[(|.q.| * ((((q `1) / |.q.|) - cn) / (1 - cn))),(|.q.| * (sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn is V28() real ext-real set
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(cn) . (0. (TOP-REAL 2)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn is V28() real ext-real set
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q `2 is V28() real ext-real Element of REAL
|.q.| is V28() real ext-real non negative Element of REAL
(q `2) / |.q.| is V28() real ext-real Element of COMPLEX
q `1 is V28() real ext-real Element of REAL
((q `2) / |.q.|) - cn is V28() real ext-real set
1 - cn is V28() real ext-real Element of REAL
(((q `2) / |.q.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
((((q `2) / |.q.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((q `2) / |.q.|) - cn) / (1 - cn)) * ((((q `2) / |.q.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((q `2) / |.q.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|[(sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 - cn)) ^2))),((((q `2) / |.q.|) - cn) / (1 - cn))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.q.| * |[(sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 - cn)) ^2))),((((q `2) / |.q.|) - cn) / (1 - cn))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
1 + cn is V28() real ext-real Element of REAL
(((q `2) / |.q.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
((((q `2) / |.q.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((q `2) / |.q.|) - cn) / (1 + cn)) * ((((q `2) / |.q.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
|[(sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2))),((((q `2) / |.q.|) - cn) / (1 + cn))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.q.| * |[(sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2))),((((q `2) / |.q.|) - cn) / (1 + cn))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn is V28() real ext-real set
cn is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn `2 is V28() real ext-real Element of REAL
|.cn.| is V28() real ext-real non negative Element of REAL
(cn `2) / |.cn.| is V28() real ext-real Element of COMPLEX
cn `1 is V28() real ext-real Element of REAL
q is V28() real ext-real set
(q) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(q) . cn is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((cn `2) / |.cn.|) - q is V28() real ext-real set
1 - q is V28() real ext-real Element of REAL
(((cn `2) / |.cn.|) - q) / (1 - q) is V28() real ext-real Element of COMPLEX
((((cn `2) / |.cn.|) - q) / (1 - q)) ^2 is V28() real ext-real Element of COMPLEX
((((cn `2) / |.cn.|) - q) / (1 - q)) * ((((cn `2) / |.cn.|) - q) / (1 - q)) is V28() real ext-real set
1 - (((((cn `2) / |.cn.|) - q) / (1 - q)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((cn `2) / |.cn.|) - q) / (1 - q)) ^2)) is V28() real ext-real Element of REAL
|.cn.| * (sqrt (1 - (((((cn `2) / |.cn.|) - q) / (1 - q)) ^2))) is V28() real ext-real Element of REAL
|.cn.| * ((((cn `2) / |.cn.|) - q) / (1 - q)) is V28() real ext-real Element of REAL
|[(|.cn.| * (sqrt (1 - (((((cn `2) / |.cn.|) - q) / (1 - q)) ^2)))),(|.cn.| * ((((cn `2) / |.cn.|) - q) / (1 - q)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(q,cn) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(sqrt (1 - (((((cn `2) / |.cn.|) - q) / (1 - q)) ^2))),((((cn `2) / |.cn.|) - q) / (1 - q))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.cn.| * |[(sqrt (1 - (((((cn `2) / |.cn.|) - q) / (1 - q)) ^2))),((((cn `2) / |.cn.|) - q) / (1 - q))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn `2 is V28() real ext-real Element of REAL
|.cn.| is V28() real ext-real non negative Element of REAL
(cn `2) / |.cn.| is V28() real ext-real Element of COMPLEX
cn `1 is V28() real ext-real Element of REAL
q is V28() real ext-real Element of REAL
(q) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(q) . cn is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((cn `2) / |.cn.|) - q is V28() real ext-real Element of REAL
1 + q is V28() real ext-real Element of REAL
(((cn `2) / |.cn.|) - q) / (1 + q) is V28() real ext-real Element of COMPLEX
((((cn `2) / |.cn.|) - q) / (1 + q)) ^2 is V28() real ext-real Element of COMPLEX
((((cn `2) / |.cn.|) - q) / (1 + q)) * ((((cn `2) / |.cn.|) - q) / (1 + q)) is V28() real ext-real set
1 - (((((cn `2) / |.cn.|) - q) / (1 + q)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((cn `2) / |.cn.|) - q) / (1 + q)) ^2)) is V28() real ext-real Element of REAL
|.cn.| * (sqrt (1 - (((((cn `2) / |.cn.|) - q) / (1 + q)) ^2))) is V28() real ext-real Element of REAL
|.cn.| * ((((cn `2) / |.cn.|) - q) / (1 + q)) is V28() real ext-real Element of REAL
|[(|.cn.| * (sqrt (1 - (((((cn `2) / |.cn.|) - q) / (1 + q)) ^2)))),(|.cn.| * ((((cn `2) / |.cn.|) - q) / (1 + q)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(q,cn) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(sqrt (1 - (((((cn `2) / |.cn.|) - q) / (1 + q)) ^2))),((((cn `2) / |.cn.|) - q) / (1 + q))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.cn.| * |[(sqrt (1 - (((((cn `2) / |.cn.|) - q) / (1 + q)) ^2))),((((cn `2) / |.cn.|) - q) / (1 + q))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
1 - q is V28() real ext-real Element of REAL
(((cn `2) / |.cn.|) - q) / (1 - q) is V28() real ext-real Element of COMPLEX
cn is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn `2 is V28() real ext-real Element of REAL
|.cn.| is V28() real ext-real non negative Element of REAL
(cn `2) / |.cn.| is V28() real ext-real Element of COMPLEX
cn `1 is V28() real ext-real Element of REAL
q is V28() real ext-real Element of REAL
(q) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(q) . cn is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((cn `2) / |.cn.|) - q is V28() real ext-real Element of REAL
1 - q is V28() real ext-real Element of REAL
(((cn `2) / |.cn.|) - q) / (1 - q) is V28() real ext-real Element of COMPLEX
((((cn `2) / |.cn.|) - q) / (1 - q)) ^2 is V28() real ext-real Element of COMPLEX
((((cn `2) / |.cn.|) - q) / (1 - q)) * ((((cn `2) / |.cn.|) - q) / (1 - q)) is V28() real ext-real set
1 - (((((cn `2) / |.cn.|) - q) / (1 - q)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((cn `2) / |.cn.|) - q) / (1 - q)) ^2)) is V28() real ext-real Element of REAL
|.cn.| * (sqrt (1 - (((((cn `2) / |.cn.|) - q) / (1 - q)) ^2))) is V28() real ext-real Element of REAL
|.cn.| * ((((cn `2) / |.cn.|) - q) / (1 - q)) is V28() real ext-real Element of REAL
|[(|.cn.| * (sqrt (1 - (((((cn `2) / |.cn.|) - q) / (1 - q)) ^2)))),(|.cn.| * ((((cn `2) / |.cn.|) - q) / (1 - q)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
1 + q is V28() real ext-real Element of REAL
(((cn `2) / |.cn.|) - q) / (1 + q) is V28() real ext-real Element of COMPLEX
((((cn `2) / |.cn.|) - q) / (1 + q)) ^2 is V28() real ext-real Element of COMPLEX
((((cn `2) / |.cn.|) - q) / (1 + q)) * ((((cn `2) / |.cn.|) - q) / (1 + q)) is V28() real ext-real set
1 - (((((cn `2) / |.cn.|) - q) / (1 + q)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((cn `2) / |.cn.|) - q) / (1 + q)) ^2)) is V28() real ext-real Element of REAL
|.cn.| * (sqrt (1 - (((((cn `2) / |.cn.|) - q) / (1 + q)) ^2))) is V28() real ext-real Element of REAL
|.cn.| * ((((cn `2) / |.cn.|) - q) / (1 + q)) is V28() real ext-real Element of REAL
|[(|.cn.| * (sqrt (1 - (((((cn `2) / |.cn.|) - q) / (1 + q)) ^2)))),(|.cn.| * ((((cn `2) / |.cn.|) - q) / (1 + q)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(q,cn) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(sqrt (1 - (((((cn `2) / |.cn.|) - q) / (1 - q)) ^2))),((((cn `2) / |.cn.|) - q) / (1 - q))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.cn.| * |[(sqrt (1 - (((((cn `2) / |.cn.|) - q) / (1 - q)) ^2))),((((cn `2) / |.cn.|) - q) / (1 - q))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.cn.| ^2 is V28() real ext-real Element of REAL
|.cn.| * |.cn.| is V28() real ext-real non negative set
(cn `1) ^2 is V28() real ext-real Element of REAL
(cn `1) * (cn `1) is V28() real ext-real set
(cn `2) ^2 is V28() real ext-real Element of REAL
(cn `2) * (cn `2) is V28() real ext-real set
((cn `1) ^2) + ((cn `2) ^2) is V28() real ext-real Element of REAL
((cn `2) ^2) / (|.cn.| ^2) is V28() real ext-real Element of COMPLEX
((cn `2) / |.cn.|) ^2 is V28() real ext-real Element of COMPLEX
((cn `2) / |.cn.|) * ((cn `2) / |.cn.|) is V28() real ext-real set
sqrt (((cn `2) / |.cn.|) ^2) is V28() real ext-real set
- ((cn `2) / |.cn.|) is V28() real ext-real Element of COMPLEX
sqrt (|.cn.| ^2) is V28() real ext-real Element of REAL
1 * |.cn.| is V28() real ext-real non negative Element of REAL
((cn `2) / |.cn.|) * |.cn.| is V28() real ext-real Element of REAL
|.cn.| ^2 is V28() real ext-real Element of REAL
|.cn.| * |.cn.| is V28() real ext-real non negative set
(cn `1) ^2 is V28() real ext-real Element of REAL
(cn `1) * (cn `1) is V28() real ext-real set
(cn `2) ^2 is V28() real ext-real Element of REAL
(cn `2) * (cn `2) is V28() real ext-real set
((cn `1) ^2) + ((cn `2) ^2) is V28() real ext-real Element of REAL
- (cn `2) is V28() real ext-real Element of REAL
- |.cn.| is V28() real ext-real non positive Element of REAL
- (1 + q) is V28() real ext-real Element of REAL
(- (1 + q)) / (1 + q) is V28() real ext-real Element of COMPLEX
cn is V28() real ext-real Element of REAL
1 - cn is V28() real ext-real Element of REAL
q is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | q is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | q) is non empty set
K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1) is set
K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1)) is set
p is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
(2) | q is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of R^1))
proj2 | q is Relation-like the carrier of ((TOP-REAL 2) | q) -defined REAL -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q),REAL))
K20( the carrier of ((TOP-REAL 2) | q),REAL) is set
K19(K20( the carrier of ((TOP-REAL 2) | q),REAL)) is set
u2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
u2 is Element of the carrier of ((TOP-REAL 2) | q)
p1 . u2 is V28() real ext-real Element of the carrier of R^1
VV0 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
u2 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
dom u2 is Element of K19( the carrier of ((TOP-REAL 2) | q))
K19( the carrier of ((TOP-REAL 2) | q)) is set
dom p is Element of K19( the carrier of ((TOP-REAL 2) | q))
u3 is set
p . u3 is set
u2 . u3 is set
q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
proj2 . q4 is V28() real ext-real Element of REAL
q4 `2 is V28() real ext-real Element of REAL
(2) . q4 is V28() real ext-real Element of the carrier of R^1
|.q4.| is V28() real ext-real non negative Element of REAL
y is Element of the carrier of ((TOP-REAL 2) | q)
VV0 . y is V28() real ext-real Element of the carrier of R^1
proj2 . y is set
p1 . y is V28() real ext-real Element of the carrier of R^1
(2) . y is set
p . q4 is set
(q4 `2) / |.q4.| is V28() real ext-real Element of COMPLEX
((q4 `2) / |.q4.|) - cn is V28() real ext-real Element of REAL
(((q4 `2) / |.q4.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
|.q4.| * ((((q4 `2) / |.q4.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
cn is V28() real ext-real Element of REAL
1 + cn is V28() real ext-real Element of REAL
q is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | q is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | q) is non empty set
K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1) is set
K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1)) is set
p is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
(2) | q is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of R^1))
proj2 | q is Relation-like the carrier of ((TOP-REAL 2) | q) -defined REAL -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q),REAL))
K20( the carrier of ((TOP-REAL 2) | q),REAL) is set
K19(K20( the carrier of ((TOP-REAL 2) | q),REAL)) is set
u2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
u2 is Element of the carrier of ((TOP-REAL 2) | q)
p1 . u2 is V28() real ext-real Element of the carrier of R^1
VV0 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
u2 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
dom u2 is Element of K19( the carrier of ((TOP-REAL 2) | q))
K19( the carrier of ((TOP-REAL 2) | q)) is set
dom p is Element of K19( the carrier of ((TOP-REAL 2) | q))
u3 is set
p . u3 is set
u2 . u3 is set
q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
proj2 . q4 is V28() real ext-real Element of REAL
q4 `2 is V28() real ext-real Element of REAL
(2) . q4 is V28() real ext-real Element of the carrier of R^1
|.q4.| is V28() real ext-real non negative Element of REAL
y is Element of the carrier of ((TOP-REAL 2) | q)
VV0 . y is V28() real ext-real Element of the carrier of R^1
proj2 . y is set
p1 . y is V28() real ext-real Element of the carrier of R^1
(2) . y is set
p . q4 is set
(q4 `2) / |.q4.| is V28() real ext-real Element of COMPLEX
((q4 `2) / |.q4.|) - cn is V28() real ext-real Element of REAL
(((q4 `2) / |.q4.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
|.q4.| * ((((q4 `2) / |.q4.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
cn is V28() real ext-real Element of REAL
1 - cn is V28() real ext-real Element of REAL
q is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | q is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | q) is non empty set
K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1) is set
K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1)) is set
p is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
(2) | q is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of R^1))
proj2 | q is Relation-like the carrier of ((TOP-REAL 2) | q) -defined REAL -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q),REAL))
K20( the carrier of ((TOP-REAL 2) | q),REAL) is set
K19(K20( the carrier of ((TOP-REAL 2) | q),REAL)) is set
u2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
u2 is Element of the carrier of ((TOP-REAL 2) | q)
p1 . u2 is V28() real ext-real Element of the carrier of R^1
VV0 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
u2 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
dom u2 is Element of K19( the carrier of ((TOP-REAL 2) | q))
K19( the carrier of ((TOP-REAL 2) | q)) is set
dom p is Element of K19( the carrier of ((TOP-REAL 2) | q))
u3 is set
p . u3 is set
u2 . u3 is set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.y.| is V28() real ext-real non negative Element of REAL
|.y.| ^2 is V28() real ext-real Element of REAL
|.y.| * |.y.| is V28() real ext-real non negative set
y `1 is V28() real ext-real Element of REAL
(y `1) ^2 is V28() real ext-real Element of REAL
(y `1) * (y `1) is V28() real ext-real set
y `2 is V28() real ext-real Element of REAL
(y `2) ^2 is V28() real ext-real Element of REAL
(y `2) * (y `2) is V28() real ext-real set
((y `1) ^2) + ((y `2) ^2) is V28() real ext-real Element of REAL
(y `2) - |.y.| is V28() real ext-real Element of REAL
(y `2) + |.y.| is V28() real ext-real Element of REAL
((y `2) - |.y.|) * ((y `2) + |.y.|) is V28() real ext-real Element of REAL
- ((y `1) ^2) is V28() real ext-real Element of REAL
(y `2) / |.y.| is V28() real ext-real Element of COMPLEX
|.y.| / |.y.| is V28() real ext-real non negative Element of COMPLEX
((y `2) / |.y.|) - cn is V28() real ext-real Element of REAL
(1 - cn) ^2 is V28() real ext-real Element of REAL
(1 - cn) * (1 - cn) is V28() real ext-real set
(1 - cn) + cn is V28() real ext-real Element of REAL
0 + cn is V28() real ext-real Element of REAL
cn - ((y `2) / |.y.|) is V28() real ext-real Element of REAL
- (1 - cn) is V28() real ext-real Element of REAL
- (cn - ((y `2) / |.y.|)) is V28() real ext-real Element of REAL
(((y `2) / |.y.|) - cn) ^2 is V28() real ext-real Element of REAL
(((y `2) / |.y.|) - cn) * (((y `2) / |.y.|) - cn) is V28() real ext-real set
((((y `2) / |.y.|) - cn) ^2) / ((1 - cn) ^2) is V28() real ext-real Element of COMPLEX
((1 - cn) ^2) / ((1 - cn) ^2) is V28() real ext-real Element of COMPLEX
(((y `2) / |.y.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
((((y `2) / |.y.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((y `2) / |.y.|) - cn) / (1 - cn)) * ((((y `2) / |.y.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((y `2) / |.y.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
abs (1 - (((((y `2) / |.y.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
p . y is set
sqrt (abs (1 - (((((y `2) / |.y.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.y.| * (sqrt (abs (1 - (((((y `2) / |.y.|) - cn) / (1 - cn)) ^2)))) is V28() real ext-real Element of REAL
proj2 . y is V28() real ext-real Element of REAL
(2) . y is V28() real ext-real Element of the carrier of R^1
q4 is Element of the carrier of ((TOP-REAL 2) | q)
VV0 . q4 is V28() real ext-real Element of the carrier of R^1
proj2 . q4 is set
p1 . q4 is V28() real ext-real Element of the carrier of R^1
(2) . q4 is set
cn is V28() real ext-real Element of REAL
1 + cn is V28() real ext-real Element of REAL
q is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | q is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | q) is non empty set
K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1) is set
K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1)) is set
p is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
(2) | q is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of R^1))
proj2 | q is Relation-like the carrier of ((TOP-REAL 2) | q) -defined REAL -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q),REAL))
K20( the carrier of ((TOP-REAL 2) | q),REAL) is set
K19(K20( the carrier of ((TOP-REAL 2) | q),REAL)) is set
u2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
u2 is Element of the carrier of ((TOP-REAL 2) | q)
p1 . u2 is V28() real ext-real Element of the carrier of R^1
VV0 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
u2 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
dom u2 is Element of K19( the carrier of ((TOP-REAL 2) | q))
K19( the carrier of ((TOP-REAL 2) | q)) is set
dom p is Element of K19( the carrier of ((TOP-REAL 2) | q))
u3 is set
p . u3 is set
u2 . u3 is set
(1 + cn) ^2 is V28() real ext-real Element of REAL
(1 + cn) * (1 + cn) is V28() real ext-real set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.y.| is V28() real ext-real non negative Element of REAL
|.y.| ^2 is V28() real ext-real Element of REAL
|.y.| * |.y.| is V28() real ext-real non negative set
y `1 is V28() real ext-real Element of REAL
(y `1) ^2 is V28() real ext-real Element of REAL
(y `1) * (y `1) is V28() real ext-real set
y `2 is V28() real ext-real Element of REAL
(y `2) ^2 is V28() real ext-real Element of REAL
(y `2) * (y `2) is V28() real ext-real set
((y `1) ^2) + ((y `2) ^2) is V28() real ext-real Element of REAL
(y `2) - |.y.| is V28() real ext-real Element of REAL
(y `2) + |.y.| is V28() real ext-real Element of REAL
((y `2) - |.y.|) * ((y `2) + |.y.|) is V28() real ext-real Element of REAL
- ((y `1) ^2) is V28() real ext-real Element of REAL
- |.y.| is V28() real ext-real non positive Element of REAL
(- |.y.|) / |.y.| is V28() real ext-real non positive Element of COMPLEX
(y `2) / |.y.| is V28() real ext-real Element of COMPLEX
(- 1) - cn is V28() real ext-real Element of REAL
((y `2) / |.y.|) - cn is V28() real ext-real Element of REAL
- (1 + cn) is V28() real ext-real Element of REAL
cn - ((y `2) / |.y.|) is V28() real ext-real Element of REAL
- (cn - ((y `2) / |.y.|)) is V28() real ext-real Element of REAL
(((y `2) / |.y.|) - cn) ^2 is V28() real ext-real Element of REAL
(((y `2) / |.y.|) - cn) * (((y `2) / |.y.|) - cn) is V28() real ext-real set
((((y `2) / |.y.|) - cn) ^2) / ((1 + cn) ^2) is V28() real ext-real Element of COMPLEX
((1 + cn) ^2) / ((1 + cn) ^2) is V28() real ext-real Element of COMPLEX
(((y `2) / |.y.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
((((y `2) / |.y.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((y `2) / |.y.|) - cn) / (1 + cn)) * ((((y `2) / |.y.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((y `2) / |.y.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
abs (1 - (((((y `2) / |.y.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
p . y is set
sqrt (abs (1 - (((((y `2) / |.y.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|.y.| * (sqrt (abs (1 - (((((y `2) / |.y.|) - cn) / (1 + cn)) ^2)))) is V28() real ext-real Element of REAL
proj2 . y is V28() real ext-real Element of REAL
(2) . y is V28() real ext-real Element of the carrier of R^1
q4 is Element of the carrier of ((TOP-REAL 2) | q)
VV0 . q4 is V28() real ext-real Element of the carrier of R^1
proj2 . q4 is set
p1 . q4 is V28() real ext-real Element of the carrier of R^1
(2) . q4 is set
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( cn <= (b<sub>1</sub> `2) / |.b₁.| & 0 <= b₁ `1 & not b<sub>1</sub> = 0. (TOP-REAL 2) ) } is set
q is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | q is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | q) is set
p is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | p is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | p) is set
K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p)) is set
K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p))) is set
(cn) | q is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p1 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of ((TOP-REAL 2) | p) -valued Function-like quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p)))
cn ^2 is V28() real ext-real Element of REAL
cn * cn is V28() real ext-real set
1 - (cn ^2) is V28() real ext-real Element of REAL
sqrt (1 - (cn ^2)) is V28() real ext-real Element of REAL
|[(sqrt (1 - (cn ^2))),cn]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(sqrt (1 - (cn ^2))),cn]| `1 is V28() real ext-real Element of REAL
|[(sqrt (1 - (cn ^2))),cn]| `2 is V28() real ext-real Element of REAL
|.|[(sqrt (1 - (cn ^2))),cn]|.| is V28() real ext-real non negative Element of REAL
(sqrt (1 - (cn ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (cn ^2))) * (sqrt (1 - (cn ^2))) is V28() real ext-real set
((sqrt (1 - (cn ^2))) ^2) + (cn ^2) is V28() real ext-real Element of REAL
sqrt (((sqrt (1 - (cn ^2))) ^2) + (cn ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (cn ^2))) is V28() real ext-real Element of REAL
- (- (sqrt (1 - (cn ^2)))) is V28() real ext-real Element of REAL
(|[(sqrt (1 - (cn ^2))),cn]| `2) / |.|[(sqrt (1 - (cn ^2))),cn]|.| is V28() real ext-real Element of COMPLEX
VV0 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(cn) | VV0 is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
proj1 * ((cn) | VV0) is Relation-like the carrier of (TOP-REAL 2) -defined REAL -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2),REAL))
rng (proj1 * ((cn) | VV0)) is V126() V127() V128() Element of K19(REAL)
u2 is set
u3 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
u3 `2 is V28() real ext-real Element of REAL
|.u3.| is V28() real ext-real non negative Element of REAL
(u3 `2) / |.u3.| is V28() real ext-real Element of COMPLEX
u3 `1 is V28() real ext-real Element of REAL
dom ((cn) | VV0) is functional Element of K19( the carrier of (TOP-REAL 2))
proj2 * ((cn) | VV0) is Relation-like the carrier of (TOP-REAL 2) -defined REAL -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2),REAL))
dom (proj2 * ((cn) | VV0)) is functional Element of K19( the carrier of (TOP-REAL 2))
u2 is set
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
(dom (cn)) /\ VV0 is functional Element of K19( the carrier of (TOP-REAL 2))
dom proj2 is functional Element of K19( the carrier of (TOP-REAL 2))
(cn) . u2 is Relation-like Function-like set
rng (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
((cn) | VV0) . u2 is Relation-like Function-like set
rng (proj2 * ((cn) | VV0)) is V126() V127() V128() Element of K19(REAL)
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
(dom (cn)) /\ VV0 is functional Element of K19( the carrier of (TOP-REAL 2))
the carrier of (TOP-REAL 2) /\ VV0 is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | VV0 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | VV0) is non empty set
K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1) is set
K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1)) is set
u2 is Relation-like the carrier of ((TOP-REAL 2) | VV0) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1))
1 - cn is V28() real ext-real Element of REAL
u3 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
u2 . u3 is set
|.u3.| is V28() real ext-real non negative Element of REAL
u3 `2 is V28() real ext-real Element of REAL
(u3 `2) / |.u3.| is V28() real ext-real Element of COMPLEX
((u3 `2) / |.u3.|) - cn is V28() real ext-real Element of REAL
(((u3 `2) / |.u3.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
|.u3.| * ((((u3 `2) / |.u3.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
(cn) . u3 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((((u3 `2) / |.u3.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((u3 `2) / |.u3.|) - cn) / (1 - cn)) * ((((u3 `2) / |.u3.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((u3 `2) / |.u3.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((u3 `2) / |.u3.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.u3.| * (sqrt (1 - (((((u3 `2) / |.u3.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|[(|.u3.| * (sqrt (1 - (((((u3 `2) / |.u3.|) - cn) / (1 - cn)) ^2)))),(|.u3.| * ((((u3 `2) / |.u3.|) - cn) / (1 - cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `2 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `2) / |.y.| is V28() real ext-real Element of COMPLEX
y `1 is V28() real ext-real Element of REAL
((cn) | VV0) . u3 is Relation-like Function-like set
proj2 . |[(|.u3.| * (sqrt (1 - (((((u3 `2) / |.u3.|) - cn) / (1 - cn)) ^2)))),(|.u3.| * ((((u3 `2) / |.u3.|) - cn) / (1 - cn)))]| is V28() real ext-real Element of REAL
|[(|.u3.| * (sqrt (1 - (((((u3 `2) / |.u3.|) - cn) / (1 - cn)) ^2)))),(|.u3.| * ((((u3 `2) / |.u3.|) - cn) / (1 - cn)))]| `2 is V28() real ext-real Element of REAL
u3 is Relation-like the carrier of ((TOP-REAL 2) | VV0) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1))
dom (proj1 * ((cn) | VV0)) is functional Element of K19( the carrier of (TOP-REAL 2))
y is set
dom proj1 is functional Element of K19( the carrier of (TOP-REAL 2))
(cn) . y is Relation-like Function-like set
rng (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
((cn) | VV0) . y is Relation-like Function-like set
y is Relation-like the carrier of ((TOP-REAL 2) | VV0) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1))
q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y . q4 is set
|.q4.| is V28() real ext-real non negative Element of REAL
q4 `2 is V28() real ext-real Element of REAL
(q4 `2) / |.q4.| is V28() real ext-real Element of COMPLEX
((q4 `2) / |.q4.|) - cn is V28() real ext-real Element of REAL
(((q4 `2) / |.q4.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
((((q4 `2) / |.q4.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((q4 `2) / |.q4.|) - cn) / (1 - cn)) * ((((q4 `2) / |.q4.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((q4 `2) / |.q4.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((q4 `2) / |.q4.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.q4.| * (sqrt (1 - (((((q4 `2) / |.q4.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
(cn) . q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.q4.| * ((((q4 `2) / |.q4.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
|[(|.q4.| * (sqrt (1 - (((((q4 `2) / |.q4.|) - cn) / (1 - cn)) ^2)))),(|.q4.| * ((((q4 `2) / |.q4.|) - cn) / (1 - cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `2 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `2) / |.y.| is V28() real ext-real Element of COMPLEX
y `1 is V28() real ext-real Element of REAL
((cn) | VV0) . q4 is Relation-like Function-like set
proj1 . |[(|.q4.| * (sqrt (1 - (((((q4 `2) / |.q4.|) - cn) / (1 - cn)) ^2)))),(|.q4.| * ((((q4 `2) / |.q4.|) - cn) / (1 - cn)))]| is V28() real ext-real Element of REAL
|[(|.q4.| * (sqrt (1 - (((((q4 `2) / |.q4.|) - cn) / (1 - cn)) ^2)))),(|.q4.| * ((((q4 `2) / |.q4.|) - cn) / (1 - cn)))]| `1 is V28() real ext-real Element of REAL
q4 is Relation-like the carrier of ((TOP-REAL 2) | VV0) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1))
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `1 is V28() real ext-real Element of REAL
y `2 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `2) / |.y.| is V28() real ext-real Element of COMPLEX
x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x `2 is V28() real ext-real Element of REAL
|.x.| is V28() real ext-real non negative Element of REAL
(x `2) / |.x.| is V28() real ext-real Element of COMPLEX
x `1 is V28() real ext-real Element of REAL
y is V28() real ext-real set
x is V28() real ext-real set
|[y,x]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x is V28() real ext-real set
q4 . |[y,x]| is set
q is V28() real ext-real set
u3 . |[y,x]| is set
p1 . |[y,x]| is set
|[x,q]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.|[y,x]|.| is V28() real ext-real non negative Element of REAL
|[y,x]| `2 is V28() real ext-real Element of REAL
(|[y,x]| `2) / |.|[y,x]|.| is V28() real ext-real Element of COMPLEX
((|[y,x]| `2) / |.|[y,x]|.|) - cn is V28() real ext-real Element of REAL
(((|[y,x]| `2) / |.|[y,x]|.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
((((|[y,x]| `2) / |.|[y,x]|.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((|[y,x]| `2) / |.|[y,x]|.|) - cn) / (1 - cn)) * ((((|[y,x]| `2) / |.|[y,x]|.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((|[y,x]| `2) / |.|[y,x]|.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((|[y,x]| `2) / |.|[y,x]|.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.|[y,x]|.| * (sqrt (1 - (((((|[y,x]| `2) / |.|[y,x]|.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
((cn) | q) . |[y,x]| is Relation-like Function-like set
(cn) . |[y,x]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.|[y,x]|.| * ((((|[y,x]| `2) / |.|[y,x]|.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
|[(|.|[y,x]|.| * (sqrt (1 - (((((|[y,x]| `2) / |.|[y,x]|.|) - cn) / (1 - cn)) ^2)))),(|.|[y,x]|.| * ((((|[y,x]| `2) / |.|[y,x]|.|) - cn) / (1 - cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K111 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K111 `2 is V28() real ext-real Element of REAL
|.K111.| is V28() real ext-real non negative Element of REAL
(K111 `2) / |.K111.| is V28() real ext-real Element of COMPLEX
K111 `1 is V28() real ext-real Element of REAL
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `1 is V28() real ext-real Element of REAL
x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x `2 is V28() real ext-real Element of REAL
|.x.| is V28() real ext-real non negative Element of REAL
(x `2) / |.x.| is V28() real ext-real Element of COMPLEX
x `1 is V28() real ext-real Element of REAL
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( (b₁ `2) / |.b<sub>1</sub>.| <= cn & 0 <= b<sub>1</sub> `1 & not b₁ = 0. (TOP-REAL 2) ) } is set
q is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | q is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | q) is set
p is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | p is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | p) is set
K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p)) is set
K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p))) is set
(cn) | q is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p1 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of ((TOP-REAL 2) | p) -valued Function-like quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p)))
cn ^2 is V28() real ext-real Element of REAL
cn * cn is V28() real ext-real set
1 - (cn ^2) is V28() real ext-real Element of REAL
sqrt (1 - (cn ^2)) is V28() real ext-real Element of REAL
|[(sqrt (1 - (cn ^2))),cn]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(sqrt (1 - (cn ^2))),cn]| `1 is V28() real ext-real Element of REAL
|[(sqrt (1 - (cn ^2))),cn]| `2 is V28() real ext-real Element of REAL
|.|[(sqrt (1 - (cn ^2))),cn]|.| is V28() real ext-real non negative Element of REAL
(sqrt (1 - (cn ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (cn ^2))) * (sqrt (1 - (cn ^2))) is V28() real ext-real set
((sqrt (1 - (cn ^2))) ^2) + (cn ^2) is V28() real ext-real Element of REAL
sqrt (((sqrt (1 - (cn ^2))) ^2) + (cn ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (cn ^2))) is V28() real ext-real Element of REAL
- (- (sqrt (1 - (cn ^2)))) is V28() real ext-real Element of REAL
(|[(sqrt (1 - (cn ^2))),cn]| `2) / |.|[(sqrt (1 - (cn ^2))),cn]|.| is V28() real ext-real Element of COMPLEX
VV0 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(cn) | VV0 is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
proj1 * ((cn) | VV0) is Relation-like the carrier of (TOP-REAL 2) -defined REAL -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2),REAL))
rng (proj1 * ((cn) | VV0)) is V126() V127() V128() Element of K19(REAL)
u2 is set
u3 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
u3 `2 is V28() real ext-real Element of REAL
|.u3.| is V28() real ext-real non negative Element of REAL
(u3 `2) / |.u3.| is V28() real ext-real Element of COMPLEX
u3 `1 is V28() real ext-real Element of REAL
dom ((cn) | VV0) is functional Element of K19( the carrier of (TOP-REAL 2))
proj2 * ((cn) | VV0) is Relation-like the carrier of (TOP-REAL 2) -defined REAL -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2),REAL))
dom (proj2 * ((cn) | VV0)) is functional Element of K19( the carrier of (TOP-REAL 2))
u2 is set
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
(dom (cn)) /\ VV0 is functional Element of K19( the carrier of (TOP-REAL 2))
dom proj2 is functional Element of K19( the carrier of (TOP-REAL 2))
(cn) . u2 is Relation-like Function-like set
rng (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
((cn) | VV0) . u2 is Relation-like Function-like set
rng (proj2 * ((cn) | VV0)) is V126() V127() V128() Element of K19(REAL)
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
(dom (cn)) /\ VV0 is functional Element of K19( the carrier of (TOP-REAL 2))
the carrier of (TOP-REAL 2) /\ VV0 is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | VV0 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | VV0) is non empty set
K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1) is set
K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1)) is set
u2 is Relation-like the carrier of ((TOP-REAL 2) | VV0) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1))
1 + cn is V28() real ext-real Element of REAL
u3 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
u2 . u3 is set
|.u3.| is V28() real ext-real non negative Element of REAL
u3 `2 is V28() real ext-real Element of REAL
(u3 `2) / |.u3.| is V28() real ext-real Element of COMPLEX
((u3 `2) / |.u3.|) - cn is V28() real ext-real Element of REAL
(((u3 `2) / |.u3.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
|.u3.| * ((((u3 `2) / |.u3.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
(cn) . u3 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((((u3 `2) / |.u3.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((u3 `2) / |.u3.|) - cn) / (1 + cn)) * ((((u3 `2) / |.u3.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((u3 `2) / |.u3.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((u3 `2) / |.u3.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
|.u3.| * (sqrt (1 - (((((u3 `2) / |.u3.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|[(|.u3.| * (sqrt (1 - (((((u3 `2) / |.u3.|) - cn) / (1 + cn)) ^2)))),(|.u3.| * ((((u3 `2) / |.u3.|) - cn) / (1 + cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `2 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `2) / |.y.| is V28() real ext-real Element of COMPLEX
y `1 is V28() real ext-real Element of REAL
((cn) | VV0) . u3 is Relation-like Function-like set
proj2 . |[(|.u3.| * (sqrt (1 - (((((u3 `2) / |.u3.|) - cn) / (1 + cn)) ^2)))),(|.u3.| * ((((u3 `2) / |.u3.|) - cn) / (1 + cn)))]| is V28() real ext-real Element of REAL
|[(|.u3.| * (sqrt (1 - (((((u3 `2) / |.u3.|) - cn) / (1 + cn)) ^2)))),(|.u3.| * ((((u3 `2) / |.u3.|) - cn) / (1 + cn)))]| `2 is V28() real ext-real Element of REAL
u3 is Relation-like the carrier of ((TOP-REAL 2) | VV0) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1))
dom (proj1 * ((cn) | VV0)) is functional Element of K19( the carrier of (TOP-REAL 2))
y is set
dom proj1 is functional Element of K19( the carrier of (TOP-REAL 2))
(cn) . y is Relation-like Function-like set
rng (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
((cn) | VV0) . y is Relation-like Function-like set
y is Relation-like the carrier of ((TOP-REAL 2) | VV0) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1))
q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y . q4 is set
|.q4.| is V28() real ext-real non negative Element of REAL
q4 `2 is V28() real ext-real Element of REAL
(q4 `2) / |.q4.| is V28() real ext-real Element of COMPLEX
((q4 `2) / |.q4.|) - cn is V28() real ext-real Element of REAL
(((q4 `2) / |.q4.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
((((q4 `2) / |.q4.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((q4 `2) / |.q4.|) - cn) / (1 + cn)) * ((((q4 `2) / |.q4.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((q4 `2) / |.q4.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((q4 `2) / |.q4.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
|.q4.| * (sqrt (1 - (((((q4 `2) / |.q4.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
(cn) . q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.q4.| * ((((q4 `2) / |.q4.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
|[(|.q4.| * (sqrt (1 - (((((q4 `2) / |.q4.|) - cn) / (1 + cn)) ^2)))),(|.q4.| * ((((q4 `2) / |.q4.|) - cn) / (1 + cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `2 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `2) / |.y.| is V28() real ext-real Element of COMPLEX
y `1 is V28() real ext-real Element of REAL
((cn) | VV0) . q4 is Relation-like Function-like set
proj1 . |[(|.q4.| * (sqrt (1 - (((((q4 `2) / |.q4.|) - cn) / (1 + cn)) ^2)))),(|.q4.| * ((((q4 `2) / |.q4.|) - cn) / (1 + cn)))]| is V28() real ext-real Element of REAL
|[(|.q4.| * (sqrt (1 - (((((q4 `2) / |.q4.|) - cn) / (1 + cn)) ^2)))),(|.q4.| * ((((q4 `2) / |.q4.|) - cn) / (1 + cn)))]| `1 is V28() real ext-real Element of REAL
q4 is Relation-like the carrier of ((TOP-REAL 2) | VV0) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1))
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `1 is V28() real ext-real Element of REAL
y `2 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `2) / |.y.| is V28() real ext-real Element of COMPLEX
x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x `2 is V28() real ext-real Element of REAL
|.x.| is V28() real ext-real non negative Element of REAL
(x `2) / |.x.| is V28() real ext-real Element of COMPLEX
x `1 is V28() real ext-real Element of REAL
y is V28() real ext-real set
x is V28() real ext-real set
|[y,x]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x is V28() real ext-real set
q4 . |[y,x]| is set
q is V28() real ext-real set
u3 . |[y,x]| is set
p1 . |[y,x]| is set
|[x,q]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.|[y,x]|.| is V28() real ext-real non negative Element of REAL
|[y,x]| `2 is V28() real ext-real Element of REAL
(|[y,x]| `2) / |.|[y,x]|.| is V28() real ext-real Element of COMPLEX
((|[y,x]| `2) / |.|[y,x]|.|) - cn is V28() real ext-real Element of REAL
(((|[y,x]| `2) / |.|[y,x]|.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
((((|[y,x]| `2) / |.|[y,x]|.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((|[y,x]| `2) / |.|[y,x]|.|) - cn) / (1 + cn)) * ((((|[y,x]| `2) / |.|[y,x]|.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((|[y,x]| `2) / |.|[y,x]|.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((|[y,x]| `2) / |.|[y,x]|.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
|.|[y,x]|.| * (sqrt (1 - (((((|[y,x]| `2) / |.|[y,x]|.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
((cn) | q) . |[y,x]| is Relation-like Function-like set
(cn) . |[y,x]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.|[y,x]|.| * ((((|[y,x]| `2) / |.|[y,x]|.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
|[(|.|[y,x]|.| * (sqrt (1 - (((((|[y,x]| `2) / |.|[y,x]|.|) - cn) / (1 + cn)) ^2)))),(|.|[y,x]|.| * ((((|[y,x]| `2) / |.|[y,x]|.|) - cn) / (1 + cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K111 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K111 `2 is V28() real ext-real Element of REAL
|.K111.| is V28() real ext-real non negative Element of REAL
(K111 `2) / |.K111.| is V28() real ext-real Element of COMPLEX
K111 `1 is V28() real ext-real Element of REAL
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `1 is V28() real ext-real Element of REAL
x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x `2 is V28() real ext-real Element of REAL
|.x.| is V28() real ext-real non negative Element of REAL
(x `2) / |.x.| is V28() real ext-real Element of COMPLEX
x `1 is V28() real ext-real Element of REAL
cn is V28() real ext-real Element of REAL
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( cn * |.b₁.| <= b₁ `2 & 0 <= b<sub>1</sub> `1 ) } is set
q is functional Element of K19( the carrier of (TOP-REAL 2))
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₁[b₁] } is set
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₂[b₁] } is set
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( S₂[b₁] & S₁[b₁] ) } is set
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₂[b₁] } /\ { b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₁[b₁] } is set
p1 is functional Element of K19( the carrier of (TOP-REAL 2))
p is functional Element of K19( the carrier of (TOP-REAL 2))
cn is V28() real ext-real Element of REAL
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( b₁ `2 <= cn * |.b<sub>1</sub>.| & 0 <= b<sub>1</sub> `1 ) } is set
q is functional Element of K19( the carrier of (TOP-REAL 2))
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₁[b₁] } is set
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₂[b₁] } is set
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( S₂[b₁] & S₁[b₁] ) } is set
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₂[b₁] } /\ { b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₁[b₁] } is set
p1 is functional Element of K19( the carrier of (TOP-REAL 2))
p is functional Element of K19( the carrier of (TOP-REAL 2))
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | q is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | q) is set
p is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | p is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | p) is set
K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p)) is set
K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p))) is set
(cn) | q is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p1 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of ((TOP-REAL 2) | p) -valued Function-like quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p)))
cn ^2 is V28() real ext-real Element of REAL
cn * cn is V28() real ext-real set
1 - (cn ^2) is V28() real ext-real Element of REAL
sqrt (1 - (cn ^2)) is V28() real ext-real Element of REAL
|[(sqrt (1 - (cn ^2))),cn]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(sqrt (1 - (cn ^2))),cn]| `1 is V28() real ext-real Element of REAL
|[(sqrt (1 - (cn ^2))),cn]| `2 is V28() real ext-real Element of REAL
|.|[(sqrt (1 - (cn ^2))),cn]|.| is V28() real ext-real non negative Element of REAL
(sqrt (1 - (cn ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (cn ^2))) * (sqrt (1 - (cn ^2))) is V28() real ext-real set
((sqrt (1 - (cn ^2))) ^2) + (cn ^2) is V28() real ext-real Element of REAL
sqrt (((sqrt (1 - (cn ^2))) ^2) + (cn ^2)) is V28() real ext-real Element of REAL
(|[(sqrt (1 - (cn ^2))),cn]| `2) / |.|[(sqrt (1 - (cn ^2))),cn]|.| is V28() real ext-real Element of COMPLEX
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( cn <= (b<sub>1</sub> `2) / |.b₁.| & 0 <= b₁ `1 & not b<sub>1</sub> = 0. (TOP-REAL 2) ) } is set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S<sub>1</sub>[b<sub>1</sub>] } is set
VV0 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | VV0 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | VV0) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S<sub>2</sub>[b<sub>1</sub>] } is set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( cn * |.b<sub>1</sub>.| <= b<sub>1</sub> `2 & 0 <= b₁ `1 ) } is set
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₃[b₁] } is set
- (sqrt (1 - (cn ^2))) is V28() real ext-real Element of REAL
- (- (sqrt (1 - (cn ^2)))) is V28() real ext-real Element of REAL
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( (b₁ `2) / |.b<sub>1</sub>.| <= cn & 0 <= b<sub>1</sub> `1 & not b₁ = 0. (TOP-REAL 2) ) } is set
[#] ((TOP-REAL 2) | VV0) is non empty non proper closed Element of K19( the carrier of ((TOP-REAL 2) | VV0))
K19( the carrier of ((TOP-REAL 2) | VV0)) is set
u2 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(cn) | u2 is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
rng ((cn) | u2) is functional Element of K19( the carrier of (TOP-REAL 2))
q4 is set
dom ((cn) | u2) is functional Element of K19( the carrier of (TOP-REAL 2))
y is set
((cn) | u2) . y is Relation-like Function-like set
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(cn) . x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(dom (cn)) /\ u2 is functional Element of K19( the carrier of (TOP-REAL 2))
the carrier of (TOP-REAL 2) /\ u2 is functional Element of K19( the carrier of (TOP-REAL 2))
x `2 is V28() real ext-real Element of REAL
|.x.| is V28() real ext-real non negative Element of REAL
(x `2) / |.x.| is V28() real ext-real Element of COMPLEX
((x `2) / |.x.|) - cn is V28() real ext-real Element of REAL
x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x `2 is V28() real ext-real Element of REAL
|.x.| is V28() real ext-real non negative Element of REAL
(x `2) / |.x.| is V28() real ext-real Element of COMPLEX
x `1 is V28() real ext-real Element of REAL
x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x `2 is V28() real ext-real Element of REAL
|.x.| is V28() real ext-real non negative Element of REAL
(x `2) / |.x.| is V28() real ext-real Element of COMPLEX
x `1 is V28() real ext-real Element of REAL
|.x.| ^2 is V28() real ext-real Element of REAL
|.x.| * |.x.| is V28() real ext-real non negative set
0 ^2 is V28() real ext-real Element of REAL
0 * 0 is Function-like functional empty V28() real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() set
1 - cn is V28() real ext-real Element of REAL
(((x `2) / |.x.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
((((x `2) / |.x.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((x `2) / |.x.|) - cn) / (1 - cn)) * ((((x `2) / |.x.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((x `2) / |.x.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((x `2) / |.x.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.x.| * (sqrt (1 - (((((x `2) / |.x.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.x.| * ((((x `2) / |.x.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
|[(|.x.| * (sqrt (1 - (((((x `2) / |.x.|) - cn) / (1 - cn)) ^2)))),(|.x.| * ((((x `2) / |.x.|) - cn) / (1 - cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.x.| * (sqrt (1 - (((((x `2) / |.x.|) - cn) / (1 - cn)) ^2)))),(|.x.| * ((((x `2) / |.x.|) - cn) / (1 - cn)))]| `2 is V28() real ext-real Element of REAL
x `1 is V28() real ext-real Element of REAL
(x `1) ^2 is V28() real ext-real Element of REAL
(x `1) * (x `1) is V28() real ext-real set
(x `2) ^2 is V28() real ext-real Element of REAL
(x `2) * (x `2) is V28() real ext-real set
0 + ((x `2) ^2) is V28() real ext-real Element of REAL
((x `1) ^2) + ((x `2) ^2) is V28() real ext-real Element of REAL
((x `2) ^2) / (|.x.| ^2) is V28() real ext-real Element of COMPLEX
(|.x.| ^2) / (|.x.| ^2) is V28() real ext-real Element of COMPLEX
((x `2) / |.x.|) ^2 is V28() real ext-real Element of COMPLEX
((x `2) / |.x.|) * ((x `2) / |.x.|) is V28() real ext-real set
- (1 - cn) is V28() real ext-real Element of REAL
- (((x `2) / |.x.|) - cn) is V28() real ext-real Element of REAL
(- (1 - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
(- (((x `2) / |.x.|) - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
((- (((x `2) / |.x.|) - cn)) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((x `2) / |.x.|) - cn)) / (1 - cn)) * ((- (((x `2) / |.x.|) - cn)) / (1 - cn)) is V28() real ext-real set
1 - (((- (((x `2) / |.x.|) - cn)) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
- ((((x `2) / |.x.|) - cn) / (1 - cn)) is V28() real ext-real Element of COMPLEX
(- ((((x `2) / |.x.|) - cn) / (1 - cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((x `2) / |.x.|) - cn) / (1 - cn))) * (- ((((x `2) / |.x.|) - cn) / (1 - cn))) is V28() real ext-real set
1 - ((- ((((x `2) / |.x.|) - cn) / (1 - cn))) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((x `2) / |.x.|) - cn)) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
(- (((x `2) / |.x.|) - cn)) ^2 is V28() real ext-real Element of REAL
(- (((x `2) / |.x.|) - cn)) * (- (((x `2) / |.x.|) - cn)) is V28() real ext-real set
(1 - cn) ^2 is V28() real ext-real Element of REAL
(1 - cn) * (1 - cn) is V28() real ext-real set
((- (((x `2) / |.x.|) - cn)) ^2) / ((1 - cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((- (((x `2) / |.x.|) - cn)) ^2) / ((1 - cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((x `2) / |.x.|) - cn)) ^2) / ((1 - cn) ^2))) is V28() real ext-real Element of REAL
(((x `2) / |.x.|) - cn) ^2 is V28() real ext-real Element of REAL
(((x `2) / |.x.|) - cn) * (((x `2) / |.x.|) - cn) is V28() real ext-real set
((((x `2) / |.x.|) - cn) ^2) / ((1 - cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((((x `2) / |.x.|) - cn) ^2) / ((1 - cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((((x `2) / |.x.|) - cn) ^2) / ((1 - cn) ^2))) is V28() real ext-real Element of REAL
|[(|.x.| * (sqrt (1 - (((((x `2) / |.x.|) - cn) / (1 - cn)) ^2)))),(|.x.| * ((((x `2) / |.x.|) - cn) / (1 - cn)))]| `1 is V28() real ext-real Element of REAL
(|[(|.x.| * (sqrt (1 - (((((x `2) / |.x.|) - cn) / (1 - cn)) ^2)))),(|.x.| * ((((x `2) / |.x.|) - cn) / (1 - cn)))]| `1) ^2 is V28() real ext-real Element of REAL
(|[(|.x.| * (sqrt (1 - (((((x `2) / |.x.|) - cn) / (1 - cn)) ^2)))),(|.x.| * ((((x `2) / |.x.|) - cn) / (1 - cn)))]| `1) * (|[(|.x.| * (sqrt (1 - (((((x `2) / |.x.|) - cn) / (1 - cn)) ^2)))),(|.x.| * ((((x `2) / |.x.|) - cn) / (1 - cn)))]| `1) is V28() real ext-real set
(sqrt (1 - (((((x `2) / |.x.|) - cn) / (1 - cn)) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((x `2) / |.x.|) - cn) / (1 - cn)) ^2))) * (sqrt (1 - (((((x `2) / |.x.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real set
(|.x.| ^2) * ((sqrt (1 - (((((x `2) / |.x.|) - cn) / (1 - cn)) ^2))) ^2) is V28() real ext-real Element of REAL
(|.x.| ^2) * (1 - (((((x `2) / |.x.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.|[(|.x.| * (sqrt (1 - (((((x `2) / |.x.|) - cn) / (1 - cn)) ^2)))),(|.x.| * ((((x `2) / |.x.|) - cn) / (1 - cn)))]|.| is V28() real ext-real non negative Element of REAL
|.|[(|.x.| * (sqrt (1 - (((((x `2) / |.x.|) - cn) / (1 - cn)) ^2)))),(|.x.| * ((((x `2) / |.x.|) - cn) / (1 - cn)))]|.| ^2 is V28() real ext-real Element of REAL
|.|[(|.x.| * (sqrt (1 - (((((x `2) / |.x.|) - cn) / (1 - cn)) ^2)))),(|.x.| * ((((x `2) / |.x.|) - cn) / (1 - cn)))]|.| * |.|[(|.x.| * (sqrt (1 - (((((x `2) / |.x.|) - cn) / (1 - cn)) ^2)))),(|.x.| * ((((x `2) / |.x.|) - cn) / (1 - cn)))]|.| is V28() real ext-real non negative set
(|[(|.x.| * (sqrt (1 - (((((x `2) / |.x.|) - cn) / (1 - cn)) ^2)))),(|.x.| * ((((x `2) / |.x.|) - cn) / (1 - cn)))]| `2) ^2 is V28() real ext-real Element of REAL
(|[(|.x.| * (sqrt (1 - (((((x `2) / |.x.|) - cn) / (1 - cn)) ^2)))),(|.x.| * ((((x `2) / |.x.|) - cn) / (1 - cn)))]| `2) * (|[(|.x.| * (sqrt (1 - (((((x `2) / |.x.|) - cn) / (1 - cn)) ^2)))),(|.x.| * ((((x `2) / |.x.|) - cn) / (1 - cn)))]| `2) is V28() real ext-real set
((|[(|.x.| * (sqrt (1 - (((((x `2) / |.x.|) - cn) / (1 - cn)) ^2)))),(|.x.| * ((((x `2) / |.x.|) - cn) / (1 - cn)))]| `1) ^2) + ((|[(|.x.| * (sqrt (1 - (((((x `2) / |.x.|) - cn) / (1 - cn)) ^2)))),(|.x.| * ((((x `2) / |.x.|) - cn) / (1 - cn)))]| `2) ^2) is V28() real ext-real Element of REAL
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q `2 is V28() real ext-real Element of REAL
|.q.| is V28() real ext-real non negative Element of REAL
(q `2) / |.q.| is V28() real ext-real Element of COMPLEX
q `1 is V28() real ext-real Element of REAL
q4 is set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `2 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `2) / |.y.| is V28() real ext-real Element of COMPLEX
y `1 is V28() real ext-real Element of REAL
q4 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
y is set
x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x `1 is V28() real ext-real Element of REAL
VV0 \/ q4 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | q4 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
y is set
x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x `2 is V28() real ext-real Element of REAL
|.x.| is V28() real ext-real non negative Element of REAL
(x `2) / |.x.| is V28() real ext-real Element of COMPLEX
x `1 is V28() real ext-real Element of REAL
u3 is functional Element of K19( the carrier of (TOP-REAL 2))
y is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(cn) | y is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
rng ((cn) | y) is functional Element of K19( the carrier of (TOP-REAL 2))
x is set
dom ((cn) | y) is functional Element of K19( the carrier of (TOP-REAL 2))
x is set
((cn) | y) . x is Relation-like Function-like set
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(cn) . q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(dom (cn)) /\ y is functional Element of K19( the carrier of (TOP-REAL 2))
the carrier of (TOP-REAL 2) /\ y is functional Element of K19( the carrier of (TOP-REAL 2))
q `2 is V28() real ext-real Element of REAL
|.q.| is V28() real ext-real non negative Element of REAL
(q `2) / |.q.| is V28() real ext-real Element of COMPLEX
((q `2) / |.q.|) - cn is V28() real ext-real Element of REAL
K004 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K004 `2 is V28() real ext-real Element of REAL
|.K004.| is V28() real ext-real non negative Element of REAL
(K004 `2) / |.K004.| is V28() real ext-real Element of COMPLEX
K004 `1 is V28() real ext-real Element of REAL
K004 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K004 `2 is V28() real ext-real Element of REAL
|.K004.| is V28() real ext-real non negative Element of REAL
(K004 `2) / |.K004.| is V28() real ext-real Element of COMPLEX
K004 `1 is V28() real ext-real Element of REAL
|.q.| ^2 is V28() real ext-real Element of REAL
|.q.| * |.q.| is V28() real ext-real non negative set
0 ^2 is V28() real ext-real Element of REAL
0 * 0 is Function-like functional empty V28() real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() set
1 + cn is V28() real ext-real Element of REAL
(((q `2) / |.q.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
((((q `2) / |.q.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((q `2) / |.q.|) - cn) / (1 + cn)) * ((((q `2) / |.q.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
|.q.| * (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|.q.| * ((((q `2) / |.q.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
|[(|.q.| * (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2)))),(|.q.| * ((((q `2) / |.q.|) - cn) / (1 + cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.q.| * (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2)))),(|.q.| * ((((q `2) / |.q.|) - cn) / (1 + cn)))]| `2 is V28() real ext-real Element of REAL
q `1 is V28() real ext-real Element of REAL
(q `1) ^2 is V28() real ext-real Element of REAL
(q `1) * (q `1) is V28() real ext-real set
(q `2) ^2 is V28() real ext-real Element of REAL
(q `2) * (q `2) is V28() real ext-real set
((q `1) ^2) + ((q `2) ^2) is V28() real ext-real Element of REAL
0 + ((q `2) ^2) is V28() real ext-real Element of REAL
((q `2) ^2) / (|.q.| ^2) is V28() real ext-real Element of COMPLEX
(|.q.| ^2) / (|.q.| ^2) is V28() real ext-real Element of COMPLEX
((q `2) / |.q.|) ^2 is V28() real ext-real Element of COMPLEX
((q `2) / |.q.|) * ((q `2) / |.q.|) is V28() real ext-real set
(- 1) - cn is V28() real ext-real Element of REAL
- (1 + cn) is V28() real ext-real Element of REAL
(- (1 + cn)) / (1 + cn) is V28() real ext-real Element of COMPLEX
- ((((q `2) / |.q.|) - cn) / (1 + cn)) is V28() real ext-real Element of COMPLEX
(- ((((q `2) / |.q.|) - cn) / (1 + cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((q `2) / |.q.|) - cn) / (1 + cn))) * (- ((((q `2) / |.q.|) - cn) / (1 + cn))) is V28() real ext-real set
1 - ((- ((((q `2) / |.q.|) - cn) / (1 + cn))) ^2) is V28() real ext-real Element of REAL
- (((q `2) / |.q.|) - cn) is V28() real ext-real Element of REAL
(- (((q `2) / |.q.|) - cn)) / (1 + cn) is V28() real ext-real Element of COMPLEX
((- (((q `2) / |.q.|) - cn)) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((q `2) / |.q.|) - cn)) / (1 + cn)) * ((- (((q `2) / |.q.|) - cn)) / (1 + cn)) is V28() real ext-real set
1 - (((- (((q `2) / |.q.|) - cn)) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((q `2) / |.q.|) - cn)) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
(- (((q `2) / |.q.|) - cn)) ^2 is V28() real ext-real Element of REAL
(- (((q `2) / |.q.|) - cn)) * (- (((q `2) / |.q.|) - cn)) is V28() real ext-real set
(1 + cn) ^2 is V28() real ext-real Element of REAL
(1 + cn) * (1 + cn) is V28() real ext-real set
((- (((q `2) / |.q.|) - cn)) ^2) / ((1 + cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((- (((q `2) / |.q.|) - cn)) ^2) / ((1 + cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((q `2) / |.q.|) - cn)) ^2) / ((1 + cn) ^2))) is V28() real ext-real Element of REAL
(((q `2) / |.q.|) - cn) ^2 is V28() real ext-real Element of REAL
(((q `2) / |.q.|) - cn) * (((q `2) / |.q.|) - cn) is V28() real ext-real set
((((q `2) / |.q.|) - cn) ^2) / ((1 + cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((((q `2) / |.q.|) - cn) ^2) / ((1 + cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((((q `2) / |.q.|) - cn) ^2) / ((1 + cn) ^2))) is V28() real ext-real Element of REAL
|[(|.q.| * (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2)))),(|.q.| * ((((q `2) / |.q.|) - cn) / (1 + cn)))]| `1 is V28() real ext-real Element of REAL
(|[(|.q.| * (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2)))),(|.q.| * ((((q `2) / |.q.|) - cn) / (1 + cn)))]| `1) ^2 is V28() real ext-real Element of REAL
(|[(|.q.| * (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2)))),(|.q.| * ((((q `2) / |.q.|) - cn) / (1 + cn)))]| `1) * (|[(|.q.| * (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2)))),(|.q.| * ((((q `2) / |.q.|) - cn) / (1 + cn)))]| `1) is V28() real ext-real set
(sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2))) * (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real set
(|.q.| ^2) * ((sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2))) ^2) is V28() real ext-real Element of REAL
(|.q.| ^2) * (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
|.|[(|.q.| * (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2)))),(|.q.| * ((((q `2) / |.q.|) - cn) / (1 + cn)))]|.| is V28() real ext-real non negative Element of REAL
|.|[(|.q.| * (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2)))),(|.q.| * ((((q `2) / |.q.|) - cn) / (1 + cn)))]|.| ^2 is V28() real ext-real Element of REAL
|.|[(|.q.| * (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2)))),(|.q.| * ((((q `2) / |.q.|) - cn) / (1 + cn)))]|.| * |.|[(|.q.| * (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2)))),(|.q.| * ((((q `2) / |.q.|) - cn) / (1 + cn)))]|.| is V28() real ext-real non negative set
(|[(|.q.| * (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2)))),(|.q.| * ((((q `2) / |.q.|) - cn) / (1 + cn)))]| `2) ^2 is V28() real ext-real Element of REAL
(|[(|.q.| * (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2)))),(|.q.| * ((((q `2) / |.q.|) - cn) / (1 + cn)))]| `2) * (|[(|.q.| * (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2)))),(|.q.| * ((((q `2) / |.q.|) - cn) / (1 + cn)))]| `2) is V28() real ext-real set
((|[(|.q.| * (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2)))),(|.q.| * ((((q `2) / |.q.|) - cn) / (1 + cn)))]| `1) ^2) + ((|[(|.q.| * (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2)))),(|.q.| * ((((q `2) / |.q.|) - cn) / (1 + cn)))]| `2) ^2) is V28() real ext-real Element of REAL
K111 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K111 `2 is V28() real ext-real Element of REAL
|.K111.| is V28() real ext-real non negative Element of REAL
(K111 `2) / |.K111.| is V28() real ext-real Element of COMPLEX
K111 `1 is V28() real ext-real Element of REAL
the carrier of ((TOP-REAL 2) | q4) is non empty set
y is non empty Element of K19( the carrier of ((TOP-REAL 2) | VV0))
p1 | y is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of ((TOP-REAL 2) | p) -valued Function-like Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p)))
rng (p1 | y) is Element of K19( the carrier of ((TOP-REAL 2) | p))
K19( the carrier of ((TOP-REAL 2) | p)) is set
dom p1 is Element of K19( the carrier of ((TOP-REAL 2) | q))
K19( the carrier of ((TOP-REAL 2) | q)) is set
dom (p1 | y) is Element of K19( the carrier of ((TOP-REAL 2) | q))
((TOP-REAL 2) | VV0) | y is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of (TOP-REAL 2) | VV0
the carrier of (((TOP-REAL 2) | VV0) | y) is non empty set
K20( the carrier of (((TOP-REAL 2) | VV0) | y), the carrier of ((TOP-REAL 2) | q4)) is set
K19(K20( the carrier of (((TOP-REAL 2) | VV0) | y), the carrier of ((TOP-REAL 2) | q4))) is set
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
dom ((cn) | u2) is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | u2 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | u2) is non empty set
K20( the carrier of ((TOP-REAL 2) | u2), the carrier of ((TOP-REAL 2) | VV0)) is set
K19(K20( the carrier of ((TOP-REAL 2) | u2), the carrier of ((TOP-REAL 2) | VV0))) is set
dom ((cn) | y) is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | y is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | y) is non empty set
K20( the carrier of ((TOP-REAL 2) | y), the carrier of ((TOP-REAL 2) | VV0)) is set
K19(K20( the carrier of ((TOP-REAL 2) | y), the carrier of ((TOP-REAL 2) | VV0))) is set
x is non empty Element of K19( the carrier of ((TOP-REAL 2) | VV0))
p1 | x is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of ((TOP-REAL 2) | p) -valued Function-like Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p)))
rng (p1 | x) is Element of K19( the carrier of ((TOP-REAL 2) | p))
dom (p1 | x) is Element of K19( the carrier of ((TOP-REAL 2) | q))
((TOP-REAL 2) | VV0) | x is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of (TOP-REAL 2) | VV0
the carrier of (((TOP-REAL 2) | VV0) | x) is non empty set
K20( the carrier of (((TOP-REAL 2) | VV0) | x), the carrier of ((TOP-REAL 2) | q4)) is set
K19(K20( the carrier of (((TOP-REAL 2) | VV0) | x), the carrier of ((TOP-REAL 2) | q4))) is set
K111 is Relation-like the carrier of (((TOP-REAL 2) | VV0) | x) -defined the carrier of ((TOP-REAL 2) | q4) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (((TOP-REAL 2) | VV0) | x), the carrier of ((TOP-REAL 2) | q4)))
K004 is Relation-like the carrier of ((TOP-REAL 2) | y) -defined the carrier of ((TOP-REAL 2) | VV0) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | y), the carrier of ((TOP-REAL 2) | VV0)))
x is Relation-like the carrier of (((TOP-REAL 2) | VV0) | y) -defined the carrier of ((TOP-REAL 2) | q4) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (((TOP-REAL 2) | VV0) | y), the carrier of ((TOP-REAL 2) | q4)))
q is Relation-like the carrier of ((TOP-REAL 2) | u2) -defined the carrier of ((TOP-REAL 2) | VV0) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | u2), the carrier of ((TOP-REAL 2) | VV0)))
dom K111 is Element of K19( the carrier of (((TOP-REAL 2) | VV0) | x))
K19( the carrier of (((TOP-REAL 2) | VV0) | x)) is set
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₄[b₁] } is set
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( b₁ `2 <= cn * |.b<sub>1</sub>.| & 0 <= b<sub>1</sub> `1 ) } is set
f4 is functional Element of K19( the carrier of (TOP-REAL 2))
f4 /\ VV0 is functional Element of K19( the carrier of (TOP-REAL 2))
T1 is set
T2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
T2 `2 is V28() real ext-real Element of REAL
|.T2.| is V28() real ext-real non negative Element of REAL
cn * |.T2.| is V28() real ext-real Element of REAL
T2 `1 is V28() real ext-real Element of REAL
(T2 `2) / |.T2.| is V28() real ext-real Element of COMPLEX
(cn * |.T2.|) / |.T2.| is V28() real ext-real Element of COMPLEX
h is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
h `1 is V28() real ext-real Element of REAL
h is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
h `1 is V28() real ext-real Element of REAL
T1 is set
T2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
T2 `2 is V28() real ext-real Element of REAL
|.T2.| is V28() real ext-real non negative Element of REAL
(T2 `2) / |.T2.| is V28() real ext-real Element of COMPLEX
T2 `1 is V28() real ext-real Element of REAL
((T2 `2) / |.T2.|) * |.T2.| is V28() real ext-real Element of REAL
cn * |.T2.| is V28() real ext-real Element of REAL
f4 /\ ([#] ((TOP-REAL 2) | VV0)) is Element of K19( the carrier of ((TOP-REAL 2) | VV0))
u3 /\ VV0 is functional Element of K19( the carrier of (TOP-REAL 2))
T1 is set
T2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.T2.| is V28() real ext-real non negative Element of REAL
cn * |.T2.| is V28() real ext-real Element of REAL
T2 `2 is V28() real ext-real Element of REAL
T2 `1 is V28() real ext-real Element of REAL
(cn * |.T2.|) / |.T2.| is V28() real ext-real Element of COMPLEX
(T2 `2) / |.T2.| is V28() real ext-real Element of COMPLEX
h is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
h `1 is V28() real ext-real Element of REAL
h is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
h `1 is V28() real ext-real Element of REAL
T1 is set
T2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
T2 `2 is V28() real ext-real Element of REAL
|.T2.| is V28() real ext-real non negative Element of REAL
(T2 `2) / |.T2.| is V28() real ext-real Element of COMPLEX
T2 `1 is V28() real ext-real Element of REAL
cn * |.T2.| is V28() real ext-real Element of REAL
((T2 `2) / |.T2.|) * |.T2.| is V28() real ext-real Element of REAL
u3 /\ ([#] ((TOP-REAL 2) | VV0)) is Element of K19( the carrier of ((TOP-REAL 2) | VV0))
[#] (((TOP-REAL 2) | VV0) | x) is non empty non proper closed Element of K19( the carrier of (((TOP-REAL 2) | VV0) | x))
[#] (((TOP-REAL 2) | VV0) | y) is non empty non proper closed Element of K19( the carrier of (((TOP-REAL 2) | VV0) | y))
K19( the carrier of (((TOP-REAL 2) | VV0) | y)) is set
([#] (((TOP-REAL 2) | VV0) | y)) /\ ([#] (((TOP-REAL 2) | VV0) | x)) is Element of K19( the carrier of (((TOP-REAL 2) | VV0) | x))
h is set
x . h is set
K111 . h is set
p1 . h is set
y \/ x is non empty Element of K19( the carrier of ((TOP-REAL 2) | VV0))
h is set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `1 is V28() real ext-real Element of REAL
y `2 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `2) / |.y.| is V28() real ext-real Element of COMPLEX
y `2 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `2) / |.y.| is V28() real ext-real Element of COMPLEX
y `2 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `2) / |.y.| is V28() real ext-real Element of COMPLEX
([#] (((TOP-REAL 2) | VV0) | y)) \/ ([#] (((TOP-REAL 2) | VV0) | x)) is non empty set
K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of ((TOP-REAL 2) | q4)) is set
K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of ((TOP-REAL 2) | q4))) is set
x +* K111 is Relation-like Function-like set
h is Relation-like the carrier of ((TOP-REAL 2) | VV0) -defined the carrier of ((TOP-REAL 2) | q4) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of ((TOP-REAL 2) | q4)))
dom h is Element of K19( the carrier of ((TOP-REAL 2) | VV0))
dom x is Element of K19( the carrier of (((TOP-REAL 2) | VV0) | y))
y is set
h . y is set
p1 . y is set
(dom x) \/ (dom K111) is set
x . y is set
(dom x) \/ (dom K111) is set
K111 . y is set
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | q is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | q) is set
p is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | p is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | p) is set
K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p)) is set
K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p))) is set
(cn) | q is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p1 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of ((TOP-REAL 2) | p) -valued Function-like quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p)))
cn ^2 is V28() real ext-real Element of REAL
cn * cn is V28() real ext-real set
1 - (cn ^2) is V28() real ext-real Element of REAL
sqrt (1 - (cn ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (cn ^2))) is V28() real ext-real Element of REAL
- cn is V28() real ext-real Element of REAL
|[(- (sqrt (1 - (cn ^2)))),(- cn)]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
- (- (sqrt (1 - (cn ^2)))) is V28() real ext-real Element of REAL
|[(- (sqrt (1 - (cn ^2)))),(- cn)]| `1 is V28() real ext-real Element of REAL
VV0 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
u2 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
u3 is set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `1 is V28() real ext-real Element of REAL
(TOP-REAL 2) | VV0 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | VV0) is non empty set
(TOP-REAL 2) | u2 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | u2) is non empty set
K19( the carrier of ((TOP-REAL 2) | u2)) is set
K19( the carrier of ((TOP-REAL 2) | VV0)) is set
u3 is Element of the carrier of ((TOP-REAL 2) | VV0)
p1 . u3 is set
y is Element of K19( the carrier of ((TOP-REAL 2) | u2))
[#] ((TOP-REAL 2) | u2) is non empty non proper closed Element of K19( the carrier of ((TOP-REAL 2) | u2))
q4 is functional Element of K19( the carrier of (TOP-REAL 2))
q4 /\ ([#] ((TOP-REAL 2) | u2)) is Element of K19( the carrier of ((TOP-REAL 2) | u2))
[#] ((TOP-REAL 2) | VV0) is non empty non proper closed Element of K19( the carrier of ((TOP-REAL 2) | VV0))
q4 /\ ([#] ((TOP-REAL 2) | VV0)) is Element of K19( the carrier of ((TOP-REAL 2) | VV0))
(cn) . u3 is Relation-like Function-like set
y is Element of K19( the carrier of ((TOP-REAL 2) | VV0))
p1 .: y is Element of K19( the carrier of ((TOP-REAL 2) | p))
K19( the carrier of ((TOP-REAL 2) | p)) is set
x is set
dom p1 is Element of K19( the carrier of ((TOP-REAL 2) | q))
K19( the carrier of ((TOP-REAL 2) | q)) is set
x is set
p1 . x is set
K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of ((TOP-REAL 2) | u2)) is set
K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of ((TOP-REAL 2) | u2))) is set
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q `1 is V28() real ext-real Element of REAL
p1 . q is set
(cn) . q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x `1 is V28() real ext-real Element of REAL
(cn) . x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | q is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | q) is set
K19( the carrier of ((TOP-REAL 2) | q)) is set
p is Element of K19( the carrier of ((TOP-REAL 2) | q))
((TOP-REAL 2) | q) | p is strict TopSpace-like T_0 T_1 T_2 SubSpace of (TOP-REAL 2) | q
the carrier of (((TOP-REAL 2) | q) | p) is set
K20( the carrier of (((TOP-REAL 2) | q) | p), the carrier of ((TOP-REAL 2) | q)) is set
K19(K20( the carrier of (((TOP-REAL 2) | q) | p), the carrier of ((TOP-REAL 2) | q))) is set
(cn) | p is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p1 is Relation-like the carrier of (((TOP-REAL 2) | q) | p) -defined the carrier of ((TOP-REAL 2) | q) -valued Function-like quasi_total Element of K19(K20( the carrier of (((TOP-REAL 2) | q) | p), the carrier of ((TOP-REAL 2) | q)))
q3 is set
VV0 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
VV0 `1 is V28() real ext-real Element of REAL
VV0 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
VV0 `1 is V28() real ext-real Element of REAL
p2 is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | p2 is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | q is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | q) is set
K19( the carrier of ((TOP-REAL 2) | q)) is set
p is Element of K19( the carrier of ((TOP-REAL 2) | q))
((TOP-REAL 2) | q) | p is strict TopSpace-like T_0 T_1 T_2 SubSpace of (TOP-REAL 2) | q
the carrier of (((TOP-REAL 2) | q) | p) is set
K20( the carrier of (((TOP-REAL 2) | q) | p), the carrier of ((TOP-REAL 2) | q)) is set
K19(K20( the carrier of (((TOP-REAL 2) | q) | p), the carrier of ((TOP-REAL 2) | q))) is set
(cn) | p is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p1 is Relation-like the carrier of (((TOP-REAL 2) | q) | p) -defined the carrier of ((TOP-REAL 2) | q) -valued Function-like quasi_total Element of K19(K20( the carrier of (((TOP-REAL 2) | q) | p), the carrier of ((TOP-REAL 2) | q)))
q3 is set
VV0 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
VV0 `1 is V28() real ext-real Element of REAL
VV0 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
VV0 `1 is V28() real ext-real Element of REAL
p2 is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | p2 is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(cn) . q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.((cn) . q).| is V28() real ext-real non negative Element of REAL
|.q.| is V28() real ext-real non negative Element of REAL
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `2 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `2) / |.p2.| is V28() real ext-real Element of COMPLEX
p2 `1 is V28() real ext-real Element of REAL
(cn) . p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((p2 `2) / |.p2.|) - cn is V28() real ext-real Element of REAL
1 - cn is V28() real ext-real Element of REAL
(((p2 `2) / |.p2.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p2 `2) / |.p2.|) - cn) / (1 - cn)) * ((((p2 `2) / |.p2.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
|[(|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2)))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 - cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q3 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q3 `1 is V28() real ext-real Element of REAL
q3 `2 is V28() real ext-real Element of REAL
|.p2.| ^2 is V28() real ext-real Element of REAL
|.p2.| * |.p2.| is V28() real ext-real non negative set
(p2 `1) ^2 is V28() real ext-real Element of REAL
(p2 `1) * (p2 `1) is V28() real ext-real set
(p2 `2) ^2 is V28() real ext-real Element of REAL
(p2 `2) * (p2 `2) is V28() real ext-real set
((p2 `1) ^2) + ((p2 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p2 `2) ^2) is V28() real ext-real Element of REAL
((p2 `2) ^2) / (|.p2.| ^2) is V28() real ext-real Element of COMPLEX
(|.p2.| ^2) / (|.p2.| ^2) is V28() real ext-real Element of COMPLEX
((p2 `2) / |.p2.|) ^2 is V28() real ext-real Element of COMPLEX
((p2 `2) / |.p2.|) * ((p2 `2) / |.p2.|) is V28() real ext-real set
(1 - cn) " is V28() real ext-real Element of REAL
(((p2 `2) / |.p2.|) - cn) * ((1 - cn) ") is V28() real ext-real Element of REAL
(((p2 `2) / |.p2.|) - cn) * 0 is V28() real ext-real Element of REAL
|.p2.| * 1 is V28() real ext-real non negative Element of REAL
|.p2.| * 0 is Function-like functional empty V28() real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() Element of REAL
|[(|.p2.| * 1),(|.p2.| * 0)]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[|.p2.|,0]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((cn) . p2) `1 is V28() real ext-real Element of REAL
((cn) . p2) `2 is V28() real ext-real Element of REAL
0 ^2 is V28() real ext-real Element of REAL
0 * 0 is Function-like functional empty V28() real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() set
(|.p2.| ^2) + (0 ^2) is V28() real ext-real Element of REAL
sqrt ((|.p2.| ^2) + (0 ^2)) is V28() real ext-real Element of REAL
- (1 - cn) is V28() real ext-real Element of REAL
- (((p2 `2) / |.p2.|) - cn) is V28() real ext-real Element of REAL
(- (1 - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
(- (((p2 `2) / |.p2.|) - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
((- (((p2 `2) / |.p2.|) - cn)) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((p2 `2) / |.p2.|) - cn)) / (1 - cn)) * ((- (((p2 `2) / |.p2.|) - cn)) / (1 - cn)) is V28() real ext-real set
1 - (((- (((p2 `2) / |.p2.|) - cn)) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
- ((((p2 `2) / |.p2.|) - cn) / (1 - cn)) is V28() real ext-real Element of COMPLEX
(- ((((p2 `2) / |.p2.|) - cn) / (1 - cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((p2 `2) / |.p2.|) - cn) / (1 - cn))) * (- ((((p2 `2) / |.p2.|) - cn) / (1 - cn))) is V28() real ext-real set
1 - ((- ((((p2 `2) / |.p2.|) - cn) / (1 - cn))) ^2) is V28() real ext-real Element of REAL
(q3 `1) ^2 is V28() real ext-real Element of REAL
(q3 `1) * (q3 `1) is V28() real ext-real set
(sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2))) * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real set
(|.p2.| ^2) * ((sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2))) ^2) is V28() real ext-real Element of REAL
(|.p2.| ^2) * (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.q3.| is V28() real ext-real non negative Element of REAL
|.q3.| ^2 is V28() real ext-real Element of REAL
|.q3.| * |.q3.| is V28() real ext-real non negative set
(q3 `2) ^2 is V28() real ext-real Element of REAL
(q3 `2) * (q3 `2) is V28() real ext-real set
((q3 `1) ^2) + ((q3 `2) ^2) is V28() real ext-real Element of REAL
sqrt (|.q3.| ^2) is V28() real ext-real Element of REAL
(p2 `2) / |.q.| is V28() real ext-real Element of COMPLEX
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `2 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `2) / |.p2.| is V28() real ext-real Element of COMPLEX
p2 `1 is V28() real ext-real Element of REAL
|.p2.| ^2 is V28() real ext-real Element of REAL
|.p2.| * |.p2.| is V28() real ext-real non negative set
((p2 `2) / |.p2.|) - cn is V28() real ext-real Element of REAL
(p2 `1) ^2 is V28() real ext-real Element of REAL
(p2 `1) * (p2 `1) is V28() real ext-real set
(p2 `2) ^2 is V28() real ext-real Element of REAL
(p2 `2) * (p2 `2) is V28() real ext-real set
((p2 `1) ^2) + ((p2 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p2 `2) ^2) is V28() real ext-real Element of REAL
((p2 `2) ^2) / (|.p2.| ^2) is V28() real ext-real Element of COMPLEX
(|.p2.| ^2) / (|.p2.| ^2) is V28() real ext-real Element of COMPLEX
((p2 `2) / |.p2.|) ^2 is V28() real ext-real Element of COMPLEX
((p2 `2) / |.p2.|) * ((p2 `2) / |.p2.|) is V28() real ext-real set
(- 1) - cn is V28() real ext-real Element of REAL
(cn) . p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
1 + cn is V28() real ext-real Element of REAL
(((p2 `2) / |.p2.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p2 `2) / |.p2.|) - cn) / (1 + cn)) * ((((p2 `2) / |.p2.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
|[(|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2)))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 + cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q3 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q3 `1 is V28() real ext-real Element of REAL
q3 `2 is V28() real ext-real Element of REAL
(1 + cn) " is V28() real ext-real Element of REAL
(((p2 `2) / |.p2.|) - cn) * ((1 + cn) ") is V28() real ext-real Element of REAL
(((p2 `2) / |.p2.|) - cn) * 0 is V28() real ext-real Element of REAL
((cn) . p2) `1 is V28() real ext-real Element of REAL
((cn) . p2) `2 is V28() real ext-real Element of REAL
0 ^2 is V28() real ext-real Element of REAL
0 * 0 is Function-like functional empty V28() real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() set
(|.p2.| ^2) + (0 ^2) is V28() real ext-real Element of REAL
sqrt ((|.p2.| ^2) + (0 ^2)) is V28() real ext-real Element of REAL
- (1 + cn) is V28() real ext-real Element of REAL
(- (1 + cn)) / (1 + cn) is V28() real ext-real Element of COMPLEX
(q3 `1) ^2 is V28() real ext-real Element of REAL
(q3 `1) * (q3 `1) is V28() real ext-real set
(sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2))) * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real set
(|.p2.| ^2) * ((sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2))) ^2) is V28() real ext-real Element of REAL
(|.p2.| ^2) * (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
|.q3.| is V28() real ext-real non negative Element of REAL
|.q3.| ^2 is V28() real ext-real Element of REAL
|.q3.| * |.q3.| is V28() real ext-real non negative set
(q3 `2) ^2 is V28() real ext-real Element of REAL
(q3 `2) * (q3 `2) is V28() real ext-real set
((q3 `1) ^2) + ((q3 `2) ^2) is V28() real ext-real Element of REAL
sqrt (|.q3.| ^2) is V28() real ext-real Element of REAL
(p2 `2) / |.q.| is V28() real ext-real Element of COMPLEX
- (1 + cn) is V28() real ext-real Element of REAL
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `1 is V28() real ext-real Element of REAL
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `2 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `2) / |.p2.| is V28() real ext-real Element of COMPLEX
p2 `1 is V28() real ext-real Element of REAL
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is set
p is set
(cn) . q is Relation-like Function-like set
p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
|.p1.| ^2 is V28() real ext-real Element of REAL
|.p1.| * |.p1.| is V28() real ext-real non negative set
p1 `2 is V28() real ext-real Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((p1 `2) / |.p1.|) - cn is V28() real ext-real Element of REAL
1 + cn is V28() real ext-real Element of REAL
(((p1 `2) / |.p1.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p1 `2) / |.p1.|) - cn) / (1 + cn)) * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `1 is V28() real ext-real Element of REAL
(p1 `1) ^2 is V28() real ext-real Element of REAL
(p1 `1) * (p1 `1) is V28() real ext-real set
(p1 `2) ^2 is V28() real ext-real Element of REAL
(p1 `2) * (p1 `2) is V28() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p1 `2) ^2) is V28() real ext-real Element of REAL
(|.p1.| ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
((p1 `2) ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
((p1 `2) / |.p1.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `2) / |.p1.|) * ((p1 `2) / |.p1.|) is V28() real ext-real set
(- 1) - cn is V28() real ext-real Element of REAL
(- 1) * (1 + cn) is V28() real ext-real Element of REAL
((- 1) * (1 + cn)) / (1 + cn) is V28() real ext-real Element of COMPLEX
p1 `2 is V28() real ext-real Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((p1 `2) / |.p1.|) - cn is V28() real ext-real Element of REAL
1 - cn is V28() real ext-real Element of REAL
(((p1 `2) / |.p1.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p1 `2) / |.p1.|) - cn) / (1 - cn)) * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `1 is V28() real ext-real Element of REAL
(p1 `1) ^2 is V28() real ext-real Element of REAL
(p1 `1) * (p1 `1) is V28() real ext-real set
(p1 `2) ^2 is V28() real ext-real Element of REAL
(p1 `2) * (p1 `2) is V28() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p1 `2) ^2) is V28() real ext-real Element of REAL
(|.p1.| ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
((p1 `2) ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
((p1 `2) / |.p1.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `2) / |.p1.|) * ((p1 `2) / |.p1.|) is V28() real ext-real set
(1 - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
- (1 - cn) is V28() real ext-real Element of REAL
cn - cn is V28() real ext-real Element of REAL
(- 1) * (1 - cn) is V28() real ext-real Element of REAL
((- 1) * (1 - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
p1 `2 is V28() real ext-real Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is set
p is set
(cn) . q is Relation-like Function-like set
p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() real ext-real Element of REAL
|[0,1]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[0,1]| `1 is V28() real ext-real Element of REAL
|[0,1]| `2 is V28() real ext-real Element of REAL
p is V28() real ext-real Element of REAL
(p) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p1 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
p1 ` is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | p1 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | p1) is non empty set
K20( the carrier of ((TOP-REAL 2) | p1), the carrier of ((TOP-REAL 2) | p1)) is set
K19(K20( the carrier of ((TOP-REAL 2) | p1), the carrier of ((TOP-REAL 2) | p1))) is set
(p) | p1 is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is functional Element of K19( the carrier of (TOP-REAL 2))
q ` is functional Element of K19( the carrier of (TOP-REAL 2))
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( S<sub>1</sub>[b<sub>1</sub>] & not b<sub>1</sub> = 0. (TOP-REAL 2) ) } is set
K19( the carrier of ((TOP-REAL 2) | p1)) is set
p2 is non empty Element of K19( the carrier of ((TOP-REAL 2) | p1))
((TOP-REAL 2) | p1) | p2 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of (TOP-REAL 2) | p1
the carrier of (((TOP-REAL 2) | p1) | p2) is non empty set
(p) | p2 is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
rng ((p) | p2) is functional Element of K19( the carrier of (TOP-REAL 2))
q3 is set
dom ((p) | p2) is functional Element of K19( the carrier of (TOP-REAL 2))
VV0 is set
((p) | p2) . VV0 is Relation-like Function-like set
dom (p) is functional Element of K19( the carrier of (TOP-REAL 2))
(dom (p)) /\ p2 is Element of K19( the carrier of ((TOP-REAL 2) | p1))
u2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(p) . u2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q3 is set
VV0 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
VV0 `1 is V28() real ext-real Element of REAL
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( S₂[b₁] & not b₁ = 0. (TOP-REAL 2) ) } is set
q3 is non empty Element of K19( the carrier of ((TOP-REAL 2) | p1))
dom ((p) | p2) is functional Element of K19( the carrier of (TOP-REAL 2))
dom (p) is functional Element of K19( the carrier of (TOP-REAL 2))
(dom (p)) /\ p2 is Element of K19( the carrier of ((TOP-REAL 2) | p1))
the carrier of (TOP-REAL 2) /\ p2 is Element of K19( the carrier of ((TOP-REAL 2) | p1))
K20( the carrier of (((TOP-REAL 2) | p1) | p2), the carrier of ((TOP-REAL 2) | p1)) is set
K19(K20( the carrier of (((TOP-REAL 2) | p1) | p2), the carrier of ((TOP-REAL 2) | p1))) is set
((TOP-REAL 2) | p1) | q3 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of (TOP-REAL 2) | p1
the carrier of (((TOP-REAL 2) | p1) | q3) is non empty set
(p) | q3 is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
rng ((p) | q3) is functional Element of K19( the carrier of (TOP-REAL 2))
u2 is set
dom ((p) | q3) is functional Element of K19( the carrier of (TOP-REAL 2))
u3 is set
((p) | q3) . u3 is Relation-like Function-like set
(dom (p)) /\ q3 is Element of K19( the carrier of ((TOP-REAL 2) | p1))
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(p) . y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
u2 is set
u3 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
u3 `1 is V28() real ext-real Element of REAL
dom ((p) | q3) is functional Element of K19( the carrier of (TOP-REAL 2))
(dom (p)) /\ q3 is Element of K19( the carrier of ((TOP-REAL 2) | p1))
the carrier of (TOP-REAL 2) /\ q3 is Element of K19( the carrier of ((TOP-REAL 2) | p1))
K20( the carrier of (((TOP-REAL 2) | p1) | q3), the carrier of ((TOP-REAL 2) | p1)) is set
K19(K20( the carrier of (((TOP-REAL 2) | p1) | q3), the carrier of ((TOP-REAL 2) | p1))) is set
[#] (((TOP-REAL 2) | p1) | q3) is non empty non proper closed Element of K19( the carrier of (((TOP-REAL 2) | p1) | q3))
K19( the carrier of (((TOP-REAL 2) | p1) | q3)) is set
p2 \/ q3 is non empty Element of K19( the carrier of ((TOP-REAL 2) | p1))
u3 is set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `1 is V28() real ext-real Element of REAL
VV0 is Relation-like the carrier of (((TOP-REAL 2) | p1) | p2) -defined the carrier of ((TOP-REAL 2) | p1) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (((TOP-REAL 2) | p1) | p2), the carrier of ((TOP-REAL 2) | p1)))
dom VV0 is Element of K19( the carrier of (((TOP-REAL 2) | p1) | p2))
K19( the carrier of (((TOP-REAL 2) | p1) | p2)) is set
[#] (((TOP-REAL 2) | p1) | p2) is non empty non proper closed Element of K19( the carrier of (((TOP-REAL 2) | p1) | p2))
([#] (((TOP-REAL 2) | p1) | p2)) /\ ([#] (((TOP-REAL 2) | p1) | q3)) is Element of K19( the carrier of (((TOP-REAL 2) | p1) | q3))
u2 is Relation-like the carrier of (((TOP-REAL 2) | p1) | q3) -defined the carrier of ((TOP-REAL 2) | p1) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (((TOP-REAL 2) | p1) | q3), the carrier of ((TOP-REAL 2) | p1)))
u3 is set
VV0 . u3 is set
u2 . u3 is set
(p) . u3 is Relation-like Function-like set
[#] ((TOP-REAL 2) | p1) is non empty non proper closed Element of K19( the carrier of ((TOP-REAL 2) | p1))
([#] (((TOP-REAL 2) | p1) | p2)) \/ ([#] (((TOP-REAL 2) | p1) | q3)) is non empty set
VV0 +* u2 is Relation-like Function-like set
u3 is Relation-like the carrier of ((TOP-REAL 2) | p1) -defined the carrier of ((TOP-REAL 2) | p1) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | p1), the carrier of ((TOP-REAL 2) | p1)))
dom u3 is Element of K19( the carrier of ((TOP-REAL 2) | p1))
dom u2 is Element of K19( the carrier of (((TOP-REAL 2) | p1) | q3))
y is set
u3 . y is set
((p) | p1) . y is Relation-like Function-like set
(p1 `) ` is functional Element of K19( the carrier of (TOP-REAL 2))
q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((p) | p1) . q4 is Relation-like Function-like set
(p) . q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
VV0 . q4 is set
u3 . q4 is set
u2 +* VV0 is Relation-like Function-like set
(u2 +* VV0) . q4 is set
q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q4 `1 is V28() real ext-real Element of REAL
((p) | p1) . q4 is Relation-like Function-like set
(p) . q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
u2 . q4 is set
dom ((p) | p1) is functional Element of K19( the carrier of (TOP-REAL 2))
the carrier of (TOP-REAL 2) /\ p1 is functional Element of K19( the carrier of (TOP-REAL 2))
q is V28() real ext-real Element of REAL
(q) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p . (0. (TOP-REAL 2)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | cn is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | cn) is non empty set
p1 is Element of the carrier of ((TOP-REAL 2) | cn)
p . p1 is Relation-like Function-like set
[#] ((TOP-REAL 2) | cn) is non empty non proper closed Element of K19( the carrier of ((TOP-REAL 2) | cn))
K19( the carrier of ((TOP-REAL 2) | cn)) is set
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `2 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `2) / |.p2.| is V28() real ext-real Element of COMPLEX
p2 `1 is V28() real ext-real Element of REAL
((p2 `2) / |.p2.|) - q is V28() real ext-real Element of REAL
1 - q is V28() real ext-real Element of REAL
(((p2 `2) / |.p2.|) - q) / (1 - q) is V28() real ext-real Element of COMPLEX
((((p2 `2) / |.p2.|) - q) / (1 - q)) ^2 is V28() real ext-real Element of COMPLEX
((((p2 `2) / |.p2.|) - q) / (1 - q)) * ((((p2 `2) / |.p2.|) - q) / (1 - q)) is V28() real ext-real set
1 - (((((p2 `2) / |.p2.|) - q) / (1 - q)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p2 `2) / |.p2.|) - q) / (1 - q)) ^2)) is V28() real ext-real Element of REAL
|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - q) / (1 - q)) ^2))) is V28() real ext-real Element of REAL
|.p2.| * ((((p2 `2) / |.p2.|) - q) / (1 - q)) is V28() real ext-real Element of REAL
|[(|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - q) / (1 - q)) ^2)))),(|.p2.| * ((((p2 `2) / |.p2.|) - q) / (1 - q)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - q) / (1 - q)) ^2)))),(|.p2.| * ((((p2 `2) / |.p2.|) - q) / (1 - q)))]| `2 is V28() real ext-real Element of REAL
0 ^2 is V28() real ext-real Element of REAL
0 * 0 is Function-like functional empty V28() real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() set
1 - (0 ^2) is V28() real ext-real Element of REAL
sqrt (1 - (0 ^2)) is V28() real ext-real Element of REAL
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `2 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `2) / |.p2.| is V28() real ext-real Element of COMPLEX
p2 `1 is V28() real ext-real Element of REAL
((p2 `2) / |.p2.|) - q is V28() real ext-real Element of REAL
1 + q is V28() real ext-real Element of REAL
(((p2 `2) / |.p2.|) - q) / (1 + q) is V28() real ext-real Element of COMPLEX
((((p2 `2) / |.p2.|) - q) / (1 + q)) ^2 is V28() real ext-real Element of COMPLEX
((((p2 `2) / |.p2.|) - q) / (1 + q)) * ((((p2 `2) / |.p2.|) - q) / (1 + q)) is V28() real ext-real set
1 - (((((p2 `2) / |.p2.|) - q) / (1 + q)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p2 `2) / |.p2.|) - q) / (1 + q)) ^2)) is V28() real ext-real Element of REAL
|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - q) / (1 + q)) ^2))) is V28() real ext-real Element of REAL
|.p2.| * ((((p2 `2) / |.p2.|) - q) / (1 + q)) is V28() real ext-real Element of REAL
|[(|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - q) / (1 + q)) ^2)))),(|.p2.| * ((((p2 `2) / |.p2.|) - q) / (1 + q)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - q) / (1 + q)) ^2)))),(|.p2.| * ((((p2 `2) / |.p2.|) - q) / (1 + q)))]| `2 is V28() real ext-real Element of REAL
0 ^2 is V28() real ext-real Element of REAL
0 * 0 is Function-like functional empty V28() real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() set
1 - (0 ^2) is V28() real ext-real Element of REAL
sqrt (1 - (0 ^2)) is V28() real ext-real Element of REAL
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `1 is V28() real ext-real Element of REAL
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `2 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `2) / |.p2.| is V28() real ext-real Element of COMPLEX
p2 `1 is V28() real ext-real Element of REAL
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `2 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `2) / |.p2.| is V28() real ext-real Element of COMPLEX
p2 `1 is V28() real ext-real Element of REAL
p2 is functional Element of K19( the carrier of (TOP-REAL 2))
the carrier of (TopSpaceMetr (Euclid 2)) is set
K19( the carrier of (TopSpaceMetr (Euclid 2))) is set
q3 is Element of K19( the carrier of (TopSpaceMetr (Euclid 2)))
p1 is Element of the carrier of (Euclid 2)
VV0 is V28() real ext-real set
Ball (p1,VV0) is bounded Element of K19( the carrier of (Euclid 2))
u2 is V28() real ext-real Element of REAL
Ball (p1,u2) is bounded Element of K19( the carrier of (Euclid 2))
u3 is functional Element of K19( the carrier of (TOP-REAL 2))
p .: u3 is functional Element of K19( the carrier of (TOP-REAL 2))
y is set
dom p is functional Element of K19( the carrier of (TOP-REAL 2))
q4 is set
p . q4 is Relation-like Function-like set
rng p is functional Element of K19( the carrier of (TOP-REAL 2))
x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x is Element of the carrier of (Euclid 2)
dist (p1,x) is V28() real ext-real Element of REAL
(0. (TOP-REAL 2)) - x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
- x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K443((TOP-REAL 2),(0. (TOP-REAL 2)),(- x)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is Relation-like K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)) -defined the carrier of (TOP-REAL 2) -valued Function-like total quasi_total Element of K19(K20(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)))
K20(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) is set
K19(K20(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2))) is set
K230( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),(0. (TOP-REAL 2)),(- x)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.((0. (TOP-REAL 2)) - x).| is V28() real ext-real non negative Element of REAL
x `1 is V28() real ext-real Element of REAL
x `2 is V28() real ext-real Element of REAL
|.x.| is V28() real ext-real non negative Element of REAL
(x `2) / |.x.| is V28() real ext-real Element of COMPLEX
x `1 is V28() real ext-real Element of REAL
((x `2) / |.x.|) - q is V28() real ext-real Element of REAL
(x `1) ^2 is V28() real ext-real Element of REAL
(x `1) * (x `1) is V28() real ext-real set
|.x.| ^2 is V28() real ext-real Element of REAL
|.x.| * |.x.| is V28() real ext-real non negative set
(x `2) ^2 is V28() real ext-real Element of REAL
(x `2) * (x `2) is V28() real ext-real set
((x `1) ^2) + ((x `2) ^2) is V28() real ext-real Element of REAL
0 + ((x `2) ^2) is V28() real ext-real Element of REAL
((x `2) ^2) / (|.x.| ^2) is V28() real ext-real Element of COMPLEX
(|.x.| ^2) / (|.x.| ^2) is V28() real ext-real Element of COMPLEX
1 - q is V28() real ext-real Element of REAL
((x `2) / |.x.|) ^2 is V28() real ext-real Element of COMPLEX
((x `2) / |.x.|) * ((x `2) / |.x.|) is V28() real ext-real set
- (1 - q) is V28() real ext-real Element of REAL
- (((x `2) / |.x.|) - q) is V28() real ext-real Element of REAL
(- (1 - q)) / (1 - q) is V28() real ext-real Element of COMPLEX
(- (((x `2) / |.x.|) - q)) / (1 - q) is V28() real ext-real Element of COMPLEX
((- (((x `2) / |.x.|) - q)) / (1 - q)) ^2 is V28() real ext-real Element of COMPLEX
((- (((x `2) / |.x.|) - q)) / (1 - q)) * ((- (((x `2) / |.x.|) - q)) / (1 - q)) is V28() real ext-real set
1 - (((- (((x `2) / |.x.|) - q)) / (1 - q)) ^2) is V28() real ext-real Element of REAL
(((x `2) / |.x.|) - q) / (1 - q) is V28() real ext-real Element of COMPLEX
- ((((x `2) / |.x.|) - q) / (1 - q)) is V28() real ext-real Element of COMPLEX
(- ((((x `2) / |.x.|) - q) / (1 - q))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((x `2) / |.x.|) - q) / (1 - q))) * (- ((((x `2) / |.x.|) - q) / (1 - q))) is V28() real ext-real set
1 - ((- ((((x `2) / |.x.|) - q) / (1 - q))) ^2) is V28() real ext-real Element of REAL
(q) . x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((((x `2) / |.x.|) - q) / (1 - q)) ^2 is V28() real ext-real Element of COMPLEX
((((x `2) / |.x.|) - q) / (1 - q)) * ((((x `2) / |.x.|) - q) / (1 - q)) is V28() real ext-real set
1 - (((((x `2) / |.x.|) - q) / (1 - q)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((x `2) / |.x.|) - q) / (1 - q)) ^2)) is V28() real ext-real Element of REAL
|.x.| * (sqrt (1 - (((((x `2) / |.x.|) - q) / (1 - q)) ^2))) is V28() real ext-real Element of REAL
|.x.| * ((((x `2) / |.x.|) - q) / (1 - q)) is V28() real ext-real Element of REAL
|[(|.x.| * (sqrt (1 - (((((x `2) / |.x.|) - q) / (1 - q)) ^2)))),(|.x.| * ((((x `2) / |.x.|) - q) / (1 - q)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `2 is V28() real ext-real Element of REAL
y `1 is V28() real ext-real Element of REAL
(y `1) ^2 is V28() real ext-real Element of REAL
(y `1) * (y `1) is V28() real ext-real set
(sqrt (1 - (((((x `2) / |.x.|) - q) / (1 - q)) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((x `2) / |.x.|) - q) / (1 - q)) ^2))) * (sqrt (1 - (((((x `2) / |.x.|) - q) / (1 - q)) ^2))) is V28() real ext-real set
(|.x.| ^2) * ((sqrt (1 - (((((x `2) / |.x.|) - q) / (1 - q)) ^2))) ^2) is V28() real ext-real Element of REAL
(|.x.| ^2) * (1 - (((((x `2) / |.x.|) - q) / (1 - q)) ^2)) is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
|.y.| ^2 is V28() real ext-real Element of REAL
|.y.| * |.y.| is V28() real ext-real non negative set
(y `2) ^2 is V28() real ext-real Element of REAL
(y `2) * (y `2) is V28() real ext-real set
((y `1) ^2) + ((y `2) ^2) is V28() real ext-real Element of REAL
sqrt (|.y.| ^2) is V28() real ext-real Element of REAL
|.(- x).| is V28() real ext-real non negative Element of REAL
- y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.(- y).| is V28() real ext-real non negative Element of REAL
(0. (TOP-REAL 2)) - y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K443((TOP-REAL 2),(0. (TOP-REAL 2)),(- y)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K230( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),(0. (TOP-REAL 2)),(- y)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.((0. (TOP-REAL 2)) - y).| is V28() real ext-real non negative Element of REAL
q is Element of the carrier of (Euclid 2)
dist (p1,q) is V28() real ext-real Element of REAL
x `2 is V28() real ext-real Element of REAL
|.x.| is V28() real ext-real non negative Element of REAL
(x `2) / |.x.| is V28() real ext-real Element of COMPLEX
x `1 is V28() real ext-real Element of REAL
(x `1) ^2 is V28() real ext-real Element of REAL
(x `1) * (x `1) is V28() real ext-real set
|.x.| ^2 is V28() real ext-real Element of REAL
|.x.| * |.x.| is V28() real ext-real non negative set
(x `2) ^2 is V28() real ext-real Element of REAL
(x `2) * (x `2) is V28() real ext-real set
((x `1) ^2) + ((x `2) ^2) is V28() real ext-real Element of REAL
0 + ((x `2) ^2) is V28() real ext-real Element of REAL
((x `2) ^2) / (|.x.| ^2) is V28() real ext-real Element of COMPLEX
(|.x.| ^2) / (|.x.| ^2) is V28() real ext-real Element of COMPLEX
1 + q is V28() real ext-real Element of REAL
((x `2) / |.x.|) ^2 is V28() real ext-real Element of COMPLEX
((x `2) / |.x.|) * ((x `2) / |.x.|) is V28() real ext-real set
- ((x `2) / |.x.|) is V28() real ext-real Element of COMPLEX
- (- 1) is V28() real ext-real non negative Element of REAL
(- ((x `2) / |.x.|)) + q is V28() real ext-real Element of REAL
((x `2) / |.x.|) - q is V28() real ext-real Element of REAL
- (((x `2) / |.x.|) - q) is V28() real ext-real Element of REAL
(- (((x `2) / |.x.|) - q)) / (1 + q) is V28() real ext-real Element of COMPLEX
q - ((x `2) / |.x.|) is V28() real ext-real Element of REAL
((- (((x `2) / |.x.|) - q)) / (1 + q)) ^2 is V28() real ext-real Element of COMPLEX
((- (((x `2) / |.x.|) - q)) / (1 + q)) * ((- (((x `2) / |.x.|) - q)) / (1 + q)) is V28() real ext-real set
1 - (((- (((x `2) / |.x.|) - q)) / (1 + q)) ^2) is V28() real ext-real Element of REAL
(((x `2) / |.x.|) - q) / (1 + q) is V28() real ext-real Element of COMPLEX
- ((((x `2) / |.x.|) - q) / (1 + q)) is V28() real ext-real Element of COMPLEX
(- ((((x `2) / |.x.|) - q) / (1 + q))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((x `2) / |.x.|) - q) / (1 + q))) * (- ((((x `2) / |.x.|) - q) / (1 + q))) is V28() real ext-real set
1 - ((- ((((x `2) / |.x.|) - q) / (1 + q))) ^2) is V28() real ext-real Element of REAL
(q) . x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((((x `2) / |.x.|) - q) / (1 + q)) ^2 is V28() real ext-real Element of COMPLEX
((((x `2) / |.x.|) - q) / (1 + q)) * ((((x `2) / |.x.|) - q) / (1 + q)) is V28() real ext-real set
1 - (((((x `2) / |.x.|) - q) / (1 + q)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((x `2) / |.x.|) - q) / (1 + q)) ^2)) is V28() real ext-real Element of REAL
|.x.| * (sqrt (1 - (((((x `2) / |.x.|) - q) / (1 + q)) ^2))) is V28() real ext-real Element of REAL
|.x.| * ((((x `2) / |.x.|) - q) / (1 + q)) is V28() real ext-real Element of REAL
|[(|.x.| * (sqrt (1 - (((((x `2) / |.x.|) - q) / (1 + q)) ^2)))),(|.x.| * ((((x `2) / |.x.|) - q) / (1 + q)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `2 is V28() real ext-real Element of REAL
y `1 is V28() real ext-real Element of REAL
(y `1) ^2 is V28() real ext-real Element of REAL
(y `1) * (y `1) is V28() real ext-real set
(sqrt (1 - (((((x `2) / |.x.|) - q) / (1 + q)) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((x `2) / |.x.|) - q) / (1 + q)) ^2))) * (sqrt (1 - (((((x `2) / |.x.|) - q) / (1 + q)) ^2))) is V28() real ext-real set
(|.x.| ^2) * ((sqrt (1 - (((((x `2) / |.x.|) - q) / (1 + q)) ^2))) ^2) is V28() real ext-real Element of REAL
(|.x.| ^2) * (1 - (((((x `2) / |.x.|) - q) / (1 + q)) ^2)) is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
|.y.| ^2 is V28() real ext-real Element of REAL
|.y.| * |.y.| is V28() real ext-real non negative set
(y `2) ^2 is V28() real ext-real Element of REAL
(y `2) * (y `2) is V28() real ext-real set
((y `1) ^2) + ((y `2) ^2) is V28() real ext-real Element of REAL
sqrt (|.y.| ^2) is V28() real ext-real Element of REAL
|.(- x).| is V28() real ext-real non negative Element of REAL
- y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.(- y).| is V28() real ext-real non negative Element of REAL
(0. (TOP-REAL 2)) - y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K443((TOP-REAL 2),(0. (TOP-REAL 2)),(- y)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K230( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),(0. (TOP-REAL 2)),(- y)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.((0. (TOP-REAL 2)) - y).| is V28() real ext-real non negative Element of REAL
q is Element of the carrier of (Euclid 2)
dist (p1,q) is V28() real ext-real Element of REAL
x `1 is V28() real ext-real Element of REAL
x `2 is V28() real ext-real Element of REAL
|.x.| is V28() real ext-real non negative Element of REAL
(x `2) / |.x.| is V28() real ext-real Element of COMPLEX
x `1 is V28() real ext-real Element of REAL
x `2 is V28() real ext-real Element of REAL
|.x.| is V28() real ext-real non negative Element of REAL
(x `2) / |.x.| is V28() real ext-real Element of COMPLEX
cn ` is functional Element of K19( the carrier of (TOP-REAL 2))
K20( the carrier of ((TOP-REAL 2) | cn), the carrier of ((TOP-REAL 2) | cn)) is set
K19(K20( the carrier of ((TOP-REAL 2) | cn), the carrier of ((TOP-REAL 2) | cn))) is set
(q) | cn is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p1 is Relation-like the carrier of ((TOP-REAL 2) | cn) -defined the carrier of ((TOP-REAL 2) | cn) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | cn), the carrier of ((TOP-REAL 2) | cn)))
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
q is set
p is set
(cn) . q is Relation-like Function-like set
(cn) . p is Relation-like Function-like set
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
1 - cn is V28() real ext-real Element of REAL
p2 `1 is V28() real ext-real Element of REAL
(cn) . p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() real ext-real Element of REAL
p1 `2 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `1 is V28() real ext-real Element of REAL
((p1 `2) / |.p1.|) - cn is V28() real ext-real Element of REAL
(((p1 `2) / |.p1.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p1 `2) / |.p1.|) - cn) / (1 - cn)) * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.p1.| ^2 is V28() real ext-real Element of REAL
|.p1.| * |.p1.| is V28() real ext-real non negative set
(p1 `1) ^2 is V28() real ext-real Element of REAL
(p1 `1) * (p1 `1) is V28() real ext-real set
(p1 `2) ^2 is V28() real ext-real Element of REAL
(p1 `2) * (p1 `2) is V28() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p1 `2) ^2) is V28() real ext-real Element of REAL
((p1 `2) ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
(|.p1.| ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
((p1 `2) / |.p1.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `2) / |.p1.|) * ((p1 `2) / |.p1.|) is V28() real ext-real set
- (1 - cn) is V28() real ext-real Element of REAL
- (((p1 `2) / |.p1.|) - cn) is V28() real ext-real Element of REAL
(- (1 - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
(- (((p1 `2) / |.p1.|) - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((- (((p1 `2) / |.p1.|) - cn)) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((p1 `2) / |.p1.|) - cn)) / (1 - cn)) * ((- (((p1 `2) / |.p1.|) - cn)) / (1 - cn)) is V28() real ext-real set
1 - (((- (((p1 `2) / |.p1.|) - cn)) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((p1 `2) / |.p1.|) - cn)) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
(- (((p1 `2) / |.p1.|) - cn)) ^2 is V28() real ext-real Element of REAL
(- (((p1 `2) / |.p1.|) - cn)) * (- (((p1 `2) / |.p1.|) - cn)) is V28() real ext-real set
(1 - cn) ^2 is V28() real ext-real Element of REAL
(1 - cn) * (1 - cn) is V28() real ext-real set
((- (((p1 `2) / |.p1.|) - cn)) ^2) / ((1 - cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((- (((p1 `2) / |.p1.|) - cn)) ^2) / ((1 - cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((p1 `2) / |.p1.|) - cn)) ^2) / ((1 - cn) ^2))) is V28() real ext-real Element of REAL
(((p1 `2) / |.p1.|) - cn) ^2 is V28() real ext-real Element of REAL
(((p1 `2) / |.p1.|) - cn) * (((p1 `2) / |.p1.|) - cn) is V28() real ext-real set
((((p1 `2) / |.p1.|) - cn) ^2) / ((1 - cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((((p1 `2) / |.p1.|) - cn) ^2) / ((1 - cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `2) / |.p1.|) - cn) ^2) / ((1 - cn) ^2))) is V28() real ext-real Element of REAL
|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]| `1 is V28() real ext-real Element of REAL
- ((((p1 `2) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real Element of COMPLEX
(- ((((p1 `2) / |.p1.|) - cn) / (1 - cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((p1 `2) / |.p1.|) - cn) / (1 - cn))) * (- ((((p1 `2) / |.p1.|) - cn) / (1 - cn))) is V28() real ext-real set
1 - ((- ((((p1 `2) / |.p1.|) - cn) / (1 - cn))) ^2) is V28() real ext-real Element of REAL
1 * (1 - cn) is V28() real ext-real Element of REAL
1 * |.p1.| is V28() real ext-real non negative Element of REAL
p1 `2 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `1 is V28() real ext-real Element of REAL
|.p1.| ^2 is V28() real ext-real Element of REAL
|.p1.| * |.p1.| is V28() real ext-real non negative set
((p1 `2) / |.p1.|) - cn is V28() real ext-real Element of REAL
1 + cn is V28() real ext-real Element of REAL
(((p1 `2) / |.p1.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p1 `2) / |.p1.|) - cn) / (1 + cn)) * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(p1 `1) ^2 is V28() real ext-real Element of REAL
(p1 `1) * (p1 `1) is V28() real ext-real set
(p1 `2) ^2 is V28() real ext-real Element of REAL
(p1 `2) * (p1 `2) is V28() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V28() real ext-real Element of REAL
- (((p1 `2) / |.p1.|) - cn) is V28() real ext-real Element of REAL
(- (((p1 `2) / |.p1.|) - cn)) / (1 + cn) is V28() real ext-real Element of COMPLEX
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
0 + ((p1 `2) ^2) is V28() real ext-real Element of REAL
((p1 `2) ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
(|.p1.| ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
((p1 `2) / |.p1.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `2) / |.p1.|) * ((p1 `2) / |.p1.|) is V28() real ext-real set
- ((p1 `2) / |.p1.|) is V28() real ext-real Element of COMPLEX
(- ((p1 `2) / |.p1.|)) ^2 is V28() real ext-real Element of COMPLEX
(- ((p1 `2) / |.p1.|)) * (- ((p1 `2) / |.p1.|)) is V28() real ext-real set
(- ((p1 `2) / |.p1.|)) + cn is V28() real ext-real Element of REAL
((- (((p1 `2) / |.p1.|) - cn)) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((p1 `2) / |.p1.|) - cn)) / (1 + cn)) * ((- (((p1 `2) / |.p1.|) - cn)) / (1 + cn)) is V28() real ext-real set
1 - (((- (((p1 `2) / |.p1.|) - cn)) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((p1 `2) / |.p1.|) - cn)) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
(- (((p1 `2) / |.p1.|) - cn)) ^2 is V28() real ext-real Element of REAL
(- (((p1 `2) / |.p1.|) - cn)) * (- (((p1 `2) / |.p1.|) - cn)) is V28() real ext-real set
(1 + cn) ^2 is V28() real ext-real Element of REAL
(1 + cn) * (1 + cn) is V28() real ext-real set
((- (((p1 `2) / |.p1.|) - cn)) ^2) / ((1 + cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((- (((p1 `2) / |.p1.|) - cn)) ^2) / ((1 + cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((p1 `2) / |.p1.|) - cn)) ^2) / ((1 + cn) ^2))) is V28() real ext-real Element of REAL
(((p1 `2) / |.p1.|) - cn) ^2 is V28() real ext-real Element of REAL
(((p1 `2) / |.p1.|) - cn) * (((p1 `2) / |.p1.|) - cn) is V28() real ext-real set
((((p1 `2) / |.p1.|) - cn) ^2) / ((1 + cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((((p1 `2) / |.p1.|) - cn) ^2) / ((1 + cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `2) / |.p1.|) - cn) ^2) / ((1 + cn) ^2))) is V28() real ext-real Element of REAL
|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]| `1 is V28() real ext-real Element of REAL
- ((((p1 `2) / |.p1.|) - cn) / (1 + cn)) is V28() real ext-real Element of COMPLEX
(- ((((p1 `2) / |.p1.|) - cn) / (1 + cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((p1 `2) / |.p1.|) - cn) / (1 + cn))) * (- ((((p1 `2) / |.p1.|) - cn) / (1 + cn))) is V28() real ext-real set
1 - ((- ((((p1 `2) / |.p1.|) - cn) / (1 + cn))) ^2) is V28() real ext-real Element of REAL
sqrt ((- ((((p1 `2) / |.p1.|) - cn) / (1 + cn))) ^2) is V28() real ext-real set
1 * (1 + cn) is V28() real ext-real Element of REAL
(1 + cn) - cn is V28() real ext-real Element of REAL
- (p1 `2) is V28() real ext-real Element of REAL
(- (p1 `2)) / |.p1.| is V28() real ext-real Element of COMPLEX
1 * |.p1.| is V28() real ext-real non negative Element of REAL
((p1 `2) ^2) - ((p1 `2) ^2) is V28() real ext-real Element of REAL
p1 `1 is V28() real ext-real Element of REAL
p1 `2 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `1 is V28() real ext-real Element of REAL
p1 `2 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
p2 `2 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `2) / |.p2.| is V28() real ext-real Element of COMPLEX
p2 `1 is V28() real ext-real Element of REAL
|.p2.| ^2 is V28() real ext-real Element of REAL
|.p2.| * |.p2.| is V28() real ext-real non negative set
((p2 `2) / |.p2.|) - cn is V28() real ext-real Element of REAL
(((p2 `2) / |.p2.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p2 `2) / |.p2.|) - cn) / (1 - cn)) * ((((p2 `2) / |.p2.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
|[(|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2)))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 - cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2)))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 - cn)))]| `2 is V28() real ext-real Element of REAL
(cn) . p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2)))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 - cn)))]| `1 is V28() real ext-real Element of REAL
p1 `1 is V28() real ext-real Element of REAL
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(p2 `1) ^2 is V28() real ext-real Element of REAL
(p2 `1) * (p2 `1) is V28() real ext-real set
(p2 `2) ^2 is V28() real ext-real Element of REAL
(p2 `2) * (p2 `2) is V28() real ext-real set
((p2 `1) ^2) + ((p2 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p2 `2) ^2) is V28() real ext-real Element of REAL
((p2 `2) ^2) / (|.p2.| ^2) is V28() real ext-real Element of COMPLEX
(|.p2.| ^2) / (|.p2.| ^2) is V28() real ext-real Element of COMPLEX
((p2 `2) / |.p2.|) ^2 is V28() real ext-real Element of COMPLEX
((p2 `2) / |.p2.|) * ((p2 `2) / |.p2.|) is V28() real ext-real set
- (1 - cn) is V28() real ext-real Element of REAL
- (((p2 `2) / |.p2.|) - cn) is V28() real ext-real Element of REAL
(- (1 - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
(- (((p2 `2) / |.p2.|) - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
((- (((p2 `2) / |.p2.|) - cn)) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((p2 `2) / |.p2.|) - cn)) / (1 - cn)) * ((- (((p2 `2) / |.p2.|) - cn)) / (1 - cn)) is V28() real ext-real set
1 - (((- (((p2 `2) / |.p2.|) - cn)) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((p2 `2) / |.p2.|) - cn)) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
(- (((p2 `2) / |.p2.|) - cn)) ^2 is V28() real ext-real Element of REAL
(- (((p2 `2) / |.p2.|) - cn)) * (- (((p2 `2) / |.p2.|) - cn)) is V28() real ext-real set
(1 - cn) ^2 is V28() real ext-real Element of REAL
(1 - cn) * (1 - cn) is V28() real ext-real set
((- (((p2 `2) / |.p2.|) - cn)) ^2) / ((1 - cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((- (((p2 `2) / |.p2.|) - cn)) ^2) / ((1 - cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((p2 `2) / |.p2.|) - cn)) ^2) / ((1 - cn) ^2))) is V28() real ext-real Element of REAL
(((p2 `2) / |.p2.|) - cn) ^2 is V28() real ext-real Element of REAL
(((p2 `2) / |.p2.|) - cn) * (((p2 `2) / |.p2.|) - cn) is V28() real ext-real set
((((p2 `2) / |.p2.|) - cn) ^2) / ((1 - cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((((p2 `2) / |.p2.|) - cn) ^2) / ((1 - cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((((p2 `2) / |.p2.|) - cn) ^2) / ((1 - cn) ^2))) is V28() real ext-real Element of REAL
- ((((p2 `2) / |.p2.|) - cn) / (1 - cn)) is V28() real ext-real Element of COMPLEX
(- ((((p2 `2) / |.p2.|) - cn) / (1 - cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((p2 `2) / |.p2.|) - cn) / (1 - cn))) * (- ((((p2 `2) / |.p2.|) - cn) / (1 - cn))) is V28() real ext-real set
1 - ((- ((((p2 `2) / |.p2.|) - cn) / (1 - cn))) ^2) is V28() real ext-real Element of REAL
1 * (1 - cn) is V28() real ext-real Element of REAL
1 * |.p2.| is V28() real ext-real non negative Element of REAL
p1 `2 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `1 is V28() real ext-real Element of REAL
(p2 `1) ^2 is V28() real ext-real Element of REAL
(p2 `1) * (p2 `1) is V28() real ext-real set
(p2 `2) ^2 is V28() real ext-real Element of REAL
(p2 `2) * (p2 `2) is V28() real ext-real set
((p2 `1) ^2) + ((p2 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p2 `2) ^2) is V28() real ext-real Element of REAL
((p2 `2) ^2) / (|.p2.| ^2) is V28() real ext-real Element of COMPLEX
(|.p2.| ^2) / (|.p2.| ^2) is V28() real ext-real Element of COMPLEX
((p2 `2) / |.p2.|) ^2 is V28() real ext-real Element of COMPLEX
((p2 `2) / |.p2.|) * ((p2 `2) / |.p2.|) is V28() real ext-real set
- (1 - cn) is V28() real ext-real Element of REAL
- (((p2 `2) / |.p2.|) - cn) is V28() real ext-real Element of REAL
(- (1 - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
(- (((p2 `2) / |.p2.|) - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
((- (((p2 `2) / |.p2.|) - cn)) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((p2 `2) / |.p2.|) - cn)) / (1 - cn)) * ((- (((p2 `2) / |.p2.|) - cn)) / (1 - cn)) is V28() real ext-real set
1 - (((- (((p2 `2) / |.p2.|) - cn)) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
- ((((p2 `2) / |.p2.|) - cn) / (1 - cn)) is V28() real ext-real Element of COMPLEX
(- ((((p2 `2) / |.p2.|) - cn) / (1 - cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((p2 `2) / |.p2.|) - cn) / (1 - cn))) * (- ((((p2 `2) / |.p2.|) - cn) / (1 - cn))) is V28() real ext-real set
1 - ((- ((((p2 `2) / |.p2.|) - cn) / (1 - cn))) ^2) is V28() real ext-real Element of REAL
(|[(|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2)))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 - cn)))]| `1) ^2 is V28() real ext-real Element of REAL
(|[(|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2)))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 - cn)))]| `1) * (|[(|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2)))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 - cn)))]| `1) is V28() real ext-real set
(sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2))) * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real set
(|.p2.| ^2) * ((sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2))) ^2) is V28() real ext-real Element of REAL
(|.p2.| ^2) * (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.|[(|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2)))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 - cn)))]|.| is V28() real ext-real non negative Element of REAL
|.|[(|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2)))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 - cn)))]|.| ^2 is V28() real ext-real Element of REAL
|.|[(|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2)))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 - cn)))]|.| * |.|[(|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2)))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 - cn)))]|.| is V28() real ext-real non negative set
(|[(|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2)))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 - cn)))]| `2) ^2 is V28() real ext-real Element of REAL
(|[(|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2)))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 - cn)))]| `2) * (|[(|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2)))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 - cn)))]| `2) is V28() real ext-real set
((|[(|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2)))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 - cn)))]| `1) ^2) + ((|[(|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2)))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 - cn)))]| `2) ^2) is V28() real ext-real Element of REAL
sqrt (|.|[(|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 - cn)) ^2)))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 - cn)))]|.| ^2) is V28() real ext-real Element of REAL
(p1 `1) ^2 is V28() real ext-real Element of REAL
(p1 `1) * (p1 `1) is V28() real ext-real set
|.p1.| ^2 is V28() real ext-real Element of REAL
|.p1.| * |.p1.| is V28() real ext-real non negative set
(p1 `2) ^2 is V28() real ext-real Element of REAL
(p1 `2) * (p1 `2) is V28() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p1 `2) ^2) is V28() real ext-real Element of REAL
((p1 `2) ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
(|.p1.| ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
((p1 `2) / |.p1.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `2) / |.p1.|) * ((p1 `2) / |.p1.|) is V28() real ext-real set
((p1 `2) / |.p1.|) - cn is V28() real ext-real Element of REAL
- (((p1 `2) / |.p1.|) - cn) is V28() real ext-real Element of REAL
(- (((p1 `2) / |.p1.|) - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
((- (((p1 `2) / |.p1.|) - cn)) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((p1 `2) / |.p1.|) - cn)) / (1 - cn)) * ((- (((p1 `2) / |.p1.|) - cn)) / (1 - cn)) is V28() real ext-real set
1 - (((- (((p1 `2) / |.p1.|) - cn)) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
(((p1 `2) / |.p1.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
- ((((p1 `2) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real Element of COMPLEX
(- ((((p1 `2) / |.p1.|) - cn) / (1 - cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((p1 `2) / |.p1.|) - cn) / (1 - cn))) * (- ((((p1 `2) / |.p1.|) - cn) / (1 - cn))) is V28() real ext-real set
1 - ((- ((((p1 `2) / |.p1.|) - cn) / (1 - cn))) ^2) is V28() real ext-real Element of REAL
((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p1 `2) / |.p1.|) - cn) / (1 - cn)) * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]| `2 is V28() real ext-real Element of REAL
|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]| `1 is V28() real ext-real Element of REAL
(|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]| `1) ^2 is V28() real ext-real Element of REAL
(|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]| `1) * (|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]| `1) is V28() real ext-real set
(sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))) * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real set
(|.p1.| ^2) * ((sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))) ^2) is V28() real ext-real Element of REAL
(|.p1.| ^2) * (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]|.| is V28() real ext-real non negative Element of REAL
|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]|.| ^2 is V28() real ext-real Element of REAL
|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]|.| * |.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]|.| is V28() real ext-real non negative set
(|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]| `2) ^2 is V28() real ext-real Element of REAL
(|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]| `2) * (|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]| `2) is V28() real ext-real set
((|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]| `1) ^2) + ((|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]| `2) ^2) is V28() real ext-real Element of REAL
sqrt (|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]|.| ^2) is V28() real ext-real Element of REAL
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 - cn))) / |.p1.| is V28() real ext-real Element of COMPLEX
((((p1 `2) / |.p1.|) - cn) / (1 - cn)) * (1 - cn) is V28() real ext-real Element of REAL
((p1 `2) / |.p1.|) * |.p1.| is V28() real ext-real Element of REAL
|[(p1 `1),(p1 `2)]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
sqrt ((p2 `1) ^2) is V28() real ext-real Element of REAL
p1 `2 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `1 is V28() real ext-real Element of REAL
((p1 `2) / |.p1.|) - cn is V28() real ext-real Element of REAL
1 + cn is V28() real ext-real Element of REAL
(((p1 `2) / |.p1.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p1 `2) / |.p1.|) - cn) / (1 + cn)) * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]| `2 is V28() real ext-real Element of REAL
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() real ext-real Element of REAL
p1 `2 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `1 is V28() real ext-real Element of REAL
p1 `2 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
p2 `2 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `2) / |.p2.| is V28() real ext-real Element of COMPLEX
p2 `1 is V28() real ext-real Element of REAL
|.p2.| ^2 is V28() real ext-real Element of REAL
|.p2.| * |.p2.| is V28() real ext-real non negative set
((p2 `2) / |.p2.|) - cn is V28() real ext-real Element of REAL
1 + cn is V28() real ext-real Element of REAL
(((p2 `2) / |.p2.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p2 `2) / |.p2.|) - cn) / (1 + cn)) * ((((p2 `2) / |.p2.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
|[(|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2)))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 + cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2)))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 + cn)))]| `2 is V28() real ext-real Element of REAL
(cn) . p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2)))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 + cn)))]| `1 is V28() real ext-real Element of REAL
p1 `1 is V28() real ext-real Element of REAL
(p2 `1) ^2 is V28() real ext-real Element of REAL
(p2 `1) * (p2 `1) is V28() real ext-real set
(p2 `2) ^2 is V28() real ext-real Element of REAL
(p2 `2) * (p2 `2) is V28() real ext-real set
((p2 `1) ^2) + ((p2 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p2 `2) ^2) is V28() real ext-real Element of REAL
((p2 `2) ^2) / (|.p2.| ^2) is V28() real ext-real Element of COMPLEX
(|.p2.| ^2) / (|.p2.| ^2) is V28() real ext-real Element of COMPLEX
((p2 `2) / |.p2.|) ^2 is V28() real ext-real Element of COMPLEX
((p2 `2) / |.p2.|) * ((p2 `2) / |.p2.|) is V28() real ext-real set
- ((p2 `2) / |.p2.|) is V28() real ext-real Element of COMPLEX
(- ((p2 `2) / |.p2.|)) ^2 is V28() real ext-real Element of COMPLEX
(- ((p2 `2) / |.p2.|)) * (- ((p2 `2) / |.p2.|)) is V28() real ext-real set
(- ((p2 `2) / |.p2.|)) + cn is V28() real ext-real Element of REAL
- (((p2 `2) / |.p2.|) - cn) is V28() real ext-real Element of REAL
(- (((p2 `2) / |.p2.|) - cn)) / (1 + cn) is V28() real ext-real Element of COMPLEX
((- (((p2 `2) / |.p2.|) - cn)) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((p2 `2) / |.p2.|) - cn)) / (1 + cn)) * ((- (((p2 `2) / |.p2.|) - cn)) / (1 + cn)) is V28() real ext-real set
1 - (((- (((p2 `2) / |.p2.|) - cn)) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
- ((((p2 `2) / |.p2.|) - cn) / (1 + cn)) is V28() real ext-real Element of COMPLEX
(- ((((p2 `2) / |.p2.|) - cn) / (1 + cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((p2 `2) / |.p2.|) - cn) / (1 + cn))) * (- ((((p2 `2) / |.p2.|) - cn) / (1 + cn))) is V28() real ext-real set
1 - ((- ((((p2 `2) / |.p2.|) - cn) / (1 + cn))) ^2) is V28() real ext-real Element of REAL
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
sqrt (1 - (((- (((p2 `2) / |.p2.|) - cn)) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
(- (((p2 `2) / |.p2.|) - cn)) ^2 is V28() real ext-real Element of REAL
(- (((p2 `2) / |.p2.|) - cn)) * (- (((p2 `2) / |.p2.|) - cn)) is V28() real ext-real set
(1 + cn) ^2 is V28() real ext-real Element of REAL
(1 + cn) * (1 + cn) is V28() real ext-real set
((- (((p2 `2) / |.p2.|) - cn)) ^2) / ((1 + cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((- (((p2 `2) / |.p2.|) - cn)) ^2) / ((1 + cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((p2 `2) / |.p2.|) - cn)) ^2) / ((1 + cn) ^2))) is V28() real ext-real Element of REAL
(((p2 `2) / |.p2.|) - cn) ^2 is V28() real ext-real Element of REAL
(((p2 `2) / |.p2.|) - cn) * (((p2 `2) / |.p2.|) - cn) is V28() real ext-real set
((((p2 `2) / |.p2.|) - cn) ^2) / ((1 + cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((((p2 `2) / |.p2.|) - cn) ^2) / ((1 + cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((((p2 `2) / |.p2.|) - cn) ^2) / ((1 + cn) ^2))) is V28() real ext-real Element of REAL
sqrt ((- ((((p2 `2) / |.p2.|) - cn) / (1 + cn))) ^2) is V28() real ext-real set
1 * (1 + cn) is V28() real ext-real Element of REAL
(1 + cn) - cn is V28() real ext-real Element of REAL
- (p2 `2) is V28() real ext-real Element of REAL
(- (p2 `2)) / |.p2.| is V28() real ext-real Element of COMPLEX
1 * |.p2.| is V28() real ext-real non negative Element of REAL
((p2 `2) ^2) - ((p2 `2) ^2) is V28() real ext-real Element of REAL
p1 `2 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `1 is V28() real ext-real Element of REAL
((p1 `2) / |.p1.|) - cn is V28() real ext-real Element of REAL
(((p1 `2) / |.p1.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p1 `2) / |.p1.|) - cn) / (1 - cn)) * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 - cn)) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 - cn)))]| `2 is V28() real ext-real Element of REAL
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 `2 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `1 is V28() real ext-real Element of REAL
(p1 `1) ^2 is V28() real ext-real Element of REAL
(p1 `1) * (p1 `1) is V28() real ext-real set
|.p1.| ^2 is V28() real ext-real Element of REAL
|.p1.| * |.p1.| is V28() real ext-real non negative set
(p1 `2) ^2 is V28() real ext-real Element of REAL
(p1 `2) * (p1 `2) is V28() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p1 `2) ^2) is V28() real ext-real Element of REAL
((p1 `2) ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
(|.p1.| ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
(p2 `1) ^2 is V28() real ext-real Element of REAL
(p2 `1) * (p2 `1) is V28() real ext-real set
(p2 `2) ^2 is V28() real ext-real Element of REAL
(p2 `2) * (p2 `2) is V28() real ext-real set
((p2 `1) ^2) + ((p2 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p2 `2) ^2) is V28() real ext-real Element of REAL
((p2 `2) ^2) / (|.p2.| ^2) is V28() real ext-real Element of COMPLEX
(|.p2.| ^2) / (|.p2.| ^2) is V28() real ext-real Element of COMPLEX
((p2 `2) / |.p2.|) ^2 is V28() real ext-real Element of COMPLEX
((p2 `2) / |.p2.|) * ((p2 `2) / |.p2.|) is V28() real ext-real set
(- 1) - cn is V28() real ext-real Element of REAL
- (((p2 `2) / |.p2.|) - cn) is V28() real ext-real Element of REAL
- ((- 1) - cn) is V28() real ext-real Element of REAL
(- (((p2 `2) / |.p2.|) - cn)) / (1 + cn) is V28() real ext-real Element of COMPLEX
((- (((p2 `2) / |.p2.|) - cn)) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((p2 `2) / |.p2.|) - cn)) / (1 + cn)) * ((- (((p2 `2) / |.p2.|) - cn)) / (1 + cn)) is V28() real ext-real set
1 - (((- (((p2 `2) / |.p2.|) - cn)) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
- ((((p2 `2) / |.p2.|) - cn) / (1 + cn)) is V28() real ext-real Element of COMPLEX
(- ((((p2 `2) / |.p2.|) - cn) / (1 + cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((p2 `2) / |.p2.|) - cn) / (1 + cn))) * (- ((((p2 `2) / |.p2.|) - cn) / (1 + cn))) is V28() real ext-real set
1 - ((- ((((p2 `2) / |.p2.|) - cn) / (1 + cn))) ^2) is V28() real ext-real Element of REAL
(|[(|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2)))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 + cn)))]| `1) ^2 is V28() real ext-real Element of REAL
(|[(|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2)))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 + cn)))]| `1) * (|[(|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2)))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 + cn)))]| `1) is V28() real ext-real set
(sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2))) * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real set
(|.p2.| ^2) * ((sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2))) ^2) is V28() real ext-real Element of REAL
(|.p2.| ^2) * (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
((p1 `2) / |.p1.|) - cn is V28() real ext-real Element of REAL
(((p1 `2) / |.p1.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p1 `2) / |.p1.|) - cn) / (1 + cn)) * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]| `2 is V28() real ext-real Element of REAL
((p1 `2) / |.p1.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `2) / |.p1.|) * ((p1 `2) / |.p1.|) is V28() real ext-real set
- (((p1 `2) / |.p1.|) - cn) is V28() real ext-real Element of REAL
(- (((p1 `2) / |.p1.|) - cn)) / (1 + cn) is V28() real ext-real Element of COMPLEX
((- (((p1 `2) / |.p1.|) - cn)) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((p1 `2) / |.p1.|) - cn)) / (1 + cn)) * ((- (((p1 `2) / |.p1.|) - cn)) / (1 + cn)) is V28() real ext-real set
1 - (((- (((p1 `2) / |.p1.|) - cn)) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
- ((((p1 `2) / |.p1.|) - cn) / (1 + cn)) is V28() real ext-real Element of COMPLEX
(- ((((p1 `2) / |.p1.|) - cn) / (1 + cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((p1 `2) / |.p1.|) - cn) / (1 + cn))) * (- ((((p1 `2) / |.p1.|) - cn) / (1 + cn))) is V28() real ext-real set
1 - ((- ((((p1 `2) / |.p1.|) - cn) / (1 + cn))) ^2) is V28() real ext-real Element of REAL
|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]| `1 is V28() real ext-real Element of REAL
(|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]| `1) ^2 is V28() real ext-real Element of REAL
(|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]| `1) * (|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]| `1) is V28() real ext-real set
(sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))) * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real set
(|.p1.| ^2) * ((sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2))) ^2) is V28() real ext-real Element of REAL
(|.p1.| ^2) * (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]|.| is V28() real ext-real non negative Element of REAL
|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]|.| ^2 is V28() real ext-real Element of REAL
|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]|.| * |.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]|.| is V28() real ext-real non negative set
(|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]| `2) ^2 is V28() real ext-real Element of REAL
(|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]| `2) * (|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]| `2) is V28() real ext-real set
((|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]| `1) ^2) + ((|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]| `2) ^2) is V28() real ext-real Element of REAL
sqrt (|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) - cn) / (1 + cn)) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) - cn) / (1 + cn)))]|.| ^2) is V28() real ext-real Element of REAL
|.|[(|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2)))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 + cn)))]|.| is V28() real ext-real non negative Element of REAL
|.|[(|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2)))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 + cn)))]|.| ^2 is V28() real ext-real Element of REAL
|.|[(|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2)))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 + cn)))]|.| * |.|[(|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2)))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 + cn)))]|.| is V28() real ext-real non negative set
(|[(|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2)))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 + cn)))]| `2) ^2 is V28() real ext-real Element of REAL
(|[(|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2)))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 + cn)))]| `2) * (|[(|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2)))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 + cn)))]| `2) is V28() real ext-real set
((|[(|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2)))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 + cn)))]| `1) ^2) + ((|[(|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2)))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 + cn)))]| `2) ^2) is V28() real ext-real Element of REAL
sqrt (|.|[(|.p2.| * (sqrt (1 - (((((p2 `2) / |.p2.|) - cn) / (1 + cn)) ^2)))),(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 + cn)))]|.| ^2) is V28() real ext-real Element of REAL
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(|.p2.| * ((((p2 `2) / |.p2.|) - cn) / (1 + cn))) / |.p1.| is V28() real ext-real Element of COMPLEX
((((p1 `2) / |.p1.|) - cn) / (1 + cn)) * (1 + cn) is V28() real ext-real Element of REAL
((p1 `2) / |.p1.|) * |.p1.| is V28() real ext-real Element of REAL
|[(p1 `1),(p1 `2)]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
sqrt ((p2 `1) ^2) is V28() real ext-real Element of REAL
p1 `1 is V28() real ext-real Element of REAL
p1 `2 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `1 is V28() real ext-real Element of REAL
p1 `2 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
p2 `1 is V28() real ext-real Element of REAL
p2 `2 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `2) / |.p2.| is V28() real ext-real Element of COMPLEX
p2 `1 is V28() real ext-real Element of REAL
p2 `2 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `2) / |.p2.| is V28() real ext-real Element of COMPLEX
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
rng (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
q is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
dom q is functional Element of K19( the carrier of (TOP-REAL 2))
rng q is functional Element of K19( the carrier of (TOP-REAL 2))
p is set
p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() real ext-real Element of REAL
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
p1 `2 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `1 is V28() real ext-real Element of REAL
1 + cn is V28() real ext-real Element of REAL
- (1 + cn) is V28() real ext-real Element of REAL
- (- (1 + cn)) is V28() real ext-real Element of REAL
(- 1) - cn is V28() real ext-real Element of REAL
- ((- 1) - cn) is V28() real ext-real Element of REAL
1 - cn is V28() real ext-real Element of REAL
((p1 `2) / |.p1.|) * (1 - cn) is V28() real ext-real Element of REAL
((- 1) - cn) + cn is V28() real ext-real Element of REAL
(((p1 `2) / |.p1.|) * (1 - cn)) + cn is V28() real ext-real Element of REAL
((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2 is V28() real ext-real Element of REAL
((((p1 `2) / |.p1.|) * (1 - cn)) + cn) * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn) is V28() real ext-real set
1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)) is V28() real ext-real Element of REAL
|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))) is V28() real ext-real Element of REAL
|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn) is V28() real ext-real Element of REAL
|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]| `2 is V28() real ext-real Element of REAL
|.p1.| ^2 is V28() real ext-real Element of REAL
|.p1.| * |.p1.| is V28() real ext-real non negative set
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
(p1 `1) ^2 is V28() real ext-real Element of REAL
(p1 `1) * (p1 `1) is V28() real ext-real set
(p1 `2) ^2 is V28() real ext-real Element of REAL
(p1 `2) * (p1 `2) is V28() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p1 `2) ^2) is V28() real ext-real Element of REAL
((p1 `2) ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
(|.p1.| ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
((p1 `2) / |.p1.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `2) / |.p1.|) * ((p1 `2) / |.p1.|) is V28() real ext-real set
1 * (1 - cn) is V28() real ext-real Element of REAL
((((p1 `2) / |.p1.|) * (1 - cn)) + cn) - cn is V28() real ext-real Element of REAL
|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]| `1 is V28() real ext-real Element of REAL
|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| is V28() real ext-real non negative Element of REAL
|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2 is V28() real ext-real Element of REAL
|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| * |.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| is V28() real ext-real non negative set
(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))) ^2 is V28() real ext-real Element of REAL
(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))) * (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))) is V28() real ext-real set
(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn)) ^2 is V28() real ext-real Element of REAL
(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn)) * (|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn)) is V28() real ext-real set
((|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))) ^2) + ((|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn)) ^2) is V28() real ext-real Element of REAL
(sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))) * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))) is V28() real ext-real set
(|.p1.| ^2) * ((sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))) ^2) is V28() real ext-real Element of REAL
(|.p1.| ^2) * (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2) is V28() real ext-real Element of REAL
((|.p1.| ^2) * ((sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))) ^2)) + ((|.p1.| ^2) * (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)) is V28() real ext-real Element of REAL
(|.p1.| ^2) * (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)) is V28() real ext-real Element of REAL
((|.p1.| ^2) * (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2))) + ((|.p1.| ^2) * (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)) is V28() real ext-real Element of REAL
sqrt (|.p1.| ^2) is V28() real ext-real Element of REAL
0 + cn is V28() real ext-real Element of REAL
(|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]| `2) / |.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| is V28() real ext-real Element of COMPLEX
(cn) . |[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]| `2) / |.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.|) - cn is V28() real ext-real Element of REAL
(((|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]| `2) / |.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
((((|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]| `2) / |.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]| `2) / |.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.|) - cn) / (1 - cn)) * ((((|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]| `2) / |.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]| `2) / |.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]| `2) / |.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| * (sqrt (1 - (((((|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]| `2) / |.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| * ((((|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]| `2) / |.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
|[(|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| * (sqrt (1 - (((((|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]| `2) / |.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.|) - cn) / (1 - cn)) ^2)))),(|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| * ((((|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]| `2) / |.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.|) - cn) / (1 - cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
((p1 `1) / |.p1.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `1) / |.p1.|) * ((p1 `1) / |.p1.|) is V28() real ext-real set
sqrt (((p1 `1) / |.p1.|) ^2) is V28() real ext-real set
|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| * (sqrt (((p1 `1) / |.p1.|) ^2)) is V28() real ext-real Element of REAL
|.p1.| * ((p1 `1) / |.p1.|) is V28() real ext-real Element of REAL
(((((p1 `2) / |.p1.|) * (1 - cn)) + cn) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
|.p1.| * ((((((p1 `2) / |.p1.|) * (1 - cn)) + cn) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
|.p1.| * ((p1 `2) / |.p1.|) is V28() real ext-real Element of REAL
(p1 `2) / |.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| is V28() real ext-real Element of COMPLEX
((p1 `2) / |.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `2) / |.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.|) * ((p1 `2) / |.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.|) is V28() real ext-real set
1 - (((p1 `2) / |.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.|) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((p1 `2) / |.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.|) ^2)) is V28() real ext-real Element of REAL
|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| * (sqrt (1 - (((p1 `2) / |.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.|) ^2))) is V28() real ext-real Element of REAL
((p1 `2) ^2) / (|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2) is V28() real ext-real Element of COMPLEX
1 - (((p1 `2) ^2) / (|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((p1 `2) ^2) / (|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2))) is V28() real ext-real Element of REAL
|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| * (sqrt (1 - (((p1 `2) ^2) / (|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2)))) is V28() real ext-real Element of REAL
(|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2) / (|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2) is V28() real ext-real Element of COMPLEX
((|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2) / (|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2)) - (((p1 `2) ^2) / (|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2)) is V28() real ext-real Element of COMPLEX
sqrt (((|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2) / (|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2)) - (((p1 `2) ^2) / (|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2))) is V28() real ext-real set
|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| * (sqrt (((|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2) / (|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2)) - (((p1 `2) ^2) / (|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2)))) is V28() real ext-real Element of REAL
(|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2) - ((p1 `2) ^2) is V28() real ext-real Element of REAL
((|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2) - ((p1 `2) ^2)) / (|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2) is V28() real ext-real Element of COMPLEX
sqrt (((|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2) - ((p1 `2) ^2)) / (|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2)) is V28() real ext-real set
|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| * (sqrt (((|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2) - ((p1 `2) ^2)) / (|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2))) is V28() real ext-real Element of REAL
(((p1 `1) ^2) + ((p1 `2) ^2)) - ((p1 `2) ^2) is V28() real ext-real Element of REAL
((((p1 `1) ^2) + ((p1 `2) ^2)) - ((p1 `2) ^2)) / (|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2) is V28() real ext-real Element of COMPLEX
sqrt (((((p1 `1) ^2) + ((p1 `2) ^2)) - ((p1 `2) ^2)) / (|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2)) is V28() real ext-real set
|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| * (sqrt (((((p1 `1) ^2) + ((p1 `2) ^2)) - ((p1 `2) ^2)) / (|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 - cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 - cn)) + cn))]|.| ^2))) is V28() real ext-real Element of REAL
p1 `2 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `1 is V28() real ext-real Element of REAL
1 + cn is V28() real ext-real Element of REAL
1 - cn is V28() real ext-real Element of REAL
((p1 `2) / |.p1.|) * (1 + cn) is V28() real ext-real Element of REAL
(((p1 `2) / |.p1.|) * (1 + cn)) + cn is V28() real ext-real Element of REAL
(1 - cn) + cn is V28() real ext-real Element of REAL
|.p1.| ^2 is V28() real ext-real Element of REAL
|.p1.| * |.p1.| is V28() real ext-real non negative set
(p1 `1) ^2 is V28() real ext-real Element of REAL
(p1 `1) * (p1 `1) is V28() real ext-real set
(p1 `2) ^2 is V28() real ext-real Element of REAL
(p1 `2) * (p1 `2) is V28() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p1 `2) ^2) is V28() real ext-real Element of REAL
((p1 `2) ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
(|.p1.| ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
((p1 `2) / |.p1.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `2) / |.p1.|) * ((p1 `2) / |.p1.|) is V28() real ext-real set
(- 1) * (1 + cn) is V28() real ext-real Element of REAL
(- 1) - cn is V28() real ext-real Element of REAL
((((p1 `2) / |.p1.|) * (1 + cn)) + cn) - cn is V28() real ext-real Element of REAL
((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2 is V28() real ext-real Element of REAL
((((p1 `2) / |.p1.|) * (1 + cn)) + cn) * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn) is V28() real ext-real set
1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)) is V28() real ext-real Element of REAL
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))) is V28() real ext-real Element of REAL
|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn) is V28() real ext-real Element of REAL
|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]| `2 is V28() real ext-real Element of REAL
|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]| `1 is V28() real ext-real Element of REAL
|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| is V28() real ext-real non negative Element of REAL
|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2 is V28() real ext-real Element of REAL
|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| * |.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| is V28() real ext-real non negative set
(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))) ^2 is V28() real ext-real Element of REAL
(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))) * (|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))) is V28() real ext-real set
(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn)) ^2 is V28() real ext-real Element of REAL
(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn)) * (|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn)) is V28() real ext-real set
((|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))) ^2) + ((|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn)) ^2) is V28() real ext-real Element of REAL
(sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))) * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))) is V28() real ext-real set
(|.p1.| ^2) * ((sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))) ^2) is V28() real ext-real Element of REAL
(|.p1.| ^2) * (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2) is V28() real ext-real Element of REAL
((|.p1.| ^2) * ((sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))) ^2)) + ((|.p1.| ^2) * (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)) is V28() real ext-real Element of REAL
(|.p1.| ^2) * (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)) is V28() real ext-real Element of REAL
((|.p1.| ^2) * (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2))) + ((|.p1.| ^2) * (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)) is V28() real ext-real Element of REAL
sqrt (|.p1.| ^2) is V28() real ext-real Element of REAL
0 + cn is V28() real ext-real Element of REAL
(|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]| `2) / |.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| is V28() real ext-real Element of COMPLEX
(cn) . |[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]| `2) / |.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.|) - cn is V28() real ext-real Element of REAL
(((|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]| `2) / |.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
((((|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]| `2) / |.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]| `2) / |.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.|) - cn) / (1 + cn)) * ((((|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]| `2) / |.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]| `2) / |.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]| `2) / |.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| * (sqrt (1 - (((((|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]| `2) / |.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| * ((((|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]| `2) / |.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
|[(|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| * (sqrt (1 - (((((|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]| `2) / |.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.|) - cn) / (1 + cn)) ^2)))),(|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| * ((((|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]| `2) / |.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.|) - cn) / (1 + cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
((p1 `1) / |.p1.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `1) / |.p1.|) * ((p1 `1) / |.p1.|) is V28() real ext-real set
sqrt (((p1 `1) / |.p1.|) ^2) is V28() real ext-real set
|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| * (sqrt (((p1 `1) / |.p1.|) ^2)) is V28() real ext-real Element of REAL
|.p1.| * ((p1 `1) / |.p1.|) is V28() real ext-real Element of REAL
(((((p1 `2) / |.p1.|) * (1 + cn)) + cn) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
|.p1.| * ((((((p1 `2) / |.p1.|) * (1 + cn)) + cn) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
|.p1.| * ((p1 `2) / |.p1.|) is V28() real ext-real Element of REAL
(p1 `2) / |.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| is V28() real ext-real Element of COMPLEX
((p1 `2) / |.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `2) / |.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.|) * ((p1 `2) / |.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.|) is V28() real ext-real set
1 - (((p1 `2) / |.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.|) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((p1 `2) / |.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.|) ^2)) is V28() real ext-real Element of REAL
|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| * (sqrt (1 - (((p1 `2) / |.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.|) ^2))) is V28() real ext-real Element of REAL
((p1 `2) ^2) / (|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2) is V28() real ext-real Element of COMPLEX
1 - (((p1 `2) ^2) / (|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((p1 `2) ^2) / (|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2))) is V28() real ext-real Element of REAL
|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| * (sqrt (1 - (((p1 `2) ^2) / (|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2)))) is V28() real ext-real Element of REAL
(|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2) / (|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2) is V28() real ext-real Element of COMPLEX
((|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2) / (|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2)) - (((p1 `2) ^2) / (|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2)) is V28() real ext-real Element of COMPLEX
sqrt (((|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2) / (|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2)) - (((p1 `2) ^2) / (|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2))) is V28() real ext-real set
|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| * (sqrt (((|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2) / (|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2)) - (((p1 `2) ^2) / (|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2)))) is V28() real ext-real Element of REAL
(|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2) - ((p1 `2) ^2) is V28() real ext-real Element of REAL
((|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2) - ((p1 `2) ^2)) / (|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2) is V28() real ext-real Element of COMPLEX
sqrt (((|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2) - ((p1 `2) ^2)) / (|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2)) is V28() real ext-real set
|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| * (sqrt (((|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2) - ((p1 `2) ^2)) / (|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2))) is V28() real ext-real Element of REAL
(((p1 `1) ^2) + ((p1 `2) ^2)) - ((p1 `2) ^2) is V28() real ext-real Element of REAL
((((p1 `1) ^2) + ((p1 `2) ^2)) - ((p1 `2) ^2)) / (|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2) is V28() real ext-real Element of COMPLEX
sqrt (((((p1 `1) ^2) + ((p1 `2) ^2)) - ((p1 `2) ^2)) / (|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2)) is V28() real ext-real set
|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| * (sqrt (((((p1 `1) ^2) + ((p1 `2) ^2)) - ((p1 `2) ^2)) / (|.|[(|.p1.| * (sqrt (1 - (((((p1 `2) / |.p1.|) * (1 + cn)) + cn) ^2)))),(|.p1.| * ((((p1 `2) / |.p1.|) * (1 + cn)) + cn))]|.| ^2))) is V28() real ext-real Element of REAL
p1 `1 is V28() real ext-real Element of REAL
p1 `2 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
q3 is set
(cn) . q3 is Relation-like Function-like set
q is V28() real ext-real Element of REAL
(q) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(q) . p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn is Element of the carrier of (Euclid 2)
|.p.| is V28() real ext-real non negative Element of REAL
|.p.| + 1 is non empty V28() real ext-real positive non negative Element of REAL
Ball (cn,(|.p.| + 1)) is bounded Element of K19( the carrier of (Euclid 2))
p1 is functional Element of K19( the carrier of (TOP-REAL 2))
cl_Ball (cn,(|.p.| + 1)) is Element of K19( the carrier of (Euclid 2))
the carrier of (TopSpaceMetr (Euclid 2)) is set
K19( the carrier of (TopSpaceMetr (Euclid 2))) is set
p2 is functional non empty closed compact bounded Element of K19( the carrier of (TOP-REAL 2))
(q) .: p2 is functional Element of K19( the carrier of (TOP-REAL 2))
y is set
dom (q) is functional Element of K19( the carrier of (TOP-REAL 2))
q4 is set
(q) . q4 is Relation-like Function-like set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x is Element of the carrier of (Euclid 2)
dist (cn,x) is V28() real ext-real Element of REAL
(0. (TOP-REAL 2)) - y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
- y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K443((TOP-REAL 2),(0. (TOP-REAL 2)),(- y)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is Relation-like K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)) -defined the carrier of (TOP-REAL 2) -valued Function-like total quasi_total Element of K19(K20(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)))
K20(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) is set
K19(K20(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2))) is set
K230( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),(0. (TOP-REAL 2)),(- y)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.((0. (TOP-REAL 2)) - y).| is V28() real ext-real non negative Element of REAL
|.(- y).| is V28() real ext-real non negative Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
rng (q) is functional Element of K19( the carrier of (TOP-REAL 2))
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.q.| is V28() real ext-real non negative Element of REAL
- q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.(- q).| is V28() real ext-real non negative Element of REAL
(0. (TOP-REAL 2)) - q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K443((TOP-REAL 2),(0. (TOP-REAL 2)),(- q)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K230( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),(0. (TOP-REAL 2)),(- q)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.((0. (TOP-REAL 2)) - q).| is V28() real ext-real non negative Element of REAL
x is Element of the carrier of (Euclid 2)
dist (cn,x) is V28() real ext-real Element of REAL
VV0 is Element of K19( the carrier of (TopSpaceMetr (Euclid 2)))
- p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.(- p).| is V28() real ext-real non negative Element of REAL
(0. (TOP-REAL 2)) - p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K443((TOP-REAL 2),(0. (TOP-REAL 2)),(- p)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is Relation-like K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)) -defined the carrier of (TOP-REAL 2) -valued Function-like total quasi_total Element of K19(K20(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)))
K20(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) is set
K19(K20(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2))) is set
K230( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),(0. (TOP-REAL 2)),(- p)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.((0. (TOP-REAL 2)) - p).| is V28() real ext-real non negative Element of REAL
u2 is Element of the carrier of (Euclid 2)
dist (cn,u2) is V28() real ext-real Element of REAL
|.((q) . p).| is V28() real ext-real non negative Element of REAL
- ((q) . p) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.(- ((q) . p)).| is V28() real ext-real non negative Element of REAL
(0. (TOP-REAL 2)) - ((q) . p) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K443((TOP-REAL 2),(0. (TOP-REAL 2)),(- ((q) . p))) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K230( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),(0. (TOP-REAL 2)),(- ((q) . p))) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.((0. (TOP-REAL 2)) - ((q) . p)).| is V28() real ext-real non negative Element of REAL
u3 is Element of the carrier of (Euclid 2)
dist (cn,u3) is V28() real ext-real Element of REAL
y is set
rng (q) is functional Element of K19( the carrier of (TOP-REAL 2))
q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
dom (q) is functional Element of K19( the carrier of (TOP-REAL 2))
y is Element of the carrier of (Euclid 2)
x is set
(q) . x is Relation-like Function-like set
x is Element of the carrier of (Euclid 2)
|.q4.| is V28() real ext-real non negative Element of REAL
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.q.| is V28() real ext-real non negative Element of REAL
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q . p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
rng (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
p is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q `1 is V28() real ext-real Element of REAL
q `2 is V28() real ext-real Element of REAL
|.q.| is V28() real ext-real non negative Element of REAL
(q `2) / |.q.| is V28() real ext-real Element of COMPLEX
(cn) . q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((q `2) / |.q.|) - cn is V28() real ext-real Element of REAL
p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p `1 is V28() real ext-real Element of REAL
p `2 is V28() real ext-real Element of REAL
1 - cn is V28() real ext-real Element of REAL
|.q.| ^2 is V28() real ext-real Element of REAL
|.q.| * |.q.| is V28() real ext-real non negative set
(q `1) ^2 is V28() real ext-real Element of REAL
(q `1) * (q `1) is V28() real ext-real set
(q `2) ^2 is V28() real ext-real Element of REAL
(q `2) * (q `2) is V28() real ext-real set
((q `1) ^2) + ((q `2) ^2) is V28() real ext-real Element of REAL
0 + ((q `2) ^2) is V28() real ext-real Element of REAL
(|.q.| ^2) / (|.q.| ^2) is V28() real ext-real Element of COMPLEX
((q `2) ^2) / (|.q.| ^2) is V28() real ext-real Element of COMPLEX
((q `2) / |.q.|) ^2 is V28() real ext-real Element of COMPLEX
((q `2) / |.q.|) * ((q `2) / |.q.|) is V28() real ext-real set
- (((q `2) / |.q.|) - cn) is V28() real ext-real Element of REAL
- (1 - cn) is V28() real ext-real Element of REAL
(- (((q `2) / |.q.|) - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
(- (1 - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
((- (((q `2) / |.q.|) - cn)) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((q `2) / |.q.|) - cn)) / (1 - cn)) * ((- (((q `2) / |.q.|) - cn)) / (1 - cn)) is V28() real ext-real set
1 - (((- (((q `2) / |.q.|) - cn)) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((q `2) / |.q.|) - cn)) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
(- (((q `2) / |.q.|) - cn)) ^2 is V28() real ext-real Element of REAL
(- (((q `2) / |.q.|) - cn)) * (- (((q `2) / |.q.|) - cn)) is V28() real ext-real set
(1 - cn) ^2 is V28() real ext-real Element of REAL
(1 - cn) * (1 - cn) is V28() real ext-real set
((- (((q `2) / |.q.|) - cn)) ^2) / ((1 - cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((- (((q `2) / |.q.|) - cn)) ^2) / ((1 - cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((q `2) / |.q.|) - cn)) ^2) / ((1 - cn) ^2))) is V28() real ext-real Element of REAL
(((q `2) / |.q.|) - cn) ^2 is V28() real ext-real Element of REAL
(((q `2) / |.q.|) - cn) * (((q `2) / |.q.|) - cn) is V28() real ext-real set
((((q `2) / |.q.|) - cn) ^2) / ((1 - cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((((q `2) / |.q.|) - cn) ^2) / ((1 - cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((((q `2) / |.q.|) - cn) ^2) / ((1 - cn) ^2))) is V28() real ext-real Element of REAL
(((q `2) / |.q.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
((((q `2) / |.q.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((q `2) / |.q.|) - cn) / (1 - cn)) * ((((q `2) / |.q.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((q `2) / |.q.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.q.| * (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.q.| * ((((q `2) / |.q.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
|[(|.q.| * (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 - cn)) ^2)))),(|.q.| * ((((q `2) / |.q.|) - cn) / (1 - cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q `1 is V28() real ext-real Element of REAL
q `2 is V28() real ext-real Element of REAL
|.q.| is V28() real ext-real non negative Element of REAL
(q `2) / |.q.| is V28() real ext-real Element of COMPLEX
(cn) . q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
1 + cn is V28() real ext-real Element of REAL
p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p `1 is V28() real ext-real Element of REAL
p `2 is V28() real ext-real Element of REAL
((q `2) / |.q.|) - cn is V28() real ext-real Element of REAL
(((q `2) / |.q.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
((((q `2) / |.q.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((q `2) / |.q.|) - cn) / (1 + cn)) * ((((q `2) / |.q.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
|.q.| * (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|.q.| * ((((q `2) / |.q.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
|[(|.q.| * (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2)))),(|.q.| * ((((q `2) / |.q.|) - cn) / (1 + cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.q.| ^2 is V28() real ext-real Element of REAL
|.q.| * |.q.| is V28() real ext-real non negative set
- (((q `2) / |.q.|) - cn) is V28() real ext-real Element of REAL
(- (((q `2) / |.q.|) - cn)) / (1 + cn) is V28() real ext-real Element of COMPLEX
- (1 + cn) is V28() real ext-real Element of REAL
(- (1 + cn)) / (1 + cn) is V28() real ext-real Element of COMPLEX
(q `1) ^2 is V28() real ext-real Element of REAL
(q `1) * (q `1) is V28() real ext-real set
(q `2) ^2 is V28() real ext-real Element of REAL
(q `2) * (q `2) is V28() real ext-real set
((q `1) ^2) + ((q `2) ^2) is V28() real ext-real Element of REAL
0 + ((q `2) ^2) is V28() real ext-real Element of REAL
(|.q.| ^2) / (|.q.| ^2) is V28() real ext-real Element of COMPLEX
((q `2) ^2) / (|.q.| ^2) is V28() real ext-real Element of COMPLEX
((q `2) / |.q.|) ^2 is V28() real ext-real Element of COMPLEX
((q `2) / |.q.|) * ((q `2) / |.q.|) is V28() real ext-real set
(- 1) - cn is V28() real ext-real Element of REAL
- (- (1 + cn)) is V28() real ext-real Element of REAL
((- (((q `2) / |.q.|) - cn)) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((q `2) / |.q.|) - cn)) / (1 + cn)) * ((- (((q `2) / |.q.|) - cn)) / (1 + cn)) is V28() real ext-real set
1 - (((- (((q `2) / |.q.|) - cn)) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((q `2) / |.q.|) - cn)) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
(- (((q `2) / |.q.|) - cn)) ^2 is V28() real ext-real Element of REAL
(- (((q `2) / |.q.|) - cn)) * (- (((q `2) / |.q.|) - cn)) is V28() real ext-real set
(1 + cn) ^2 is V28() real ext-real Element of REAL
(1 + cn) * (1 + cn) is V28() real ext-real set
((- (((q `2) / |.q.|) - cn)) ^2) / ((1 + cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((- (((q `2) / |.q.|) - cn)) ^2) / ((1 + cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((q `2) / |.q.|) - cn)) ^2) / ((1 + cn) ^2))) is V28() real ext-real Element of REAL
(((q `2) / |.q.|) - cn) ^2 is V28() real ext-real Element of REAL
(((q `2) / |.q.|) - cn) * (((q `2) / |.q.|) - cn) is V28() real ext-real set
((((q `2) / |.q.|) - cn) ^2) / ((1 + cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((((q `2) / |.q.|) - cn) ^2) / ((1 + cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((((q `2) / |.q.|) - cn) ^2) / ((1 + cn) ^2))) is V28() real ext-real Element of REAL
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q `1 is V28() real ext-real Element of REAL
q `2 is V28() real ext-real Element of REAL
|.q.| is V28() real ext-real non negative Element of REAL
(q `2) / |.q.| is V28() real ext-real Element of COMPLEX
p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p `1 is V28() real ext-real Element of REAL
p `2 is V28() real ext-real Element of REAL
|.p.| is V28() real ext-real non negative Element of REAL
(p `2) / |.p.| is V28() real ext-real Element of COMPLEX
(cn) . q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(cn) . p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((p `2) / |.p.|) - cn is V28() real ext-real Element of REAL
((q `2) / |.q.|) - cn is V28() real ext-real Element of REAL
1 - cn is V28() real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `2 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `2) / |.p2.| is V28() real ext-real Element of COMPLEX
p1 `2 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
(((p `2) / |.p.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
((((p `2) / |.p.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p `2) / |.p.|) - cn) / (1 - cn)) * ((((p `2) / |.p.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((p `2) / |.p.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p `2) / |.p.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.p.| * (sqrt (1 - (((((p `2) / |.p.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.p.| * ((((p `2) / |.p.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
|[(|.p.| * (sqrt (1 - (((((p `2) / |.p.|) - cn) / (1 - cn)) ^2)))),(|.p.| * ((((p `2) / |.p.|) - cn) / (1 - cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(((q `2) / |.q.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
((((q `2) / |.q.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((q `2) / |.q.|) - cn) / (1 - cn)) * ((((q `2) / |.q.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((q `2) / |.q.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.q.| * (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.q.| * ((((q `2) / |.q.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
|[(|.q.| * (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 - cn)) ^2)))),(|.q.| * ((((q `2) / |.q.|) - cn) / (1 - cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q `1 is V28() real ext-real Element of REAL
q `2 is V28() real ext-real Element of REAL
|.q.| is V28() real ext-real non negative Element of REAL
(q `2) / |.q.| is V28() real ext-real Element of COMPLEX
p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p `1 is V28() real ext-real Element of REAL
p `2 is V28() real ext-real Element of REAL
|.p.| is V28() real ext-real non negative Element of REAL
(p `2) / |.p.| is V28() real ext-real Element of COMPLEX
(cn) . q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(cn) . p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((p `2) / |.p.|) - cn is V28() real ext-real Element of REAL
((q `2) / |.q.|) - cn is V28() real ext-real Element of REAL
1 + cn is V28() real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `2 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `2) / |.p2.| is V28() real ext-real Element of COMPLEX
p1 `2 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
(((p `2) / |.p.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
((((p `2) / |.p.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p `2) / |.p.|) - cn) / (1 + cn)) * ((((p `2) / |.p.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((p `2) / |.p.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p `2) / |.p.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
|.p.| * (sqrt (1 - (((((p `2) / |.p.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|.p.| * ((((p `2) / |.p.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
|[(|.p.| * (sqrt (1 - (((((p `2) / |.p.|) - cn) / (1 + cn)) ^2)))),(|.p.| * ((((p `2) / |.p.|) - cn) / (1 + cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(((q `2) / |.q.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
((((q `2) / |.q.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((q `2) / |.q.|) - cn) / (1 + cn)) * ((((q `2) / |.q.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
|.q.| * (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|.q.| * ((((q `2) / |.q.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
|[(|.q.| * (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 + cn)) ^2)))),(|.q.| * ((((q `2) / |.q.|) - cn) / (1 + cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q `1 is V28() real ext-real Element of REAL
p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p `1 is V28() real ext-real Element of REAL
p `2 is V28() real ext-real Element of REAL
|.p.| is V28() real ext-real non negative Element of REAL
(p `2) / |.p.| is V28() real ext-real Element of COMPLEX
q `2 is V28() real ext-real Element of REAL
|.q.| is V28() real ext-real non negative Element of REAL
(q `2) / |.q.| is V28() real ext-real Element of COMPLEX
(cn) . q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(cn) . p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `2 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `2) / |.p2.| is V28() real ext-real Element of COMPLEX
p1 `2 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q `1 is V28() real ext-real Element of REAL
q `2 is V28() real ext-real Element of REAL
|.q.| is V28() real ext-real non negative Element of REAL
(q `2) / |.q.| is V28() real ext-real Element of COMPLEX
(cn) . q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((q `2) / |.q.|) - cn is V28() real ext-real Element of REAL
- (((q `2) / |.q.|) - cn) is V28() real ext-real Element of REAL
1 - cn is V28() real ext-real Element of REAL
(- (((q `2) / |.q.|) - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
((- (((q `2) / |.q.|) - cn)) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((q `2) / |.q.|) - cn)) / (1 - cn)) * ((- (((q `2) / |.q.|) - cn)) / (1 - cn)) is V28() real ext-real set
1 - (((- (((q `2) / |.q.|) - cn)) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((q `2) / |.q.|) - cn)) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p `1 is V28() real ext-real Element of REAL
p `2 is V28() real ext-real Element of REAL
(((q `2) / |.q.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
((((q `2) / |.q.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((q `2) / |.q.|) - cn) / (1 - cn)) * ((((q `2) / |.q.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((q `2) / |.q.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.q.| * (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.q.| * ((((q `2) / |.q.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
|[(|.q.| * (sqrt (1 - (((((q `2) / |.q.|) - cn) / (1 - cn)) ^2)))),(|.q.| * ((((q `2) / |.q.|) - cn) / (1 - cn)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn is V28() real ext-real set
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(cn) . (0. (TOP-REAL 2)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn is V28() real ext-real set
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q `1 is V28() real ext-real Element of REAL
|.q.| is V28() real ext-real non negative Element of REAL
(q `1) / |.q.| is V28() real ext-real Element of COMPLEX
q `2 is V28() real ext-real Element of REAL
((q `1) / |.q.|) - cn is V28() real ext-real set
1 - cn is V28() real ext-real Element of REAL
(((q `1) / |.q.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
((((q `1) / |.q.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((q `1) / |.q.|) - cn) / (1 - cn)) * ((((q `1) / |.q.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|[((((q `1) / |.q.|) - cn) / (1 - cn)),(- (sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.q.| * |[((((q `1) / |.q.|) - cn) / (1 - cn)),(- (sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
1 + cn is V28() real ext-real Element of REAL
(((q `1) / |.q.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
((((q `1) / |.q.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((q `1) / |.q.|) - cn) / (1 + cn)) * ((((q `1) / |.q.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((q `1) / |.q.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|[((((q `1) / |.q.|) - cn) / (1 + cn)),(- (sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 + cn)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.q.| * |[((((q `1) / |.q.|) - cn) / (1 + cn)),(- (sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 + cn)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn is V28() real ext-real set
cn is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn `1 is V28() real ext-real Element of REAL
|.cn.| is V28() real ext-real non negative Element of REAL
(cn `1) / |.cn.| is V28() real ext-real Element of COMPLEX
cn `2 is V28() real ext-real Element of REAL
q is V28() real ext-real set
(q) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(q) . cn is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((cn `1) / |.cn.|) - q is V28() real ext-real set
1 - q is V28() real ext-real Element of REAL
(((cn `1) / |.cn.|) - q) / (1 - q) is V28() real ext-real Element of COMPLEX
|.cn.| * ((((cn `1) / |.cn.|) - q) / (1 - q)) is V28() real ext-real Element of REAL
((((cn `1) / |.cn.|) - q) / (1 - q)) ^2 is V28() real ext-real Element of COMPLEX
((((cn `1) / |.cn.|) - q) / (1 - q)) * ((((cn `1) / |.cn.|) - q) / (1 - q)) is V28() real ext-real set
1 - (((((cn `1) / |.cn.|) - q) / (1 - q)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((cn `1) / |.cn.|) - q) / (1 - q)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((cn `1) / |.cn.|) - q) / (1 - q)) ^2))) is V28() real ext-real Element of REAL
|.cn.| * (- (sqrt (1 - (((((cn `1) / |.cn.|) - q) / (1 - q)) ^2)))) is V28() real ext-real Element of REAL
|[(|.cn.| * ((((cn `1) / |.cn.|) - q) / (1 - q))),(|.cn.| * (- (sqrt (1 - (((((cn `1) / |.cn.|) - q) / (1 - q)) ^2)))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(q,cn) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[((((cn `1) / |.cn.|) - q) / (1 - q)),(- (sqrt (1 - (((((cn `1) / |.cn.|) - q) / (1 - q)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.cn.| * |[((((cn `1) / |.cn.|) - q) / (1 - q)),(- (sqrt (1 - (((((cn `1) / |.cn.|) - q) / (1 - q)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn `1 is V28() real ext-real Element of REAL
|.cn.| is V28() real ext-real non negative Element of REAL
(cn `1) / |.cn.| is V28() real ext-real Element of COMPLEX
cn `2 is V28() real ext-real Element of REAL
q is V28() real ext-real Element of REAL
(q) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(q) . cn is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((cn `1) / |.cn.|) - q is V28() real ext-real Element of REAL
1 + q is V28() real ext-real Element of REAL
(((cn `1) / |.cn.|) - q) / (1 + q) is V28() real ext-real Element of COMPLEX
|.cn.| * ((((cn `1) / |.cn.|) - q) / (1 + q)) is V28() real ext-real Element of REAL
((((cn `1) / |.cn.|) - q) / (1 + q)) ^2 is V28() real ext-real Element of COMPLEX
((((cn `1) / |.cn.|) - q) / (1 + q)) * ((((cn `1) / |.cn.|) - q) / (1 + q)) is V28() real ext-real set
1 - (((((cn `1) / |.cn.|) - q) / (1 + q)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((cn `1) / |.cn.|) - q) / (1 + q)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((cn `1) / |.cn.|) - q) / (1 + q)) ^2))) is V28() real ext-real Element of REAL
|.cn.| * (- (sqrt (1 - (((((cn `1) / |.cn.|) - q) / (1 + q)) ^2)))) is V28() real ext-real Element of REAL
|[(|.cn.| * ((((cn `1) / |.cn.|) - q) / (1 + q))),(|.cn.| * (- (sqrt (1 - (((((cn `1) / |.cn.|) - q) / (1 + q)) ^2)))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(q,cn) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[((((cn `1) / |.cn.|) - q) / (1 + q)),(- (sqrt (1 - (((((cn `1) / |.cn.|) - q) / (1 + q)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.cn.| * |[((((cn `1) / |.cn.|) - q) / (1 + q)),(- (sqrt (1 - (((((cn `1) / |.cn.|) - q) / (1 + q)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
1 - q is V28() real ext-real Element of REAL
(((cn `1) / |.cn.|) - q) / (1 - q) is V28() real ext-real Element of COMPLEX
cn is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn `1 is V28() real ext-real Element of REAL
|.cn.| is V28() real ext-real non negative Element of REAL
(cn `1) / |.cn.| is V28() real ext-real Element of COMPLEX
cn `2 is V28() real ext-real Element of REAL
q is V28() real ext-real Element of REAL
(q) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(q) . cn is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((cn `1) / |.cn.|) - q is V28() real ext-real Element of REAL
1 - q is V28() real ext-real Element of REAL
(((cn `1) / |.cn.|) - q) / (1 - q) is V28() real ext-real Element of COMPLEX
|.cn.| * ((((cn `1) / |.cn.|) - q) / (1 - q)) is V28() real ext-real Element of REAL
((((cn `1) / |.cn.|) - q) / (1 - q)) ^2 is V28() real ext-real Element of COMPLEX
((((cn `1) / |.cn.|) - q) / (1 - q)) * ((((cn `1) / |.cn.|) - q) / (1 - q)) is V28() real ext-real set
1 - (((((cn `1) / |.cn.|) - q) / (1 - q)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((cn `1) / |.cn.|) - q) / (1 - q)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((cn `1) / |.cn.|) - q) / (1 - q)) ^2))) is V28() real ext-real Element of REAL
|.cn.| * (- (sqrt (1 - (((((cn `1) / |.cn.|) - q) / (1 - q)) ^2)))) is V28() real ext-real Element of REAL
|[(|.cn.| * ((((cn `1) / |.cn.|) - q) / (1 - q))),(|.cn.| * (- (sqrt (1 - (((((cn `1) / |.cn.|) - q) / (1 - q)) ^2)))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
1 + q is V28() real ext-real Element of REAL
(((cn `1) / |.cn.|) - q) / (1 + q) is V28() real ext-real Element of COMPLEX
|.cn.| * ((((cn `1) / |.cn.|) - q) / (1 + q)) is V28() real ext-real Element of REAL
((((cn `1) / |.cn.|) - q) / (1 + q)) ^2 is V28() real ext-real Element of COMPLEX
((((cn `1) / |.cn.|) - q) / (1 + q)) * ((((cn `1) / |.cn.|) - q) / (1 + q)) is V28() real ext-real set
1 - (((((cn `1) / |.cn.|) - q) / (1 + q)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((cn `1) / |.cn.|) - q) / (1 + q)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((cn `1) / |.cn.|) - q) / (1 + q)) ^2))) is V28() real ext-real Element of REAL
|.cn.| * (- (sqrt (1 - (((((cn `1) / |.cn.|) - q) / (1 + q)) ^2)))) is V28() real ext-real Element of REAL
|[(|.cn.| * ((((cn `1) / |.cn.|) - q) / (1 + q))),(|.cn.| * (- (sqrt (1 - (((((cn `1) / |.cn.|) - q) / (1 + q)) ^2)))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(q,cn) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[((((cn `1) / |.cn.|) - q) / (1 - q)),(- (sqrt (1 - (((((cn `1) / |.cn.|) - q) / (1 - q)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.cn.| * |[((((cn `1) / |.cn.|) - q) / (1 - q)),(- (sqrt (1 - (((((cn `1) / |.cn.|) - q) / (1 - q)) ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.cn.| ^2 is V28() real ext-real Element of REAL
|.cn.| * |.cn.| is V28() real ext-real non negative set
(cn `1) ^2 is V28() real ext-real Element of REAL
(cn `1) * (cn `1) is V28() real ext-real set
(cn `2) ^2 is V28() real ext-real Element of REAL
(cn `2) * (cn `2) is V28() real ext-real set
((cn `1) ^2) + ((cn `2) ^2) is V28() real ext-real Element of REAL
((cn `1) ^2) / (|.cn.| ^2) is V28() real ext-real Element of COMPLEX
((cn `1) / |.cn.|) ^2 is V28() real ext-real Element of COMPLEX
((cn `1) / |.cn.|) * ((cn `1) / |.cn.|) is V28() real ext-real set
sqrt (((cn `1) / |.cn.|) ^2) is V28() real ext-real set
- ((cn `1) / |.cn.|) is V28() real ext-real Element of COMPLEX
sqrt (|.cn.| ^2) is V28() real ext-real Element of REAL
1 * |.cn.| is V28() real ext-real non negative Element of REAL
((cn `1) / |.cn.|) * |.cn.| is V28() real ext-real Element of REAL
|.cn.| ^2 is V28() real ext-real Element of REAL
|.cn.| * |.cn.| is V28() real ext-real non negative set
(cn `1) ^2 is V28() real ext-real Element of REAL
(cn `1) * (cn `1) is V28() real ext-real set
(cn `2) ^2 is V28() real ext-real Element of REAL
(cn `2) * (cn `2) is V28() real ext-real set
((cn `1) ^2) + ((cn `2) ^2) is V28() real ext-real Element of REAL
- (cn `1) is V28() real ext-real Element of REAL
- |.cn.| is V28() real ext-real non positive Element of REAL
- (1 + q) is V28() real ext-real Element of REAL
(- (1 + q)) / (1 + q) is V28() real ext-real Element of COMPLEX
cn is V28() real ext-real Element of REAL
1 - cn is V28() real ext-real Element of REAL
q is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | q is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | q) is non empty set
K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1) is set
K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1)) is set
p is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
(2) | q is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of R^1))
proj1 | q is Relation-like the carrier of ((TOP-REAL 2) | q) -defined REAL -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q),REAL))
K20( the carrier of ((TOP-REAL 2) | q),REAL) is set
K19(K20( the carrier of ((TOP-REAL 2) | q),REAL)) is set
u2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
u2 is Element of the carrier of ((TOP-REAL 2) | q)
p1 . u2 is V28() real ext-real Element of the carrier of R^1
VV0 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
u2 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
dom u2 is Element of K19( the carrier of ((TOP-REAL 2) | q))
K19( the carrier of ((TOP-REAL 2) | q)) is set
dom p is Element of K19( the carrier of ((TOP-REAL 2) | q))
u3 is set
p . u3 is set
u2 . u3 is set
q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
proj1 . q4 is V28() real ext-real Element of REAL
q4 `1 is V28() real ext-real Element of REAL
(2) . q4 is V28() real ext-real Element of the carrier of R^1
|.q4.| is V28() real ext-real non negative Element of REAL
y is Element of the carrier of ((TOP-REAL 2) | q)
VV0 . y is V28() real ext-real Element of the carrier of R^1
proj1 . y is set
p1 . y is V28() real ext-real Element of the carrier of R^1
(2) . y is set
p . q4 is set
(q4 `1) / |.q4.| is V28() real ext-real Element of COMPLEX
((q4 `1) / |.q4.|) - cn is V28() real ext-real Element of REAL
(((q4 `1) / |.q4.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
|.q4.| * ((((q4 `1) / |.q4.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
cn is V28() real ext-real Element of REAL
1 + cn is V28() real ext-real Element of REAL
q is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | q is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | q) is non empty set
K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1) is set
K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1)) is set
p is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
(2) | q is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of R^1))
proj1 | q is Relation-like the carrier of ((TOP-REAL 2) | q) -defined REAL -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q),REAL))
K20( the carrier of ((TOP-REAL 2) | q),REAL) is set
K19(K20( the carrier of ((TOP-REAL 2) | q),REAL)) is set
u2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
u2 is Element of the carrier of ((TOP-REAL 2) | q)
p1 . u2 is V28() real ext-real Element of the carrier of R^1
VV0 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
u2 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
dom u2 is Element of K19( the carrier of ((TOP-REAL 2) | q))
K19( the carrier of ((TOP-REAL 2) | q)) is set
dom p is Element of K19( the carrier of ((TOP-REAL 2) | q))
u3 is set
p . u3 is set
u2 . u3 is set
q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
proj1 . q4 is V28() real ext-real Element of REAL
q4 `1 is V28() real ext-real Element of REAL
(2) . q4 is V28() real ext-real Element of the carrier of R^1
|.q4.| is V28() real ext-real non negative Element of REAL
y is Element of the carrier of ((TOP-REAL 2) | q)
VV0 . y is V28() real ext-real Element of the carrier of R^1
proj1 . y is set
p1 . y is V28() real ext-real Element of the carrier of R^1
(2) . y is set
p . q4 is set
(q4 `1) / |.q4.| is V28() real ext-real Element of COMPLEX
((q4 `1) / |.q4.|) - cn is V28() real ext-real Element of REAL
(((q4 `1) / |.q4.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
|.q4.| * ((((q4 `1) / |.q4.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
cn is V28() real ext-real Element of REAL
1 - cn is V28() real ext-real Element of REAL
q is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | q is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | q) is non empty set
K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1) is set
K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1)) is set
p is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
(2) | q is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of R^1))
proj1 | q is Relation-like the carrier of ((TOP-REAL 2) | q) -defined REAL -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q),REAL))
K20( the carrier of ((TOP-REAL 2) | q),REAL) is set
K19(K20( the carrier of ((TOP-REAL 2) | q),REAL)) is set
u2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
u2 is Element of the carrier of ((TOP-REAL 2) | q)
p1 . u2 is V28() real ext-real Element of the carrier of R^1
VV0 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
u2 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
dom u2 is Element of K19( the carrier of ((TOP-REAL 2) | q))
K19( the carrier of ((TOP-REAL 2) | q)) is set
dom p is Element of K19( the carrier of ((TOP-REAL 2) | q))
u3 is set
p . u3 is set
u2 . u3 is set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.y.| is V28() real ext-real non negative Element of REAL
|.y.| ^2 is V28() real ext-real Element of REAL
|.y.| * |.y.| is V28() real ext-real non negative set
y `1 is V28() real ext-real Element of REAL
(y `1) ^2 is V28() real ext-real Element of REAL
(y `1) * (y `1) is V28() real ext-real set
y `2 is V28() real ext-real Element of REAL
(y `2) ^2 is V28() real ext-real Element of REAL
(y `2) * (y `2) is V28() real ext-real set
((y `1) ^2) + ((y `2) ^2) is V28() real ext-real Element of REAL
(y `1) - |.y.| is V28() real ext-real Element of REAL
(y `1) + |.y.| is V28() real ext-real Element of REAL
((y `1) - |.y.|) * ((y `1) + |.y.|) is V28() real ext-real Element of REAL
- ((y `2) ^2) is V28() real ext-real Element of REAL
(y `1) / |.y.| is V28() real ext-real Element of COMPLEX
|.y.| / |.y.| is V28() real ext-real non negative Element of COMPLEX
((y `1) / |.y.|) - cn is V28() real ext-real Element of REAL
(1 - cn) ^2 is V28() real ext-real Element of REAL
(1 - cn) * (1 - cn) is V28() real ext-real set
(1 - cn) + cn is V28() real ext-real Element of REAL
0 + cn is V28() real ext-real Element of REAL
cn - ((y `1) / |.y.|) is V28() real ext-real Element of REAL
- (1 - cn) is V28() real ext-real Element of REAL
- (cn - ((y `1) / |.y.|)) is V28() real ext-real Element of REAL
(((y `1) / |.y.|) - cn) ^2 is V28() real ext-real Element of REAL
(((y `1) / |.y.|) - cn) * (((y `1) / |.y.|) - cn) is V28() real ext-real set
((((y `1) / |.y.|) - cn) ^2) / ((1 - cn) ^2) is V28() real ext-real Element of COMPLEX
((1 - cn) ^2) / ((1 - cn) ^2) is V28() real ext-real Element of COMPLEX
(((y `1) / |.y.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
((((y `1) / |.y.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((y `1) / |.y.|) - cn) / (1 - cn)) * ((((y `1) / |.y.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((y `1) / |.y.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
abs (1 - (((((y `1) / |.y.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
p . y is set
sqrt (abs (1 - (((((y `1) / |.y.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
- (sqrt (abs (1 - (((((y `1) / |.y.|) - cn) / (1 - cn)) ^2)))) is V28() real ext-real Element of REAL
|.y.| * (- (sqrt (abs (1 - (((((y `1) / |.y.|) - cn) / (1 - cn)) ^2))))) is V28() real ext-real Element of REAL
proj1 . y is V28() real ext-real Element of REAL
(2) . y is V28() real ext-real Element of the carrier of R^1
q4 is Element of the carrier of ((TOP-REAL 2) | q)
VV0 . q4 is V28() real ext-real Element of the carrier of R^1
proj1 . q4 is set
p1 . q4 is V28() real ext-real Element of the carrier of R^1
(2) . q4 is set
cn is V28() real ext-real Element of REAL
1 + cn is V28() real ext-real Element of REAL
q is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | q is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | q) is non empty set
K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1) is set
K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1)) is set
p is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
(2) | q is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of R^1))
proj1 | q is Relation-like the carrier of ((TOP-REAL 2) | q) -defined REAL -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q),REAL))
K20( the carrier of ((TOP-REAL 2) | q),REAL) is set
K19(K20( the carrier of ((TOP-REAL 2) | q),REAL)) is set
u2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
u2 is Element of the carrier of ((TOP-REAL 2) | q)
p1 . u2 is V28() real ext-real Element of the carrier of R^1
VV0 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
u2 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of R^1))
dom u2 is Element of K19( the carrier of ((TOP-REAL 2) | q))
K19( the carrier of ((TOP-REAL 2) | q)) is set
dom p is Element of K19( the carrier of ((TOP-REAL 2) | q))
u3 is set
p . u3 is set
u2 . u3 is set
(1 + cn) ^2 is V28() real ext-real Element of REAL
(1 + cn) * (1 + cn) is V28() real ext-real set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.y.| is V28() real ext-real non negative Element of REAL
|.y.| ^2 is V28() real ext-real Element of REAL
|.y.| * |.y.| is V28() real ext-real non negative set
y `1 is V28() real ext-real Element of REAL
(y `1) ^2 is V28() real ext-real Element of REAL
(y `1) * (y `1) is V28() real ext-real set
y `2 is V28() real ext-real Element of REAL
(y `2) ^2 is V28() real ext-real Element of REAL
(y `2) * (y `2) is V28() real ext-real set
((y `1) ^2) + ((y `2) ^2) is V28() real ext-real Element of REAL
(y `1) - |.y.| is V28() real ext-real Element of REAL
(y `1) + |.y.| is V28() real ext-real Element of REAL
((y `1) - |.y.|) * ((y `1) + |.y.|) is V28() real ext-real Element of REAL
- ((y `2) ^2) is V28() real ext-real Element of REAL
- |.y.| is V28() real ext-real non positive Element of REAL
(- |.y.|) / |.y.| is V28() real ext-real non positive Element of COMPLEX
(y `1) / |.y.| is V28() real ext-real Element of COMPLEX
(- 1) - cn is V28() real ext-real Element of REAL
((y `1) / |.y.|) - cn is V28() real ext-real Element of REAL
- (1 + cn) is V28() real ext-real Element of REAL
cn - ((y `1) / |.y.|) is V28() real ext-real Element of REAL
- (cn - ((y `1) / |.y.|)) is V28() real ext-real Element of REAL
(((y `1) / |.y.|) - cn) ^2 is V28() real ext-real Element of REAL
(((y `1) / |.y.|) - cn) * (((y `1) / |.y.|) - cn) is V28() real ext-real set
((((y `1) / |.y.|) - cn) ^2) / ((1 + cn) ^2) is V28() real ext-real Element of COMPLEX
((1 + cn) ^2) / ((1 + cn) ^2) is V28() real ext-real Element of COMPLEX
(((y `1) / |.y.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
((((y `1) / |.y.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((y `1) / |.y.|) - cn) / (1 + cn)) * ((((y `1) / |.y.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((y `1) / |.y.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
abs (1 - (((((y `1) / |.y.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
p . y is set
sqrt (abs (1 - (((((y `1) / |.y.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
- (sqrt (abs (1 - (((((y `1) / |.y.|) - cn) / (1 + cn)) ^2)))) is V28() real ext-real Element of REAL
|.y.| * (- (sqrt (abs (1 - (((((y `1) / |.y.|) - cn) / (1 + cn)) ^2))))) is V28() real ext-real Element of REAL
proj1 . y is V28() real ext-real Element of REAL
(2) . y is V28() real ext-real Element of the carrier of R^1
q4 is Element of the carrier of ((TOP-REAL 2) | q)
VV0 . q4 is V28() real ext-real Element of the carrier of R^1
proj1 . q4 is set
p1 . q4 is V28() real ext-real Element of the carrier of R^1
(2) . q4 is set
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( cn <= (b₁ `1) / |.b<sub>1</sub>.| & b<sub>1</sub> `2 <= 0 & not b₁ = 0. (TOP-REAL 2) ) } is set
q is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | q is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | q) is set
p is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | p is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | p) is set
K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p)) is set
K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p))) is set
(cn) | q is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p1 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of ((TOP-REAL 2) | p) -valued Function-like quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p)))
cn ^2 is V28() real ext-real Element of REAL
cn * cn is V28() real ext-real set
1 - (cn ^2) is V28() real ext-real Element of REAL
sqrt (1 - (cn ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (cn ^2))) is V28() real ext-real Element of REAL
|[cn,(- (sqrt (1 - (cn ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[cn,(- (sqrt (1 - (cn ^2))))]| `2 is V28() real ext-real Element of REAL
|[cn,(- (sqrt (1 - (cn ^2))))]| `1 is V28() real ext-real Element of REAL
|.|[cn,(- (sqrt (1 - (cn ^2))))]|.| is V28() real ext-real non negative Element of REAL
(- (sqrt (1 - (cn ^2)))) ^2 is V28() real ext-real Element of REAL
(- (sqrt (1 - (cn ^2)))) * (- (sqrt (1 - (cn ^2)))) is V28() real ext-real set
((- (sqrt (1 - (cn ^2)))) ^2) + (cn ^2) is V28() real ext-real Element of REAL
sqrt (((- (sqrt (1 - (cn ^2)))) ^2) + (cn ^2)) is V28() real ext-real Element of REAL
- (- (sqrt (1 - (cn ^2)))) is V28() real ext-real Element of REAL
- (- (- (sqrt (1 - (cn ^2))))) is V28() real ext-real Element of REAL
(- (- (sqrt (1 - (cn ^2))))) ^2 is V28() real ext-real Element of REAL
(- (- (sqrt (1 - (cn ^2))))) * (- (- (sqrt (1 - (cn ^2))))) is V28() real ext-real set
(|[cn,(- (sqrt (1 - (cn ^2))))]| `1) / |.|[cn,(- (sqrt (1 - (cn ^2))))]|.| is V28() real ext-real Element of COMPLEX
VV0 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(cn) | VV0 is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
proj2 * ((cn) | VV0) is Relation-like the carrier of (TOP-REAL 2) -defined REAL -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2),REAL))
rng (proj2 * ((cn) | VV0)) is V126() V127() V128() Element of K19(REAL)
u2 is set
u3 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
u3 `1 is V28() real ext-real Element of REAL
|.u3.| is V28() real ext-real non negative Element of REAL
(u3 `1) / |.u3.| is V28() real ext-real Element of COMPLEX
u3 `2 is V28() real ext-real Element of REAL
dom ((cn) | VV0) is functional Element of K19( the carrier of (TOP-REAL 2))
proj1 * ((cn) | VV0) is Relation-like the carrier of (TOP-REAL 2) -defined REAL -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2),REAL))
dom (proj1 * ((cn) | VV0)) is functional Element of K19( the carrier of (TOP-REAL 2))
u2 is set
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
(dom (cn)) /\ VV0 is functional Element of K19( the carrier of (TOP-REAL 2))
dom proj1 is functional Element of K19( the carrier of (TOP-REAL 2))
(cn) . u2 is Relation-like Function-like set
rng (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
((cn) | VV0) . u2 is Relation-like Function-like set
rng (proj1 * ((cn) | VV0)) is V126() V127() V128() Element of K19(REAL)
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
(dom (cn)) /\ VV0 is functional Element of K19( the carrier of (TOP-REAL 2))
the carrier of (TOP-REAL 2) /\ VV0 is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | VV0 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | VV0) is non empty set
K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1) is set
K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1)) is set
u2 is Relation-like the carrier of ((TOP-REAL 2) | VV0) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1))
1 - cn is V28() real ext-real Element of REAL
u3 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
u2 . u3 is set
|.u3.| is V28() real ext-real non negative Element of REAL
u3 `1 is V28() real ext-real Element of REAL
(u3 `1) / |.u3.| is V28() real ext-real Element of COMPLEX
((u3 `1) / |.u3.|) - cn is V28() real ext-real Element of REAL
(((u3 `1) / |.u3.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
|.u3.| * ((((u3 `1) / |.u3.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
(cn) . u3 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((((u3 `1) / |.u3.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((u3 `1) / |.u3.|) - cn) / (1 - cn)) * ((((u3 `1) / |.u3.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((u3 `1) / |.u3.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((u3 `1) / |.u3.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((u3 `1) / |.u3.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.u3.| * (- (sqrt (1 - (((((u3 `1) / |.u3.|) - cn) / (1 - cn)) ^2)))) is V28() real ext-real Element of REAL
|[(|.u3.| * ((((u3 `1) / |.u3.|) - cn) / (1 - cn))),(|.u3.| * (- (sqrt (1 - (((((u3 `1) / |.u3.|) - cn) / (1 - cn)) ^2)))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `1 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `1) / |.y.| is V28() real ext-real Element of COMPLEX
y `2 is V28() real ext-real Element of REAL
((cn) | VV0) . u3 is Relation-like Function-like set
proj1 . |[(|.u3.| * ((((u3 `1) / |.u3.|) - cn) / (1 - cn))),(|.u3.| * (- (sqrt (1 - (((((u3 `1) / |.u3.|) - cn) / (1 - cn)) ^2)))))]| is V28() real ext-real Element of REAL
|[(|.u3.| * ((((u3 `1) / |.u3.|) - cn) / (1 - cn))),(|.u3.| * (- (sqrt (1 - (((((u3 `1) / |.u3.|) - cn) / (1 - cn)) ^2)))))]| `1 is V28() real ext-real Element of REAL
u3 is Relation-like the carrier of ((TOP-REAL 2) | VV0) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1))
dom (proj2 * ((cn) | VV0)) is functional Element of K19( the carrier of (TOP-REAL 2))
y is set
dom proj2 is functional Element of K19( the carrier of (TOP-REAL 2))
(cn) . y is Relation-like Function-like set
rng (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
((cn) | VV0) . y is Relation-like Function-like set
y is Relation-like the carrier of ((TOP-REAL 2) | VV0) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1))
q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y . q4 is set
|.q4.| is V28() real ext-real non negative Element of REAL
q4 `1 is V28() real ext-real Element of REAL
(q4 `1) / |.q4.| is V28() real ext-real Element of COMPLEX
((q4 `1) / |.q4.|) - cn is V28() real ext-real Element of REAL
(((q4 `1) / |.q4.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
((((q4 `1) / |.q4.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((q4 `1) / |.q4.|) - cn) / (1 - cn)) * ((((q4 `1) / |.q4.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((q4 `1) / |.q4.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((q4 `1) / |.q4.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((q4 `1) / |.q4.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.q4.| * (- (sqrt (1 - (((((q4 `1) / |.q4.|) - cn) / (1 - cn)) ^2)))) is V28() real ext-real Element of REAL
(cn) . q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.q4.| * ((((q4 `1) / |.q4.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
|[(|.q4.| * ((((q4 `1) / |.q4.|) - cn) / (1 - cn))),(|.q4.| * (- (sqrt (1 - (((((q4 `1) / |.q4.|) - cn) / (1 - cn)) ^2)))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `1 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `1) / |.y.| is V28() real ext-real Element of COMPLEX
y `2 is V28() real ext-real Element of REAL
((cn) | VV0) . q4 is Relation-like Function-like set
proj2 . |[(|.q4.| * ((((q4 `1) / |.q4.|) - cn) / (1 - cn))),(|.q4.| * (- (sqrt (1 - (((((q4 `1) / |.q4.|) - cn) / (1 - cn)) ^2)))))]| is V28() real ext-real Element of REAL
|[(|.q4.| * ((((q4 `1) / |.q4.|) - cn) / (1 - cn))),(|.q4.| * (- (sqrt (1 - (((((q4 `1) / |.q4.|) - cn) / (1 - cn)) ^2)))))]| `2 is V28() real ext-real Element of REAL
q4 is Relation-like the carrier of ((TOP-REAL 2) | VV0) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1))
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `2 is V28() real ext-real Element of REAL
y `1 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `1) / |.y.| is V28() real ext-real Element of COMPLEX
x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x `1 is V28() real ext-real Element of REAL
|.x.| is V28() real ext-real non negative Element of REAL
(x `1) / |.x.| is V28() real ext-real Element of COMPLEX
x `2 is V28() real ext-real Element of REAL
y is V28() real ext-real set
x is V28() real ext-real set
|[y,x]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x is V28() real ext-real set
u3 . |[y,x]| is set
q is V28() real ext-real set
q4 . |[y,x]| is set
p1 . |[y,x]| is set
|[x,q]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.|[y,x]|.| is V28() real ext-real non negative Element of REAL
|[y,x]| `1 is V28() real ext-real Element of REAL
(|[y,x]| `1) / |.|[y,x]|.| is V28() real ext-real Element of COMPLEX
((|[y,x]| `1) / |.|[y,x]|.|) - cn is V28() real ext-real Element of REAL
(((|[y,x]| `1) / |.|[y,x]|.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
((((|[y,x]| `1) / |.|[y,x]|.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((|[y,x]| `1) / |.|[y,x]|.|) - cn) / (1 - cn)) * ((((|[y,x]| `1) / |.|[y,x]|.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((|[y,x]| `1) / |.|[y,x]|.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((|[y,x]| `1) / |.|[y,x]|.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((|[y,x]| `1) / |.|[y,x]|.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.|[y,x]|.| * (- (sqrt (1 - (((((|[y,x]| `1) / |.|[y,x]|.|) - cn) / (1 - cn)) ^2)))) is V28() real ext-real Element of REAL
((cn) | q) . |[y,x]| is Relation-like Function-like set
(cn) . |[y,x]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.|[y,x]|.| * ((((|[y,x]| `1) / |.|[y,x]|.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
|[(|.|[y,x]|.| * ((((|[y,x]| `1) / |.|[y,x]|.|) - cn) / (1 - cn))),(|.|[y,x]|.| * (- (sqrt (1 - (((((|[y,x]| `1) / |.|[y,x]|.|) - cn) / (1 - cn)) ^2)))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K111 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K111 `1 is V28() real ext-real Element of REAL
|.K111.| is V28() real ext-real non negative Element of REAL
(K111 `1) / |.K111.| is V28() real ext-real Element of COMPLEX
K111 `2 is V28() real ext-real Element of REAL
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `2 is V28() real ext-real Element of REAL
x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x `1 is V28() real ext-real Element of REAL
|.x.| is V28() real ext-real non negative Element of REAL
(x `1) / |.x.| is V28() real ext-real Element of COMPLEX
x `2 is V28() real ext-real Element of REAL
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( (b₁ `1) / |.b<sub>1</sub>.| <= cn & b<sub>1</sub> `2 <= 0 & not b₁ = 0. (TOP-REAL 2) ) } is set
q is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | q is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | q) is set
p is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | p is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | p) is set
K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p)) is set
K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p))) is set
(cn) | q is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p1 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of ((TOP-REAL 2) | p) -valued Function-like quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p)))
cn ^2 is V28() real ext-real Element of REAL
cn * cn is V28() real ext-real set
1 - (cn ^2) is V28() real ext-real Element of REAL
sqrt (1 - (cn ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (cn ^2))) is V28() real ext-real Element of REAL
|[cn,(- (sqrt (1 - (cn ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[cn,(- (sqrt (1 - (cn ^2))))]| `2 is V28() real ext-real Element of REAL
|[cn,(- (sqrt (1 - (cn ^2))))]| `1 is V28() real ext-real Element of REAL
|.|[cn,(- (sqrt (1 - (cn ^2))))]|.| is V28() real ext-real non negative Element of REAL
(- (sqrt (1 - (cn ^2)))) ^2 is V28() real ext-real Element of REAL
(- (sqrt (1 - (cn ^2)))) * (- (sqrt (1 - (cn ^2)))) is V28() real ext-real set
((- (sqrt (1 - (cn ^2)))) ^2) + (cn ^2) is V28() real ext-real Element of REAL
sqrt (((- (sqrt (1 - (cn ^2)))) ^2) + (cn ^2)) is V28() real ext-real Element of REAL
- (- (sqrt (1 - (cn ^2)))) is V28() real ext-real Element of REAL
- (- (- (sqrt (1 - (cn ^2))))) is V28() real ext-real Element of REAL
(- (- (sqrt (1 - (cn ^2))))) ^2 is V28() real ext-real Element of REAL
(- (- (sqrt (1 - (cn ^2))))) * (- (- (sqrt (1 - (cn ^2))))) is V28() real ext-real set
(|[cn,(- (sqrt (1 - (cn ^2))))]| `1) / |.|[cn,(- (sqrt (1 - (cn ^2))))]|.| is V28() real ext-real Element of COMPLEX
VV0 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(cn) | VV0 is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
proj2 * ((cn) | VV0) is Relation-like the carrier of (TOP-REAL 2) -defined REAL -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2),REAL))
rng (proj2 * ((cn) | VV0)) is V126() V127() V128() Element of K19(REAL)
u2 is set
u3 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
u3 `1 is V28() real ext-real Element of REAL
|.u3.| is V28() real ext-real non negative Element of REAL
(u3 `1) / |.u3.| is V28() real ext-real Element of COMPLEX
u3 `2 is V28() real ext-real Element of REAL
dom ((cn) | VV0) is functional Element of K19( the carrier of (TOP-REAL 2))
proj1 * ((cn) | VV0) is Relation-like the carrier of (TOP-REAL 2) -defined REAL -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2),REAL))
dom (proj1 * ((cn) | VV0)) is functional Element of K19( the carrier of (TOP-REAL 2))
u2 is set
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
(dom (cn)) /\ VV0 is functional Element of K19( the carrier of (TOP-REAL 2))
dom proj1 is functional Element of K19( the carrier of (TOP-REAL 2))
(cn) . u2 is Relation-like Function-like set
rng (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
((cn) | VV0) . u2 is Relation-like Function-like set
rng (proj1 * ((cn) | VV0)) is V126() V127() V128() Element of K19(REAL)
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
(dom (cn)) /\ VV0 is functional Element of K19( the carrier of (TOP-REAL 2))
the carrier of (TOP-REAL 2) /\ VV0 is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | VV0 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | VV0) is non empty set
K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1) is set
K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1)) is set
u2 is Relation-like the carrier of ((TOP-REAL 2) | VV0) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1))
1 + cn is V28() real ext-real Element of REAL
u3 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
u2 . u3 is set
|.u3.| is V28() real ext-real non negative Element of REAL
u3 `1 is V28() real ext-real Element of REAL
(u3 `1) / |.u3.| is V28() real ext-real Element of COMPLEX
((u3 `1) / |.u3.|) - cn is V28() real ext-real Element of REAL
(((u3 `1) / |.u3.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
|.u3.| * ((((u3 `1) / |.u3.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
(cn) . u3 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((((u3 `1) / |.u3.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((u3 `1) / |.u3.|) - cn) / (1 + cn)) * ((((u3 `1) / |.u3.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((u3 `1) / |.u3.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((u3 `1) / |.u3.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((u3 `1) / |.u3.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|.u3.| * (- (sqrt (1 - (((((u3 `1) / |.u3.|) - cn) / (1 + cn)) ^2)))) is V28() real ext-real Element of REAL
|[(|.u3.| * ((((u3 `1) / |.u3.|) - cn) / (1 + cn))),(|.u3.| * (- (sqrt (1 - (((((u3 `1) / |.u3.|) - cn) / (1 + cn)) ^2)))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `1 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `1) / |.y.| is V28() real ext-real Element of COMPLEX
y `2 is V28() real ext-real Element of REAL
((cn) | VV0) . u3 is Relation-like Function-like set
proj1 . |[(|.u3.| * ((((u3 `1) / |.u3.|) - cn) / (1 + cn))),(|.u3.| * (- (sqrt (1 - (((((u3 `1) / |.u3.|) - cn) / (1 + cn)) ^2)))))]| is V28() real ext-real Element of REAL
|[(|.u3.| * ((((u3 `1) / |.u3.|) - cn) / (1 + cn))),(|.u3.| * (- (sqrt (1 - (((((u3 `1) / |.u3.|) - cn) / (1 + cn)) ^2)))))]| `1 is V28() real ext-real Element of REAL
u3 is Relation-like the carrier of ((TOP-REAL 2) | VV0) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1))
dom (proj2 * ((cn) | VV0)) is functional Element of K19( the carrier of (TOP-REAL 2))
y is set
dom proj2 is functional Element of K19( the carrier of (TOP-REAL 2))
(cn) . y is Relation-like Function-like set
rng (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
((cn) | VV0) . y is Relation-like Function-like set
y is Relation-like the carrier of ((TOP-REAL 2) | VV0) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1))
q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y . q4 is set
|.q4.| is V28() real ext-real non negative Element of REAL
q4 `1 is V28() real ext-real Element of REAL
(q4 `1) / |.q4.| is V28() real ext-real Element of COMPLEX
((q4 `1) / |.q4.|) - cn is V28() real ext-real Element of REAL
(((q4 `1) / |.q4.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
((((q4 `1) / |.q4.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((q4 `1) / |.q4.|) - cn) / (1 + cn)) * ((((q4 `1) / |.q4.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((q4 `1) / |.q4.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((q4 `1) / |.q4.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((q4 `1) / |.q4.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|.q4.| * (- (sqrt (1 - (((((q4 `1) / |.q4.|) - cn) / (1 + cn)) ^2)))) is V28() real ext-real Element of REAL
(cn) . q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.q4.| * ((((q4 `1) / |.q4.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
|[(|.q4.| * ((((q4 `1) / |.q4.|) - cn) / (1 + cn))),(|.q4.| * (- (sqrt (1 - (((((q4 `1) / |.q4.|) - cn) / (1 + cn)) ^2)))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `1 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `1) / |.y.| is V28() real ext-real Element of COMPLEX
y `2 is V28() real ext-real Element of REAL
((cn) | VV0) . q4 is Relation-like Function-like set
proj2 . |[(|.q4.| * ((((q4 `1) / |.q4.|) - cn) / (1 + cn))),(|.q4.| * (- (sqrt (1 - (((((q4 `1) / |.q4.|) - cn) / (1 + cn)) ^2)))))]| is V28() real ext-real Element of REAL
|[(|.q4.| * ((((q4 `1) / |.q4.|) - cn) / (1 + cn))),(|.q4.| * (- (sqrt (1 - (((((q4 `1) / |.q4.|) - cn) / (1 + cn)) ^2)))))]| `2 is V28() real ext-real Element of REAL
q4 is Relation-like the carrier of ((TOP-REAL 2) | VV0) -defined the carrier of R^1 -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of R^1))
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `2 is V28() real ext-real Element of REAL
y `1 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `1) / |.y.| is V28() real ext-real Element of COMPLEX
x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x `1 is V28() real ext-real Element of REAL
|.x.| is V28() real ext-real non negative Element of REAL
(x `1) / |.x.| is V28() real ext-real Element of COMPLEX
x `2 is V28() real ext-real Element of REAL
y is V28() real ext-real set
x is V28() real ext-real set
|[y,x]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x is V28() real ext-real set
u3 . |[y,x]| is set
q is V28() real ext-real set
q4 . |[y,x]| is set
p1 . |[y,x]| is set
|[x,q]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.|[y,x]|.| is V28() real ext-real non negative Element of REAL
|[y,x]| `1 is V28() real ext-real Element of REAL
(|[y,x]| `1) / |.|[y,x]|.| is V28() real ext-real Element of COMPLEX
((|[y,x]| `1) / |.|[y,x]|.|) - cn is V28() real ext-real Element of REAL
(((|[y,x]| `1) / |.|[y,x]|.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
((((|[y,x]| `1) / |.|[y,x]|.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((|[y,x]| `1) / |.|[y,x]|.|) - cn) / (1 + cn)) * ((((|[y,x]| `1) / |.|[y,x]|.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((|[y,x]| `1) / |.|[y,x]|.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((|[y,x]| `1) / |.|[y,x]|.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((|[y,x]| `1) / |.|[y,x]|.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|.|[y,x]|.| * (- (sqrt (1 - (((((|[y,x]| `1) / |.|[y,x]|.|) - cn) / (1 + cn)) ^2)))) is V28() real ext-real Element of REAL
((cn) | q) . |[y,x]| is Relation-like Function-like set
(cn) . |[y,x]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.|[y,x]|.| * ((((|[y,x]| `1) / |.|[y,x]|.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
|[(|.|[y,x]|.| * ((((|[y,x]| `1) / |.|[y,x]|.|) - cn) / (1 + cn))),(|.|[y,x]|.| * (- (sqrt (1 - (((((|[y,x]| `1) / |.|[y,x]|.|) - cn) / (1 + cn)) ^2)))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K111 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K111 `1 is V28() real ext-real Element of REAL
|.K111.| is V28() real ext-real non negative Element of REAL
(K111 `1) / |.K111.| is V28() real ext-real Element of COMPLEX
K111 `2 is V28() real ext-real Element of REAL
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `2 is V28() real ext-real Element of REAL
x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x `1 is V28() real ext-real Element of REAL
|.x.| is V28() real ext-real non negative Element of REAL
(x `1) / |.x.| is V28() real ext-real Element of COMPLEX
x `2 is V28() real ext-real Element of REAL
cn is V28() real ext-real Element of REAL
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( cn * |.b₁.| <= b₁ `1 & b<sub>1</sub> `2 <= 0 ) } is set
q is functional Element of K19( the carrier of (TOP-REAL 2))
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₁[b₁] } is set
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₂[b₁] } is set
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( S₂[b₁] & S₁[b₁] ) } is set
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₂[b₁] } /\ { b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₁[b₁] } is set
p1 is functional Element of K19( the carrier of (TOP-REAL 2))
p is functional Element of K19( the carrier of (TOP-REAL 2))
cn is V28() real ext-real Element of REAL
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( b₁ `1 <= cn * |.b<sub>1</sub>.| & b<sub>1</sub> `2 <= 0 ) } is set
q is functional Element of K19( the carrier of (TOP-REAL 2))
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₁[b₁] } is set
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₂[b₁] } is set
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( S₂[b₁] & S₁[b₁] ) } is set
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₂[b₁] } /\ { b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₁[b₁] } is set
p1 is functional Element of K19( the carrier of (TOP-REAL 2))
p is functional Element of K19( the carrier of (TOP-REAL 2))
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | q is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | q) is set
p is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | p is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | p) is set
K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p)) is set
K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p))) is set
(cn) | q is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p1 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of ((TOP-REAL 2) | p) -valued Function-like quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p)))
cn ^2 is V28() real ext-real Element of REAL
cn * cn is V28() real ext-real set
1 - (cn ^2) is V28() real ext-real Element of REAL
sqrt (1 - (cn ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (cn ^2))) is V28() real ext-real Element of REAL
|[cn,(- (sqrt (1 - (cn ^2))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[cn,(- (sqrt (1 - (cn ^2))))]| `2 is V28() real ext-real Element of REAL
|[cn,(- (sqrt (1 - (cn ^2))))]| `1 is V28() real ext-real Element of REAL
|.|[cn,(- (sqrt (1 - (cn ^2))))]|.| is V28() real ext-real non negative Element of REAL
(- (sqrt (1 - (cn ^2)))) ^2 is V28() real ext-real Element of REAL
(- (sqrt (1 - (cn ^2)))) * (- (sqrt (1 - (cn ^2)))) is V28() real ext-real set
((- (sqrt (1 - (cn ^2)))) ^2) + (cn ^2) is V28() real ext-real Element of REAL
sqrt (((- (sqrt (1 - (cn ^2)))) ^2) + (cn ^2)) is V28() real ext-real Element of REAL
- (- (sqrt (1 - (cn ^2)))) is V28() real ext-real Element of REAL
- (- (- (sqrt (1 - (cn ^2))))) is V28() real ext-real Element of REAL
(- (- (sqrt (1 - (cn ^2))))) ^2 is V28() real ext-real Element of REAL
(- (- (sqrt (1 - (cn ^2))))) * (- (- (sqrt (1 - (cn ^2))))) is V28() real ext-real set
(|[cn,(- (sqrt (1 - (cn ^2))))]| `1) / |.|[cn,(- (sqrt (1 - (cn ^2))))]|.| is V28() real ext-real Element of COMPLEX
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( cn <= (b<sub>1</sub> `1) / |.b₁.| & b₁ `2 <= 0 & not b<sub>1</sub> = 0. (TOP-REAL 2) ) } is set
VV0 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
u2 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
u3 is set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `2 is V28() real ext-real Element of REAL
VV0 \/ u2 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | VV0 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
(TOP-REAL 2) | u2 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( (b₁ `1) / |.b<sub>1</sub>.| <= cn & b<sub>1</sub> `2 <= 0 & not b₁ = 0. (TOP-REAL 2) ) } is set
u3 is set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `1 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `1) / |.y.| is V28() real ext-real Element of COMPLEX
y `2 is V28() real ext-real Element of REAL
u3 is set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `1 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `1) / |.y.| is V28() real ext-real Element of COMPLEX
y `2 is V28() real ext-real Element of REAL
the carrier of ((TOP-REAL 2) | VV0) is non empty set
K19( the carrier of ((TOP-REAL 2) | VV0)) is set
the carrier of ((TOP-REAL 2) | u2) is non empty set
u3 is non empty Element of K19( the carrier of ((TOP-REAL 2) | VV0))
p1 | u3 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of ((TOP-REAL 2) | p) -valued Function-like Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p)))
rng (p1 | u3) is Element of K19( the carrier of ((TOP-REAL 2) | p))
K19( the carrier of ((TOP-REAL 2) | p)) is set
y is non empty Element of K19( the carrier of ((TOP-REAL 2) | VV0))
p1 | y is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of ((TOP-REAL 2) | p) -valued Function-like Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p)))
rng (p1 | y) is Element of K19( the carrier of ((TOP-REAL 2) | p))
dom p1 is Element of K19( the carrier of ((TOP-REAL 2) | q))
K19( the carrier of ((TOP-REAL 2) | q)) is set
dom (p1 | u3) is Element of K19( the carrier of ((TOP-REAL 2) | q))
((TOP-REAL 2) | VV0) | u3 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of (TOP-REAL 2) | VV0
the carrier of (((TOP-REAL 2) | VV0) | u3) is non empty set
K20( the carrier of (((TOP-REAL 2) | VV0) | u3), the carrier of ((TOP-REAL 2) | u2)) is set
K19(K20( the carrier of (((TOP-REAL 2) | VV0) | u3), the carrier of ((TOP-REAL 2) | u2))) is set
dom (p1 | y) is Element of K19( the carrier of ((TOP-REAL 2) | q))
((TOP-REAL 2) | VV0) | y is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of (TOP-REAL 2) | VV0
the carrier of (((TOP-REAL 2) | VV0) | y) is non empty set
K20( the carrier of (((TOP-REAL 2) | VV0) | y), the carrier of ((TOP-REAL 2) | u2)) is set
K19(K20( the carrier of (((TOP-REAL 2) | VV0) | y), the carrier of ((TOP-REAL 2) | u2))) is set
y is Relation-like the carrier of (((TOP-REAL 2) | VV0) | y) -defined the carrier of ((TOP-REAL 2) | u2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (((TOP-REAL 2) | VV0) | y), the carrier of ((TOP-REAL 2) | u2)))
dom y is Element of K19( the carrier of (((TOP-REAL 2) | VV0) | y))
K19( the carrier of (((TOP-REAL 2) | VV0) | y)) is set
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₁[b₁] } is set
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₂[b₁] } is set
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( cn * |.b₁.| <= b₁ `1 & b<sub>1</sub> `2 <= 0 ) } is set
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S₃[b₁] } is set
x is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(cn) | x is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
rng ((cn) | x) is functional Element of K19( the carrier of (TOP-REAL 2))
q is set
dom ((cn) | x) is functional Element of K19( the carrier of (TOP-REAL 2))
K004 is set
((cn) | x) . K004 is Relation-like Function-like set
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
K111 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(cn) . K111 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(dom (cn)) /\ x is functional Element of K19( the carrier of (TOP-REAL 2))
the carrier of (TOP-REAL 2) /\ x is functional Element of K19( the carrier of (TOP-REAL 2))
K111 `1 is V28() real ext-real Element of REAL
|.K111.| is V28() real ext-real non negative Element of REAL
(K111 `1) / |.K111.| is V28() real ext-real Element of COMPLEX
((K111 `1) / |.K111.|) - cn is V28() real ext-real Element of REAL
f4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
f4 `1 is V28() real ext-real Element of REAL
|.f4.| is V28() real ext-real non negative Element of REAL
(f4 `1) / |.f4.| is V28() real ext-real Element of COMPLEX
f4 `2 is V28() real ext-real Element of REAL
f4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
f4 `1 is V28() real ext-real Element of REAL
|.f4.| is V28() real ext-real non negative Element of REAL
(f4 `1) / |.f4.| is V28() real ext-real Element of COMPLEX
f4 `2 is V28() real ext-real Element of REAL
|.K111.| ^2 is V28() real ext-real Element of REAL
|.K111.| * |.K111.| is V28() real ext-real non negative set
0 ^2 is V28() real ext-real Element of REAL
0 * 0 is Function-like functional empty V28() real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() set
1 - cn is V28() real ext-real Element of REAL
(((K111 `1) / |.K111.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
|.K111.| * ((((K111 `1) / |.K111.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((K111 `1) / |.K111.|) - cn) / (1 - cn)) * ((((K111 `1) / |.K111.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.K111.| * (- (sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2)))) is V28() real ext-real Element of REAL
|[(|.K111.| * ((((K111 `1) / |.K111.|) - cn) / (1 - cn))),(|.K111.| * (- (sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2)))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.K111.| * ((((K111 `1) / |.K111.|) - cn) / (1 - cn))),(|.K111.| * (- (sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2)))))]| `1 is V28() real ext-real Element of REAL
K111 `2 is V28() real ext-real Element of REAL
(K111 `2) ^2 is V28() real ext-real Element of REAL
(K111 `2) * (K111 `2) is V28() real ext-real set
(K111 `1) ^2 is V28() real ext-real Element of REAL
(K111 `1) * (K111 `1) is V28() real ext-real set
0 + ((K111 `1) ^2) is V28() real ext-real Element of REAL
((K111 `1) ^2) + ((K111 `2) ^2) is V28() real ext-real Element of REAL
((K111 `1) ^2) / (|.K111.| ^2) is V28() real ext-real Element of COMPLEX
(|.K111.| ^2) / (|.K111.| ^2) is V28() real ext-real Element of COMPLEX
((K111 `1) / |.K111.|) ^2 is V28() real ext-real Element of COMPLEX
((K111 `1) / |.K111.|) * ((K111 `1) / |.K111.|) is V28() real ext-real set
- (1 - cn) is V28() real ext-real Element of REAL
- (((K111 `1) / |.K111.|) - cn) is V28() real ext-real Element of REAL
(- (1 - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
(- (((K111 `1) / |.K111.|) - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
((- (((K111 `1) / |.K111.|) - cn)) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((K111 `1) / |.K111.|) - cn)) / (1 - cn)) * ((- (((K111 `1) / |.K111.|) - cn)) / (1 - cn)) is V28() real ext-real set
1 - (((- (((K111 `1) / |.K111.|) - cn)) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
- ((((K111 `1) / |.K111.|) - cn) / (1 - cn)) is V28() real ext-real Element of COMPLEX
(- ((((K111 `1) / |.K111.|) - cn) / (1 - cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((K111 `1) / |.K111.|) - cn) / (1 - cn))) * (- ((((K111 `1) / |.K111.|) - cn) / (1 - cn))) is V28() real ext-real set
1 - ((- ((((K111 `1) / |.K111.|) - cn) / (1 - cn))) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((K111 `1) / |.K111.|) - cn)) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
(- (((K111 `1) / |.K111.|) - cn)) ^2 is V28() real ext-real Element of REAL
(- (((K111 `1) / |.K111.|) - cn)) * (- (((K111 `1) / |.K111.|) - cn)) is V28() real ext-real set
(1 - cn) ^2 is V28() real ext-real Element of REAL
(1 - cn) * (1 - cn) is V28() real ext-real set
((- (((K111 `1) / |.K111.|) - cn)) ^2) / ((1 - cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((- (((K111 `1) / |.K111.|) - cn)) ^2) / ((1 - cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((K111 `1) / |.K111.|) - cn)) ^2) / ((1 - cn) ^2))) is V28() real ext-real Element of REAL
(((K111 `1) / |.K111.|) - cn) ^2 is V28() real ext-real Element of REAL
(((K111 `1) / |.K111.|) - cn) * (((K111 `1) / |.K111.|) - cn) is V28() real ext-real set
((((K111 `1) / |.K111.|) - cn) ^2) / ((1 - cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((((K111 `1) / |.K111.|) - cn) ^2) / ((1 - cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((((K111 `1) / |.K111.|) - cn) ^2) / ((1 - cn) ^2))) is V28() real ext-real Element of REAL
|[(|.K111.| * ((((K111 `1) / |.K111.|) - cn) / (1 - cn))),(|.K111.| * (- (sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2)))))]| `2 is V28() real ext-real Element of REAL
(|[(|.K111.| * ((((K111 `1) / |.K111.|) - cn) / (1 - cn))),(|.K111.| * (- (sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2)))))]| `2) ^2 is V28() real ext-real Element of REAL
(|[(|.K111.| * ((((K111 `1) / |.K111.|) - cn) / (1 - cn))),(|.K111.| * (- (sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2)))))]| `2) * (|[(|.K111.| * ((((K111 `1) / |.K111.|) - cn) / (1 - cn))),(|.K111.| * (- (sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2)))))]| `2) is V28() real ext-real set
(sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2))) * (sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real set
(|.K111.| ^2) * ((sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2))) ^2) is V28() real ext-real Element of REAL
(|.K111.| ^2) * (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.|[(|.K111.| * ((((K111 `1) / |.K111.|) - cn) / (1 - cn))),(|.K111.| * (- (sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2)))))]|.| is V28() real ext-real non negative Element of REAL
|.|[(|.K111.| * ((((K111 `1) / |.K111.|) - cn) / (1 - cn))),(|.K111.| * (- (sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2)))))]|.| ^2 is V28() real ext-real Element of REAL
|.|[(|.K111.| * ((((K111 `1) / |.K111.|) - cn) / (1 - cn))),(|.K111.| * (- (sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2)))))]|.| * |.|[(|.K111.| * ((((K111 `1) / |.K111.|) - cn) / (1 - cn))),(|.K111.| * (- (sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2)))))]|.| is V28() real ext-real non negative set
(|[(|.K111.| * ((((K111 `1) / |.K111.|) - cn) / (1 - cn))),(|.K111.| * (- (sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2)))))]| `1) ^2 is V28() real ext-real Element of REAL
(|[(|.K111.| * ((((K111 `1) / |.K111.|) - cn) / (1 - cn))),(|.K111.| * (- (sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2)))))]| `1) * (|[(|.K111.| * ((((K111 `1) / |.K111.|) - cn) / (1 - cn))),(|.K111.| * (- (sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2)))))]| `1) is V28() real ext-real set
((|[(|.K111.| * ((((K111 `1) / |.K111.|) - cn) / (1 - cn))),(|.K111.| * (- (sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2)))))]| `1) ^2) + ((|[(|.K111.| * ((((K111 `1) / |.K111.|) - cn) / (1 - cn))),(|.K111.| * (- (sqrt (1 - (((((K111 `1) / |.K111.|) - cn) / (1 - cn)) ^2)))))]| `2) ^2) is V28() real ext-real Element of REAL
T1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
T1 `1 is V28() real ext-real Element of REAL
|.T1.| is V28() real ext-real non negative Element of REAL
(T1 `1) / |.T1.| is V28() real ext-real Element of COMPLEX
T1 `2 is V28() real ext-real Element of REAL
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
dom ((cn) | x) is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | x is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | x) is non empty set
K20( the carrier of ((TOP-REAL 2) | x), the carrier of ((TOP-REAL 2) | VV0)) is set
K19(K20( the carrier of ((TOP-REAL 2) | x), the carrier of ((TOP-REAL 2) | VV0))) is set
x is functional Element of K19( the carrier of (TOP-REAL 2))
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : S<sub>4</sub>[b<sub>1</sub>] } is set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( b<sub>1</sub> `1 <= cn * |.b₁.| & b₁ `2 <= 0 ) } is set
K004 is functional Element of K19( the carrier of (TOP-REAL 2))
K004 /\ VV0 is functional Element of K19( the carrier of (TOP-REAL 2))
K111 is set
f4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
f4 `1 is V28() real ext-real Element of REAL
|.f4.| is V28() real ext-real non negative Element of REAL
cn * |.f4.| is V28() real ext-real Element of REAL
f4 `2 is V28() real ext-real Element of REAL
(f4 `1) / |.f4.| is V28() real ext-real Element of COMPLEX
(cn * |.f4.|) / |.f4.| is V28() real ext-real Element of COMPLEX
T1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
T1 `2 is V28() real ext-real Element of REAL
T1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
T1 `2 is V28() real ext-real Element of REAL
q4 is Relation-like the carrier of (((TOP-REAL 2) | VV0) | u3) -defined the carrier of ((TOP-REAL 2) | u2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (((TOP-REAL 2) | VV0) | u3), the carrier of ((TOP-REAL 2) | u2)))
q is Relation-like the carrier of ((TOP-REAL 2) | x) -defined the carrier of ((TOP-REAL 2) | VV0) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | x), the carrier of ((TOP-REAL 2) | VV0)))
[#] ((TOP-REAL 2) | VV0) is non empty non proper closed Element of K19( the carrier of ((TOP-REAL 2) | VV0))
K111 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(cn) | K111 is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
rng ((cn) | K111) is functional Element of K19( the carrier of (TOP-REAL 2))
f4 is set
dom ((cn) | K111) is functional Element of K19( the carrier of (TOP-REAL 2))
T1 is set
((cn) | K111) . T1 is Relation-like Function-like set
T2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(cn) . T2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(dom (cn)) /\ K111 is functional Element of K19( the carrier of (TOP-REAL 2))
the carrier of (TOP-REAL 2) /\ K111 is functional Element of K19( the carrier of (TOP-REAL 2))
T2 `1 is V28() real ext-real Element of REAL
|.T2.| is V28() real ext-real non negative Element of REAL
(T2 `1) / |.T2.| is V28() real ext-real Element of COMPLEX
((T2 `1) / |.T2.|) - cn is V28() real ext-real Element of REAL
h is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
h `1 is V28() real ext-real Element of REAL
|.h.| is V28() real ext-real non negative Element of REAL
(h `1) / |.h.| is V28() real ext-real Element of COMPLEX
h `2 is V28() real ext-real Element of REAL
h is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
h `1 is V28() real ext-real Element of REAL
|.h.| is V28() real ext-real non negative Element of REAL
(h `1) / |.h.| is V28() real ext-real Element of COMPLEX
h `2 is V28() real ext-real Element of REAL
|.T2.| ^2 is V28() real ext-real Element of REAL
|.T2.| * |.T2.| is V28() real ext-real non negative set
0 ^2 is V28() real ext-real Element of REAL
0 * 0 is Function-like functional empty V28() real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() set
1 + cn is V28() real ext-real Element of REAL
(((T2 `1) / |.T2.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
|.T2.| * ((((T2 `1) / |.T2.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
((((T2 `1) / |.T2.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((T2 `1) / |.T2.|) - cn) / (1 + cn)) * ((((T2 `1) / |.T2.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((T2 `1) / |.T2.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((T2 `1) / |.T2.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((T2 `1) / |.T2.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|.T2.| * (- (sqrt (1 - (((((T2 `1) / |.T2.|) - cn) / (1 + cn)) ^2)))) is V28() real ext-real Element of REAL
|[(|.T2.| * ((((T2 `1) / |.T2.|) - cn) / (1 + cn))),(|.T2.| * (- (sqrt (1 - (((((T2 `1) / |.T2.|) - cn) / (1 + cn)) ^2)))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.T2.| * ((((T2 `1) / |.T2.|) - cn) / (1 + cn))),(|.T2.| * (- (sqrt (1 - (((((T2 `1) / |.T2.|) - cn) / (1 + cn)) ^2)))))]| `1 is V28() real ext-real Element of REAL
T2 `2 is V28() real ext-real Element of REAL
(T2 `2) ^2 is V28() real ext-real Element of REAL
(T2 `2) * (T2 `2) is V28() real ext-real set
(T2 `1) ^2 is V28() real ext-real Element of REAL
(T2 `1) * (T2 `1) is V28() real ext-real set
((T2 `1) ^2) + ((T2 `2) ^2) is V28() real ext-real Element of REAL
0 + ((T2 `1) ^2) is V28() real ext-real Element of REAL
((T2 `1) ^2) / (|.T2.| ^2) is V28() real ext-real Element of COMPLEX
(|.T2.| ^2) / (|.T2.| ^2) is V28() real ext-real Element of COMPLEX
((T2 `1) / |.T2.|) ^2 is V28() real ext-real Element of COMPLEX
((T2 `1) / |.T2.|) * ((T2 `1) / |.T2.|) is V28() real ext-real set
(- 1) - cn is V28() real ext-real Element of REAL
- (1 + cn) is V28() real ext-real Element of REAL
(- (1 + cn)) / (1 + cn) is V28() real ext-real Element of COMPLEX
- ((((T2 `1) / |.T2.|) - cn) / (1 + cn)) is V28() real ext-real Element of COMPLEX
(- ((((T2 `1) / |.T2.|) - cn) / (1 + cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((T2 `1) / |.T2.|) - cn) / (1 + cn))) * (- ((((T2 `1) / |.T2.|) - cn) / (1 + cn))) is V28() real ext-real set
1 - ((- ((((T2 `1) / |.T2.|) - cn) / (1 + cn))) ^2) is V28() real ext-real Element of REAL
- (((T2 `1) / |.T2.|) - cn) is V28() real ext-real Element of REAL
(- (((T2 `1) / |.T2.|) - cn)) / (1 + cn) is V28() real ext-real Element of COMPLEX
((- (((T2 `1) / |.T2.|) - cn)) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((T2 `1) / |.T2.|) - cn)) / (1 + cn)) * ((- (((T2 `1) / |.T2.|) - cn)) / (1 + cn)) is V28() real ext-real set
1 - (((- (((T2 `1) / |.T2.|) - cn)) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((T2 `1) / |.T2.|) - cn)) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
(- (((T2 `1) / |.T2.|) - cn)) ^2 is V28() real ext-real Element of REAL
(- (((T2 `1) / |.T2.|) - cn)) * (- (((T2 `1) / |.T2.|) - cn)) is V28() real ext-real set
(1 + cn) ^2 is V28() real ext-real Element of REAL
(1 + cn) * (1 + cn) is V28() real ext-real set
((- (((T2 `1) / |.T2.|) - cn)) ^2) / ((1 + cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((- (((T2 `1) / |.T2.|) - cn)) ^2) / ((1 + cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((T2 `1) / |.T2.|) - cn)) ^2) / ((1 + cn) ^2))) is V28() real ext-real Element of REAL
(((T2 `1) / |.T2.|) - cn) ^2 is V28() real ext-real Element of REAL
(((T2 `1) / |.T2.|) - cn) * (((T2 `1) / |.T2.|) - cn) is V28() real ext-real set
((((T2 `1) / |.T2.|) - cn) ^2) / ((1 + cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((((T2 `1) / |.T2.|) - cn) ^2) / ((1 + cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((((T2 `1) / |.T2.|) - cn) ^2) / ((1 + cn) ^2))) is V28() real ext-real Element of REAL
|[(|.T2.| * ((((T2 `1) / |.T2.|) - cn) / (1 + cn))),(|.T2.| * (- (sqrt (1 - (((((T2 `1) / |.T2.|) - cn) / (1 + cn)) ^2)))))]| `2 is V28() real ext-real Element of REAL
(|[(|.T2.| * ((((T2 `1) / |.T2.|) - cn) / (1 + cn))),(|.T2.| * (- (sqrt (1 - (((((T2 `1) / |.T2.|) - cn) / (1 + cn)) ^2)))))]| `2) ^2 is V28() real ext-real Element of REAL
(|[(|.T2.| * ((((T2 `1) / |.T2.|) - cn) / (1 + cn))),(|.T2.| * (- (sqrt (1 - (((((T2 `1) / |.T2.|) - cn) / (1 + cn)) ^2)))))]| `2) * (|[(|.T2.| * ((((T2 `1) / |.T2.|) - cn) / (1 + cn))),(|.T2.| * (- (sqrt (1 - (((((T2 `1) / |.T2.|) - cn) / (1 + cn)) ^2)))))]| `2) is V28() real ext-real set
(sqrt (1 - (((((T2 `1) / |.T2.|) - cn) / (1 + cn)) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((T2 `1) / |.T2.|) - cn) / (1 + cn)) ^2))) * (sqrt (1 - (((((T2 `1) / |.T2.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real set
(|.T2.| ^2) * ((sqrt (1 - (((((T2 `1) / |.T2.|) - cn) / (1 + cn)) ^2))) ^2) is V28() real ext-real Element of REAL
(|.T2.| ^2) * (1 - (((((T2 `1) / |.T2.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
|.|[(|.T2.| * ((((T2 `1) / |.T2.|) - cn) / (1 + cn))),(|.T2.| * (- (sqrt (1 - (((((T2 `1) / |.T2.|) - cn) / (1 + cn)) ^2)))))]|.| is V28() real ext-real non negative Element of REAL
|.|[(|.T2.| * ((((T2 `1) / |.T2.|) - cn) / (1 + cn))),(|.T2.| * (- (sqrt (1 - (((((T2 `1) / |.T2.|) - cn) / (1 + cn)) ^2)))))]|.| ^2 is V28() real ext-real Element of REAL
|.|[(|.T2.| * ((((T2 `1) / |.T2.|) - cn) / (1 + cn))),(|.T2.| * (- (sqrt (1 - (((((T2 `1) / |.T2.|) - cn) / (1 + cn)) ^2)))))]|.| * |.|[(|.T2.| * ((((T2 `1) / |.T2.|) - cn) / (1 + cn))),(|.T2.| * (- (sqrt (1 - (((((T2 `1) / |.T2.|) - cn) / (1 + cn)) ^2)))))]|.| is V28() real ext-real non negative set
(|[(|.T2.| * ((((T2 `1) / |.T2.|) - cn) / (1 + cn))),(|.T2.| * (- (sqrt (1 - (((((T2 `1) / |.T2.|) - cn) / (1 + cn)) ^2)))))]| `1) ^2 is V28() real ext-real Element of REAL
(|[(|.T2.| * ((((T2 `1) / |.T2.|) - cn) / (1 + cn))),(|.T2.| * (- (sqrt (1 - (((((T2 `1) / |.T2.|) - cn) / (1 + cn)) ^2)))))]| `1) * (|[(|.T2.| * ((((T2 `1) / |.T2.|) - cn) / (1 + cn))),(|.T2.| * (- (sqrt (1 - (((((T2 `1) / |.T2.|) - cn) / (1 + cn)) ^2)))))]| `1) is V28() real ext-real set
((|[(|.T2.| * ((((T2 `1) / |.T2.|) - cn) / (1 + cn))),(|.T2.| * (- (sqrt (1 - (((((T2 `1) / |.T2.|) - cn) / (1 + cn)) ^2)))))]| `1) ^2) + ((|[(|.T2.| * ((((T2 `1) / |.T2.|) - cn) / (1 + cn))),(|.T2.| * (- (sqrt (1 - (((((T2 `1) / |.T2.|) - cn) / (1 + cn)) ^2)))))]| `2) ^2) is V28() real ext-real Element of REAL
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `1 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `1) / |.y.| is V28() real ext-real Element of COMPLEX
y `2 is V28() real ext-real Element of REAL
dom ((cn) | K111) is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | K111 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | K111) is non empty set
K20( the carrier of ((TOP-REAL 2) | K111), the carrier of ((TOP-REAL 2) | VV0)) is set
K19(K20( the carrier of ((TOP-REAL 2) | K111), the carrier of ((TOP-REAL 2) | VV0))) is set
f4 is Relation-like the carrier of ((TOP-REAL 2) | K111) -defined the carrier of ((TOP-REAL 2) | VV0) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | K111), the carrier of ((TOP-REAL 2) | VV0)))
[#] (((TOP-REAL 2) | VV0) | y) is non empty non proper closed Element of K19( the carrier of (((TOP-REAL 2) | VV0) | y))
h is set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `1 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `1) / |.y.| is V28() real ext-real Element of COMPLEX
y `2 is V28() real ext-real Element of REAL
((y `1) / |.y.|) * |.y.| is V28() real ext-real Element of REAL
cn * |.y.| is V28() real ext-real Element of REAL
K004 /\ ([#] ((TOP-REAL 2) | VV0)) is Element of K19( the carrier of ((TOP-REAL 2) | VV0))
x /\ VV0 is functional Element of K19( the carrier of (TOP-REAL 2))
h is set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.y.| is V28() real ext-real non negative Element of REAL
cn * |.y.| is V28() real ext-real Element of REAL
y `1 is V28() real ext-real Element of REAL
y `2 is V28() real ext-real Element of REAL
(cn * |.y.|) / |.y.| is V28() real ext-real Element of COMPLEX
(y `1) / |.y.| is V28() real ext-real Element of COMPLEX
c<sub>23</sub> is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
c<sub>23</sub> `2 is V28() real ext-real Element of REAL
c₂₃ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
c₂₃ `2 is V28() real ext-real Element of REAL
[#] (((TOP-REAL 2) | VV0) | u3) is non empty non proper closed Element of K19( the carrier of (((TOP-REAL 2) | VV0) | u3))
K19( the carrier of (((TOP-REAL 2) | VV0) | u3)) is set
([#] (((TOP-REAL 2) | VV0) | u3)) /\ ([#] (((TOP-REAL 2) | VV0) | y)) is Element of K19( the carrier of (((TOP-REAL 2) | VV0) | y))
h is set
q4 . h is set
y . h is set
p1 . h is set
h is set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `1 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `1) / |.y.| is V28() real ext-real Element of COMPLEX
y `2 is V28() real ext-real Element of REAL
cn * |.y.| is V28() real ext-real Element of REAL
((y `1) / |.y.|) * |.y.| is V28() real ext-real Element of REAL
x /\ ([#] ((TOP-REAL 2) | VV0)) is Element of K19( the carrier of ((TOP-REAL 2) | VV0))
u3 \/ y is non empty Element of K19( the carrier of ((TOP-REAL 2) | VV0))
h is set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `2 is V28() real ext-real Element of REAL
y `1 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `1) / |.y.| is V28() real ext-real Element of COMPLEX
y `1 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `1) / |.y.| is V28() real ext-real Element of COMPLEX
y `1 is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
(y `1) / |.y.| is V28() real ext-real Element of COMPLEX
([#] (((TOP-REAL 2) | VV0) | u3)) \/ ([#] (((TOP-REAL 2) | VV0) | y)) is non empty set
K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of ((TOP-REAL 2) | u2)) is set
K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of ((TOP-REAL 2) | u2))) is set
q4 +* y is Relation-like Function-like set
h is Relation-like the carrier of ((TOP-REAL 2) | VV0) -defined the carrier of ((TOP-REAL 2) | u2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of ((TOP-REAL 2) | u2)))
dom h is Element of K19( the carrier of ((TOP-REAL 2) | VV0))
dom q4 is Element of K19( the carrier of (((TOP-REAL 2) | VV0) | u3))
y is set
h . y is set
p1 . y is set
(dom q4) \/ (dom y) is set
q4 . y is set
(dom q4) \/ (dom y) is set
y . y is set
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | q is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | q) is set
p is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | p is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | p) is set
K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p)) is set
K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p))) is set
(cn) | q is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p1 is Relation-like the carrier of ((TOP-REAL 2) | q) -defined the carrier of ((TOP-REAL 2) | p) -valued Function-like quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | q), the carrier of ((TOP-REAL 2) | p)))
cn ^2 is V28() real ext-real Element of REAL
cn * cn is V28() real ext-real set
1 - (cn ^2) is V28() real ext-real Element of REAL
sqrt (1 - (cn ^2)) is V28() real ext-real Element of REAL
|[cn,(sqrt (1 - (cn ^2)))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[cn,(sqrt (1 - (cn ^2)))]| `2 is V28() real ext-real Element of REAL
VV0 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
u2 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
u3 is set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `2 is V28() real ext-real Element of REAL
(TOP-REAL 2) | VV0 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | VV0) is non empty set
(TOP-REAL 2) | u2 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | u2) is non empty set
K19( the carrier of ((TOP-REAL 2) | u2)) is set
K19( the carrier of ((TOP-REAL 2) | VV0)) is set
u3 is Element of the carrier of ((TOP-REAL 2) | VV0)
p1 . u3 is set
y is Element of K19( the carrier of ((TOP-REAL 2) | u2))
[#] ((TOP-REAL 2) | u2) is non empty non proper closed Element of K19( the carrier of ((TOP-REAL 2) | u2))
q4 is functional Element of K19( the carrier of (TOP-REAL 2))
q4 /\ ([#] ((TOP-REAL 2) | u2)) is Element of K19( the carrier of ((TOP-REAL 2) | u2))
[#] ((TOP-REAL 2) | VV0) is non empty non proper closed Element of K19( the carrier of ((TOP-REAL 2) | VV0))
q4 /\ ([#] ((TOP-REAL 2) | VV0)) is Element of K19( the carrier of ((TOP-REAL 2) | VV0))
(cn) . u3 is Relation-like Function-like set
y is Element of K19( the carrier of ((TOP-REAL 2) | VV0))
p1 .: y is Element of K19( the carrier of ((TOP-REAL 2) | p))
K19( the carrier of ((TOP-REAL 2) | p)) is set
x is set
dom p1 is Element of K19( the carrier of ((TOP-REAL 2) | q))
K19( the carrier of ((TOP-REAL 2) | q)) is set
x is set
p1 . x is set
K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of ((TOP-REAL 2) | u2)) is set
K19(K20( the carrier of ((TOP-REAL 2) | VV0), the carrier of ((TOP-REAL 2) | u2))) is set
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q `2 is V28() real ext-real Element of REAL
p1 . q is set
(cn) . q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x `2 is V28() real ext-real Element of REAL
(cn) . x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | q is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | q) is set
K19( the carrier of ((TOP-REAL 2) | q)) is set
p is Element of K19( the carrier of ((TOP-REAL 2) | q))
((TOP-REAL 2) | q) | p is strict TopSpace-like T_0 T_1 T_2 SubSpace of (TOP-REAL 2) | q
the carrier of (((TOP-REAL 2) | q) | p) is set
K20( the carrier of (((TOP-REAL 2) | q) | p), the carrier of ((TOP-REAL 2) | q)) is set
K19(K20( the carrier of (((TOP-REAL 2) | q) | p), the carrier of ((TOP-REAL 2) | q))) is set
(cn) | p is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p1 is Relation-like the carrier of (((TOP-REAL 2) | q) | p) -defined the carrier of ((TOP-REAL 2) | q) -valued Function-like quasi_total Element of K19(K20( the carrier of (((TOP-REAL 2) | q) | p), the carrier of ((TOP-REAL 2) | q)))
q3 is set
VV0 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
VV0 `2 is V28() real ext-real Element of REAL
VV0 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
VV0 `2 is V28() real ext-real Element of REAL
p2 is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | p2 is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | q is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | q) is set
K19( the carrier of ((TOP-REAL 2) | q)) is set
p is Element of K19( the carrier of ((TOP-REAL 2) | q))
((TOP-REAL 2) | q) | p is strict TopSpace-like T_0 T_1 T_2 SubSpace of (TOP-REAL 2) | q
the carrier of (((TOP-REAL 2) | q) | p) is set
K20( the carrier of (((TOP-REAL 2) | q) | p), the carrier of ((TOP-REAL 2) | q)) is set
K19(K20( the carrier of (((TOP-REAL 2) | q) | p), the carrier of ((TOP-REAL 2) | q))) is set
(cn) | p is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p1 is Relation-like the carrier of (((TOP-REAL 2) | q) | p) -defined the carrier of ((TOP-REAL 2) | q) -valued Function-like quasi_total Element of K19(K20( the carrier of (((TOP-REAL 2) | q) | p), the carrier of ((TOP-REAL 2) | q)))
q3 is set
VV0 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
VV0 `2 is V28() real ext-real Element of REAL
VV0 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
VV0 `2 is V28() real ext-real Element of REAL
p2 is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | p2 is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(cn) . q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.((cn) . q).| is V28() real ext-real non negative Element of REAL
|.q.| is V28() real ext-real non negative Element of REAL
q `1 is V28() real ext-real Element of REAL
(q `1) / |.q.| is V28() real ext-real Element of COMPLEX
q `2 is V28() real ext-real Element of REAL
((q `1) / |.q.|) - cn is V28() real ext-real Element of REAL
1 - cn is V28() real ext-real Element of REAL
(((q `1) / |.q.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
|.q.| * ((((q `1) / |.q.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
((((q `1) / |.q.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((q `1) / |.q.|) - cn) / (1 - cn)) * ((((q `1) / |.q.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.q.| * (- (sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2)))) is V28() real ext-real Element of REAL
|[(|.q.| * ((((q `1) / |.q.|) - cn) / (1 - cn))),(|.q.| * (- (sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2)))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q3 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q3 `2 is V28() real ext-real Element of REAL
q3 `1 is V28() real ext-real Element of REAL
|.q.| ^2 is V28() real ext-real Element of REAL
|.q.| * |.q.| is V28() real ext-real non negative set
(q `1) ^2 is V28() real ext-real Element of REAL
(q `1) * (q `1) is V28() real ext-real set
(q `2) ^2 is V28() real ext-real Element of REAL
(q `2) * (q `2) is V28() real ext-real set
((q `1) ^2) + ((q `2) ^2) is V28() real ext-real Element of REAL
0 + ((q `1) ^2) is V28() real ext-real Element of REAL
((q `1) ^2) / (|.q.| ^2) is V28() real ext-real Element of COMPLEX
(|.q.| ^2) / (|.q.| ^2) is V28() real ext-real Element of COMPLEX
((q `1) / |.q.|) ^2 is V28() real ext-real Element of COMPLEX
((q `1) / |.q.|) * ((q `1) / |.q.|) is V28() real ext-real set
(1 - cn) " is V28() real ext-real Element of REAL
(((q `1) / |.q.|) - cn) * ((1 - cn) ") is V28() real ext-real Element of REAL
(((q `1) / |.q.|) - cn) * 0 is V28() real ext-real Element of REAL
|.q.| * 0 is Function-like functional empty V28() real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() Element of REAL
|.q.| * (- 1) is V28() real ext-real non positive Element of REAL
|[(|.q.| * 0),(|.q.| * (- 1))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
- |.q.| is V28() real ext-real non positive Element of REAL
|[0,(- |.q.|)]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((cn) . q) `2 is V28() real ext-real Element of REAL
((cn) . q) `1 is V28() real ext-real Element of REAL
(- |.q.|) ^2 is V28() real ext-real Element of REAL
(- |.q.|) * (- |.q.|) is V28() real ext-real non negative set
0 ^2 is V28() real ext-real Element of REAL
0 * 0 is Function-like functional empty V28() real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() set
((- |.q.|) ^2) + (0 ^2) is V28() real ext-real Element of REAL
sqrt (((- |.q.|) ^2) + (0 ^2)) is V28() real ext-real Element of REAL
sqrt (|.q.| ^2) is V28() real ext-real Element of REAL
- (1 - cn) is V28() real ext-real Element of REAL
- (((q `1) / |.q.|) - cn) is V28() real ext-real Element of REAL
(- (1 - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
(- (((q `1) / |.q.|) - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
((- (((q `1) / |.q.|) - cn)) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((q `1) / |.q.|) - cn)) / (1 - cn)) * ((- (((q `1) / |.q.|) - cn)) / (1 - cn)) is V28() real ext-real set
1 - (((- (((q `1) / |.q.|) - cn)) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
- ((((q `1) / |.q.|) - cn) / (1 - cn)) is V28() real ext-real Element of COMPLEX
(- ((((q `1) / |.q.|) - cn) / (1 - cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((q `1) / |.q.|) - cn) / (1 - cn))) * (- ((((q `1) / |.q.|) - cn) / (1 - cn))) is V28() real ext-real set
1 - ((- ((((q `1) / |.q.|) - cn) / (1 - cn))) ^2) is V28() real ext-real Element of REAL
(q3 `2) ^2 is V28() real ext-real Element of REAL
(q3 `2) * (q3 `2) is V28() real ext-real set
(sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2))) * (sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real set
(|.q.| ^2) * ((sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2))) ^2) is V28() real ext-real Element of REAL
(|.q.| ^2) * (1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.q3.| is V28() real ext-real non negative Element of REAL
|.q3.| ^2 is V28() real ext-real Element of REAL
|.q3.| * |.q3.| is V28() real ext-real non negative set
(q3 `1) ^2 is V28() real ext-real Element of REAL
(q3 `1) * (q3 `1) is V28() real ext-real set
((q3 `1) ^2) + ((q3 `2) ^2) is V28() real ext-real Element of REAL
sqrt (|.q3.| ^2) is V28() real ext-real Element of REAL
q `1 is V28() real ext-real Element of REAL
(q `1) / |.q.| is V28() real ext-real Element of COMPLEX
q `2 is V28() real ext-real Element of REAL
|.q.| ^2 is V28() real ext-real Element of REAL
|.q.| * |.q.| is V28() real ext-real non negative set
((q `1) / |.q.|) - cn is V28() real ext-real Element of REAL
(q `1) ^2 is V28() real ext-real Element of REAL
(q `1) * (q `1) is V28() real ext-real set
(q `2) ^2 is V28() real ext-real Element of REAL
(q `2) * (q `2) is V28() real ext-real set
((q `1) ^2) + ((q `2) ^2) is V28() real ext-real Element of REAL
0 + ((q `1) ^2) is V28() real ext-real Element of REAL
((q `1) ^2) / (|.q.| ^2) is V28() real ext-real Element of COMPLEX
(|.q.| ^2) / (|.q.| ^2) is V28() real ext-real Element of COMPLEX
((q `1) / |.q.|) ^2 is V28() real ext-real Element of COMPLEX
((q `1) / |.q.|) * ((q `1) / |.q.|) is V28() real ext-real set
(- 1) - cn is V28() real ext-real Element of REAL
1 + cn is V28() real ext-real Element of REAL
(((q `1) / |.q.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
|.q.| * ((((q `1) / |.q.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
((((q `1) / |.q.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((q `1) / |.q.|) - cn) / (1 + cn)) * ((((q `1) / |.q.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((q `1) / |.q.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|.q.| * (- (sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 + cn)) ^2)))) is V28() real ext-real Element of REAL
|[(|.q.| * ((((q `1) / |.q.|) - cn) / (1 + cn))),(|.q.| * (- (sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 + cn)) ^2)))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q3 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q3 `2 is V28() real ext-real Element of REAL
q3 `1 is V28() real ext-real Element of REAL
(1 + cn) " is V28() real ext-real Element of REAL
(((q `1) / |.q.|) - cn) * ((1 + cn) ") is V28() real ext-real Element of REAL
(((q `1) / |.q.|) - cn) * 0 is V28() real ext-real Element of REAL
((cn) . q) `2 is V28() real ext-real Element of REAL
- |.q.| is V28() real ext-real non positive Element of REAL
((cn) . q) `1 is V28() real ext-real Element of REAL
(- |.q.|) ^2 is V28() real ext-real Element of REAL
(- |.q.|) * (- |.q.|) is V28() real ext-real non negative set
0 ^2 is V28() real ext-real Element of REAL
0 * 0 is Function-like functional empty V28() real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() set
((- |.q.|) ^2) + (0 ^2) is V28() real ext-real Element of REAL
sqrt (((- |.q.|) ^2) + (0 ^2)) is V28() real ext-real Element of REAL
sqrt (|.q.| ^2) is V28() real ext-real Element of REAL
- (1 + cn) is V28() real ext-real Element of REAL
(- (1 + cn)) / (1 + cn) is V28() real ext-real Element of COMPLEX
(q3 `2) ^2 is V28() real ext-real Element of REAL
(q3 `2) * (q3 `2) is V28() real ext-real set
(sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 + cn)) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 + cn)) ^2))) * (sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real set
(|.q.| ^2) * ((sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 + cn)) ^2))) ^2) is V28() real ext-real Element of REAL
(|.q.| ^2) * (1 - (((((q `1) / |.q.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
|.q3.| is V28() real ext-real non negative Element of REAL
|.q3.| ^2 is V28() real ext-real Element of REAL
|.q3.| * |.q3.| is V28() real ext-real non negative set
(q3 `1) ^2 is V28() real ext-real Element of REAL
(q3 `1) * (q3 `1) is V28() real ext-real set
((q3 `1) ^2) + ((q3 `2) ^2) is V28() real ext-real Element of REAL
sqrt (|.q3.| ^2) is V28() real ext-real Element of REAL
- (1 + cn) is V28() real ext-real Element of REAL
q `2 is V28() real ext-real Element of REAL
q `1 is V28() real ext-real Element of REAL
(q `1) / |.q.| is V28() real ext-real Element of COMPLEX
q `2 is V28() real ext-real Element of REAL
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is set
p is set
(cn) . q is Relation-like Function-like set
p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 `2 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
|.p1.| ^2 is V28() real ext-real Element of REAL
|.p1.| * |.p1.| is V28() real ext-real non negative set
p1 `1 is V28() real ext-real Element of REAL
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((p1 `1) / |.p1.|) - cn is V28() real ext-real Element of REAL
1 + cn is V28() real ext-real Element of REAL
(((p1 `1) / |.p1.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p1 `1) / |.p1.|) - cn) / (1 + cn)) * ((((p1 `1) / |.p1.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2)))) is V28() real ext-real Element of REAL
|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn))),(|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2)))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `2 is V28() real ext-real Element of REAL
(p1 `1) ^2 is V28() real ext-real Element of REAL
(p1 `1) * (p1 `1) is V28() real ext-real set
(p1 `2) ^2 is V28() real ext-real Element of REAL
(p1 `2) * (p1 `2) is V28() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p1 `1) ^2) is V28() real ext-real Element of REAL
(|.p1.| ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
((p1 `1) ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
((p1 `1) / |.p1.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `1) / |.p1.|) * ((p1 `1) / |.p1.|) is V28() real ext-real set
(- 1) - cn is V28() real ext-real Element of REAL
(- 1) * (1 + cn) is V28() real ext-real Element of REAL
((- 1) * (1 + cn)) / (1 + cn) is V28() real ext-real Element of COMPLEX
- (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2)))) is V28() real ext-real Element of REAL
p1 `1 is V28() real ext-real Element of REAL
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((p1 `1) / |.p1.|) - cn is V28() real ext-real Element of REAL
1 - cn is V28() real ext-real Element of REAL
(((p1 `1) / |.p1.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p1 `1) / |.p1.|) - cn) / (1 - cn)) * ((((p1 `1) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2)))) is V28() real ext-real Element of REAL
|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn))),(|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2)))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `2 is V28() real ext-real Element of REAL
(p1 `1) ^2 is V28() real ext-real Element of REAL
(p1 `1) * (p1 `1) is V28() real ext-real set
(p1 `2) ^2 is V28() real ext-real Element of REAL
(p1 `2) * (p1 `2) is V28() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p1 `1) ^2) is V28() real ext-real Element of REAL
(|.p1.| ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
((p1 `1) ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
((p1 `1) / |.p1.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `1) / |.p1.|) * ((p1 `1) / |.p1.|) is V28() real ext-real set
(1 - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
- (1 - cn) is V28() real ext-real Element of REAL
cn - cn is V28() real ext-real Element of REAL
(- 1) * (1 - cn) is V28() real ext-real Element of REAL
((- 1) * (1 - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
- (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2)))) is V28() real ext-real Element of REAL
p1 `1 is V28() real ext-real Element of REAL
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is set
p is set
(cn) . q is Relation-like Function-like set
p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 `2 is V28() real ext-real Element of REAL
|[0,1]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p is V28() real ext-real Element of REAL
(p) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p1 is functional non empty Element of K19( the carrier of (TOP-REAL 2))
p1 ` is functional Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | p1 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | p1) is non empty set
K20( the carrier of ((TOP-REAL 2) | p1), the carrier of ((TOP-REAL 2) | p1)) is set
K19(K20( the carrier of ((TOP-REAL 2) | p1), the carrier of ((TOP-REAL 2) | p1))) is set
(p) | p1 is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
dom (p) is functional Element of K19( the carrier of (TOP-REAL 2))
dom ((p) | p1) is functional Element of K19( the carrier of (TOP-REAL 2))
the carrier of (TOP-REAL 2) /\ p1 is functional Element of K19( the carrier of (TOP-REAL 2))
|[0,(- 1)]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[0,(- 1)]| `2 is V28() real ext-real Element of REAL
|[0,1]| `2 is V28() real ext-real Element of REAL
q is functional Element of K19( the carrier of (TOP-REAL 2))
q ` is functional Element of K19( the carrier of (TOP-REAL 2))
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( S₁[b₁] & not b₁ = 0. (TOP-REAL 2) ) } is set
K19( the carrier of ((TOP-REAL 2) | p1)) is set
p2 is non empty Element of K19( the carrier of ((TOP-REAL 2) | p1))
((TOP-REAL 2) | p1) | p2 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of (TOP-REAL 2) | p1
the carrier of (((TOP-REAL 2) | p1) | p2) is non empty set
{ b₁ where b₁ is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2) : ( S₂[b₁] & not b₁ = 0. (TOP-REAL 2) ) } is set
q3 is non empty Element of K19( the carrier of ((TOP-REAL 2) | p1))
(p) | p2 is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
rng ((p) | p2) is functional Element of K19( the carrier of (TOP-REAL 2))
VV0 is set
dom ((p) | p2) is functional Element of K19( the carrier of (TOP-REAL 2))
u2 is set
((p) | p2) . u2 is Relation-like Function-like set
(dom (p)) /\ p2 is Element of K19( the carrier of ((TOP-REAL 2) | p1))
u3 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(p) . u3 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
VV0 is set
u2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
u2 `2 is V28() real ext-real Element of REAL
dom ((p) | p2) is functional Element of K19( the carrier of (TOP-REAL 2))
(dom (p)) /\ p2 is Element of K19( the carrier of ((TOP-REAL 2) | p1))
the carrier of (TOP-REAL 2) /\ p2 is Element of K19( the carrier of ((TOP-REAL 2) | p1))
K20( the carrier of (((TOP-REAL 2) | p1) | p2), the carrier of ((TOP-REAL 2) | p1)) is set
K19(K20( the carrier of (((TOP-REAL 2) | p1) | p2), the carrier of ((TOP-REAL 2) | p1))) is set
((TOP-REAL 2) | p1) | q3 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of (TOP-REAL 2) | p1
the carrier of (((TOP-REAL 2) | p1) | q3) is non empty set
(p) | q3 is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
rng ((p) | q3) is functional Element of K19( the carrier of (TOP-REAL 2))
u2 is set
dom ((p) | q3) is functional Element of K19( the carrier of (TOP-REAL 2))
u3 is set
((p) | q3) . u3 is Relation-like Function-like set
(dom (p)) /\ q3 is Element of K19( the carrier of ((TOP-REAL 2) | p1))
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(p) . y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
u2 is set
u3 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
u3 `2 is V28() real ext-real Element of REAL
dom ((p) | q3) is functional Element of K19( the carrier of (TOP-REAL 2))
(dom (p)) /\ q3 is Element of K19( the carrier of ((TOP-REAL 2) | p1))
the carrier of (TOP-REAL 2) /\ q3 is Element of K19( the carrier of ((TOP-REAL 2) | p1))
K20( the carrier of (((TOP-REAL 2) | p1) | q3), the carrier of ((TOP-REAL 2) | p1)) is set
K19(K20( the carrier of (((TOP-REAL 2) | p1) | q3), the carrier of ((TOP-REAL 2) | p1))) is set
[#] (((TOP-REAL 2) | p1) | q3) is non empty non proper closed Element of K19( the carrier of (((TOP-REAL 2) | p1) | q3))
K19( the carrier of (((TOP-REAL 2) | p1) | q3)) is set
p2 \/ q3 is non empty Element of K19( the carrier of ((TOP-REAL 2) | p1))
u3 is set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `2 is V28() real ext-real Element of REAL
VV0 is Relation-like the carrier of (((TOP-REAL 2) | p1) | p2) -defined the carrier of ((TOP-REAL 2) | p1) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (((TOP-REAL 2) | p1) | p2), the carrier of ((TOP-REAL 2) | p1)))
dom VV0 is Element of K19( the carrier of (((TOP-REAL 2) | p1) | p2))
K19( the carrier of (((TOP-REAL 2) | p1) | p2)) is set
[#] (((TOP-REAL 2) | p1) | p2) is non empty non proper closed Element of K19( the carrier of (((TOP-REAL 2) | p1) | p2))
([#] (((TOP-REAL 2) | p1) | p2)) /\ ([#] (((TOP-REAL 2) | p1) | q3)) is Element of K19( the carrier of (((TOP-REAL 2) | p1) | q3))
u2 is Relation-like the carrier of (((TOP-REAL 2) | p1) | q3) -defined the carrier of ((TOP-REAL 2) | p1) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (((TOP-REAL 2) | p1) | q3), the carrier of ((TOP-REAL 2) | p1)))
u3 is set
VV0 . u3 is set
u2 . u3 is set
(p) . u3 is Relation-like Function-like set
[#] ((TOP-REAL 2) | p1) is non empty non proper closed Element of K19( the carrier of ((TOP-REAL 2) | p1))
([#] (((TOP-REAL 2) | p1) | p2)) \/ ([#] (((TOP-REAL 2) | p1) | q3)) is non empty set
VV0 +* u2 is Relation-like Function-like set
u3 is Relation-like the carrier of ((TOP-REAL 2) | p1) -defined the carrier of ((TOP-REAL 2) | p1) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | p1), the carrier of ((TOP-REAL 2) | p1)))
dom u2 is Element of K19( the carrier of (((TOP-REAL 2) | p1) | q3))
dom u3 is Element of K19( the carrier of ((TOP-REAL 2) | p1))
y is set
u3 . y is set
((p) | p1) . y is Relation-like Function-like set
q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((p) | p1) . q4 is Relation-like Function-like set
(p) . q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
VV0 . q4 is set
u3 . q4 is set
u2 +* VV0 is Relation-like Function-like set
(u2 +* VV0) . q4 is set
q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q4 `2 is V28() real ext-real Element of REAL
((p) | p1) . q4 is Relation-like Function-like set
(p) . q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
u2 . q4 is set
q is V28() real ext-real Element of REAL
(q) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p . (0. (TOP-REAL 2)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn is functional non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | cn is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | cn) is non empty set
p1 is Element of the carrier of ((TOP-REAL 2) | cn)
p . p1 is Relation-like Function-like set
[#] ((TOP-REAL 2) | cn) is non empty non proper closed Element of K19( the carrier of ((TOP-REAL 2) | cn))
K19( the carrier of ((TOP-REAL 2) | cn)) is set
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `1 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `1) / |.p2.| is V28() real ext-real Element of COMPLEX
p2 `2 is V28() real ext-real Element of REAL
((p2 `1) / |.p2.|) - q is V28() real ext-real Element of REAL
1 - q is V28() real ext-real Element of REAL
(((p2 `1) / |.p2.|) - q) / (1 - q) is V28() real ext-real Element of COMPLEX
|.p2.| * ((((p2 `1) / |.p2.|) - q) / (1 - q)) is V28() real ext-real Element of REAL
((((p2 `1) / |.p2.|) - q) / (1 - q)) ^2 is V28() real ext-real Element of COMPLEX
((((p2 `1) / |.p2.|) - q) / (1 - q)) * ((((p2 `1) / |.p2.|) - q) / (1 - q)) is V28() real ext-real set
1 - (((((p2 `1) / |.p2.|) - q) / (1 - q)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p2 `1) / |.p2.|) - q) / (1 - q)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((p2 `1) / |.p2.|) - q) / (1 - q)) ^2))) is V28() real ext-real Element of REAL
|.p2.| * (- (sqrt (1 - (((((p2 `1) / |.p2.|) - q) / (1 - q)) ^2)))) is V28() real ext-real Element of REAL
|[(|.p2.| * ((((p2 `1) / |.p2.|) - q) / (1 - q))),(|.p2.| * (- (sqrt (1 - (((((p2 `1) / |.p2.|) - q) / (1 - q)) ^2)))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p2.| * ((((p2 `1) / |.p2.|) - q) / (1 - q))),(|.p2.| * (- (sqrt (1 - (((((p2 `1) / |.p2.|) - q) / (1 - q)) ^2)))))]| `1 is V28() real ext-real Element of REAL
|[(|.p2.| * ((((p2 `1) / |.p2.|) - q) / (1 - q))),(|.p2.| * (- (sqrt (1 - (((((p2 `1) / |.p2.|) - q) / (1 - q)) ^2)))))]| `2 is V28() real ext-real Element of REAL
0 ^2 is V28() real ext-real Element of REAL
0 * 0 is Function-like functional empty V28() real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() set
1 - 0 is non empty V28() real ext-real positive non negative Element of REAL
sqrt (1 - 0) is V28() real ext-real Element of REAL
- (sqrt (1 - 0)) is V28() real ext-real Element of REAL
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `1 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `1) / |.p2.| is V28() real ext-real Element of COMPLEX
p2 `2 is V28() real ext-real Element of REAL
((p2 `1) / |.p2.|) - q is V28() real ext-real Element of REAL
1 + q is V28() real ext-real Element of REAL
(((p2 `1) / |.p2.|) - q) / (1 + q) is V28() real ext-real Element of COMPLEX
|.p2.| * ((((p2 `1) / |.p2.|) - q) / (1 + q)) is V28() real ext-real Element of REAL
((((p2 `1) / |.p2.|) - q) / (1 + q)) ^2 is V28() real ext-real Element of COMPLEX
((((p2 `1) / |.p2.|) - q) / (1 + q)) * ((((p2 `1) / |.p2.|) - q) / (1 + q)) is V28() real ext-real set
1 - (((((p2 `1) / |.p2.|) - q) / (1 + q)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p2 `1) / |.p2.|) - q) / (1 + q)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((p2 `1) / |.p2.|) - q) / (1 + q)) ^2))) is V28() real ext-real Element of REAL
|.p2.| * (- (sqrt (1 - (((((p2 `1) / |.p2.|) - q) / (1 + q)) ^2)))) is V28() real ext-real Element of REAL
|[(|.p2.| * ((((p2 `1) / |.p2.|) - q) / (1 + q))),(|.p2.| * (- (sqrt (1 - (((((p2 `1) / |.p2.|) - q) / (1 + q)) ^2)))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p2.| * ((((p2 `1) / |.p2.|) - q) / (1 + q))),(|.p2.| * (- (sqrt (1 - (((((p2 `1) / |.p2.|) - q) / (1 + q)) ^2)))))]| `1 is V28() real ext-real Element of REAL
|[(|.p2.| * ((((p2 `1) / |.p2.|) - q) / (1 + q))),(|.p2.| * (- (sqrt (1 - (((((p2 `1) / |.p2.|) - q) / (1 + q)) ^2)))))]| `2 is V28() real ext-real Element of REAL
0 ^2 is V28() real ext-real Element of REAL
0 * 0 is Function-like functional empty V28() real ext-real non positive non negative V126() V127() V128() V129() V130() V131() V132() set
1 - 0 is non empty V28() real ext-real positive non negative Element of REAL
sqrt (1 - 0) is V28() real ext-real Element of REAL
- (sqrt (1 - 0)) is V28() real ext-real Element of REAL
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `2 is V28() real ext-real Element of REAL
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `1 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `1) / |.p2.| is V28() real ext-real Element of COMPLEX
p2 `2 is V28() real ext-real Element of REAL
p2 is functional Element of K19( the carrier of (TOP-REAL 2))
the carrier of (TopSpaceMetr (Euclid 2)) is set
K19( the carrier of (TopSpaceMetr (Euclid 2))) is set
q3 is Element of K19( the carrier of (TopSpaceMetr (Euclid 2)))
p1 is Element of the carrier of (Euclid 2)
VV0 is V28() real ext-real set
Ball (p1,VV0) is bounded Element of K19( the carrier of (Euclid 2))
u2 is V28() real ext-real Element of REAL
Ball (p1,u2) is bounded Element of K19( the carrier of (Euclid 2))
u3 is functional Element of K19( the carrier of (TOP-REAL 2))
p .: u3 is functional Element of K19( the carrier of (TOP-REAL 2))
y is set
dom p is functional Element of K19( the carrier of (TOP-REAL 2))
q4 is set
p . q4 is Relation-like Function-like set
rng p is functional Element of K19( the carrier of (TOP-REAL 2))
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q is Element of the carrier of (Euclid 2)
dist (p1,q) is V28() real ext-real Element of REAL
(0. (TOP-REAL 2)) - x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
- x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K443((TOP-REAL 2),(0. (TOP-REAL 2)),(- x)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is Relation-like K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)) -defined the carrier of (TOP-REAL 2) -valued Function-like total quasi_total Element of K19(K20(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)))
K20(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) is set
K19(K20(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2))) is set
K230( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),(0. (TOP-REAL 2)),(- x)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.((0. (TOP-REAL 2)) - x).| is V28() real ext-real non negative Element of REAL
x `2 is V28() real ext-real Element of REAL
x `1 is V28() real ext-real Element of REAL
|.x.| is V28() real ext-real non negative Element of REAL
(x `1) / |.x.| is V28() real ext-real Element of COMPLEX
x `2 is V28() real ext-real Element of REAL
((x `1) / |.x.|) - q is V28() real ext-real Element of REAL
(x `2) ^2 is V28() real ext-real Element of REAL
(x `2) * (x `2) is V28() real ext-real set
|.x.| ^2 is V28() real ext-real Element of REAL
|.x.| * |.x.| is V28() real ext-real non negative set
(x `1) ^2 is V28() real ext-real Element of REAL
(x `1) * (x `1) is V28() real ext-real set
((x `1) ^2) + ((x `2) ^2) is V28() real ext-real Element of REAL
0 + ((x `1) ^2) is V28() real ext-real Element of REAL
((x `1) ^2) / (|.x.| ^2) is V28() real ext-real Element of COMPLEX
(|.x.| ^2) / (|.x.| ^2) is V28() real ext-real Element of COMPLEX
1 - q is V28() real ext-real Element of REAL
((x `1) / |.x.|) ^2 is V28() real ext-real Element of COMPLEX
((x `1) / |.x.|) * ((x `1) / |.x.|) is V28() real ext-real set
- (1 - q) is V28() real ext-real Element of REAL
- (((x `1) / |.x.|) - q) is V28() real ext-real Element of REAL
(- (1 - q)) / (1 - q) is V28() real ext-real Element of COMPLEX
(- (((x `1) / |.x.|) - q)) / (1 - q) is V28() real ext-real Element of COMPLEX
((- (((x `1) / |.x.|) - q)) / (1 - q)) ^2 is V28() real ext-real Element of COMPLEX
((- (((x `1) / |.x.|) - q)) / (1 - q)) * ((- (((x `1) / |.x.|) - q)) / (1 - q)) is V28() real ext-real set
1 - (((- (((x `1) / |.x.|) - q)) / (1 - q)) ^2) is V28() real ext-real Element of REAL
(((x `1) / |.x.|) - q) / (1 - q) is V28() real ext-real Element of COMPLEX
- ((((x `1) / |.x.|) - q) / (1 - q)) is V28() real ext-real Element of COMPLEX
(- ((((x `1) / |.x.|) - q) / (1 - q))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((x `1) / |.x.|) - q) / (1 - q))) * (- ((((x `1) / |.x.|) - q) / (1 - q))) is V28() real ext-real set
1 - ((- ((((x `1) / |.x.|) - q) / (1 - q))) ^2) is V28() real ext-real Element of REAL
(q) . x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.x.| * ((((x `1) / |.x.|) - q) / (1 - q)) is V28() real ext-real Element of REAL
((((x `1) / |.x.|) - q) / (1 - q)) ^2 is V28() real ext-real Element of COMPLEX
((((x `1) / |.x.|) - q) / (1 - q)) * ((((x `1) / |.x.|) - q) / (1 - q)) is V28() real ext-real set
1 - (((((x `1) / |.x.|) - q) / (1 - q)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((x `1) / |.x.|) - q) / (1 - q)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((x `1) / |.x.|) - q) / (1 - q)) ^2))) is V28() real ext-real Element of REAL
|.x.| * (- (sqrt (1 - (((((x `1) / |.x.|) - q) / (1 - q)) ^2)))) is V28() real ext-real Element of REAL
|[(|.x.| * ((((x `1) / |.x.|) - q) / (1 - q))),(|.x.| * (- (sqrt (1 - (((((x `1) / |.x.|) - q) / (1 - q)) ^2)))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `1 is V28() real ext-real Element of REAL
y `2 is V28() real ext-real Element of REAL
(y `2) ^2 is V28() real ext-real Element of REAL
(y `2) * (y `2) is V28() real ext-real set
(sqrt (1 - (((((x `1) / |.x.|) - q) / (1 - q)) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((x `1) / |.x.|) - q) / (1 - q)) ^2))) * (sqrt (1 - (((((x `1) / |.x.|) - q) / (1 - q)) ^2))) is V28() real ext-real set
(|.x.| ^2) * ((sqrt (1 - (((((x `1) / |.x.|) - q) / (1 - q)) ^2))) ^2) is V28() real ext-real Element of REAL
(|.x.| ^2) * (1 - (((((x `1) / |.x.|) - q) / (1 - q)) ^2)) is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
|.y.| ^2 is V28() real ext-real Element of REAL
|.y.| * |.y.| is V28() real ext-real non negative set
(y `1) ^2 is V28() real ext-real Element of REAL
(y `1) * (y `1) is V28() real ext-real set
((y `1) ^2) + ((y `2) ^2) is V28() real ext-real Element of REAL
sqrt (|.y.| ^2) is V28() real ext-real Element of REAL
|.(- x).| is V28() real ext-real non negative Element of REAL
- y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.(- y).| is V28() real ext-real non negative Element of REAL
(0. (TOP-REAL 2)) - y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K443((TOP-REAL 2),(0. (TOP-REAL 2)),(- y)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K230( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),(0. (TOP-REAL 2)),(- y)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.((0. (TOP-REAL 2)) - y).| is V28() real ext-real non negative Element of REAL
x is Element of the carrier of (Euclid 2)
dist (p1,x) is V28() real ext-real Element of REAL
x `1 is V28() real ext-real Element of REAL
|.x.| is V28() real ext-real non negative Element of REAL
(x `1) / |.x.| is V28() real ext-real Element of COMPLEX
x `2 is V28() real ext-real Element of REAL
(x `2) ^2 is V28() real ext-real Element of REAL
(x `2) * (x `2) is V28() real ext-real set
|.x.| ^2 is V28() real ext-real Element of REAL
|.x.| * |.x.| is V28() real ext-real non negative set
(x `1) ^2 is V28() real ext-real Element of REAL
(x `1) * (x `1) is V28() real ext-real set
((x `1) ^2) + ((x `2) ^2) is V28() real ext-real Element of REAL
0 + ((x `1) ^2) is V28() real ext-real Element of REAL
((x `1) ^2) / (|.x.| ^2) is V28() real ext-real Element of COMPLEX
(|.x.| ^2) / (|.x.| ^2) is V28() real ext-real Element of COMPLEX
1 + q is V28() real ext-real Element of REAL
((x `1) / |.x.|) ^2 is V28() real ext-real Element of COMPLEX
((x `1) / |.x.|) * ((x `1) / |.x.|) is V28() real ext-real set
- ((x `1) / |.x.|) is V28() real ext-real Element of COMPLEX
- (- 1) is V28() real ext-real non negative Element of REAL
(- ((x `1) / |.x.|)) + q is V28() real ext-real Element of REAL
((x `1) / |.x.|) - q is V28() real ext-real Element of REAL
- (((x `1) / |.x.|) - q) is V28() real ext-real Element of REAL
(- (((x `1) / |.x.|) - q)) / (1 + q) is V28() real ext-real Element of COMPLEX
q - ((x `1) / |.x.|) is V28() real ext-real Element of REAL
((- (((x `1) / |.x.|) - q)) / (1 + q)) ^2 is V28() real ext-real Element of COMPLEX
((- (((x `1) / |.x.|) - q)) / (1 + q)) * ((- (((x `1) / |.x.|) - q)) / (1 + q)) is V28() real ext-real set
1 - (((- (((x `1) / |.x.|) - q)) / (1 + q)) ^2) is V28() real ext-real Element of REAL
(((x `1) / |.x.|) - q) / (1 + q) is V28() real ext-real Element of COMPLEX
- ((((x `1) / |.x.|) - q) / (1 + q)) is V28() real ext-real Element of COMPLEX
(- ((((x `1) / |.x.|) - q) / (1 + q))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((x `1) / |.x.|) - q) / (1 + q))) * (- ((((x `1) / |.x.|) - q) / (1 + q))) is V28() real ext-real set
1 - ((- ((((x `1) / |.x.|) - q) / (1 + q))) ^2) is V28() real ext-real Element of REAL
(q) . x is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.x.| * ((((x `1) / |.x.|) - q) / (1 + q)) is V28() real ext-real Element of REAL
((((x `1) / |.x.|) - q) / (1 + q)) ^2 is V28() real ext-real Element of COMPLEX
((((x `1) / |.x.|) - q) / (1 + q)) * ((((x `1) / |.x.|) - q) / (1 + q)) is V28() real ext-real set
1 - (((((x `1) / |.x.|) - q) / (1 + q)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((x `1) / |.x.|) - q) / (1 + q)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((x `1) / |.x.|) - q) / (1 + q)) ^2))) is V28() real ext-real Element of REAL
|.x.| * (- (sqrt (1 - (((((x `1) / |.x.|) - q) / (1 + q)) ^2)))) is V28() real ext-real Element of REAL
|[(|.x.| * ((((x `1) / |.x.|) - q) / (1 + q))),(|.x.| * (- (sqrt (1 - (((((x `1) / |.x.|) - q) / (1 + q)) ^2)))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
y `1 is V28() real ext-real Element of REAL
y `2 is V28() real ext-real Element of REAL
(y `2) ^2 is V28() real ext-real Element of REAL
(y `2) * (y `2) is V28() real ext-real set
(sqrt (1 - (((((x `1) / |.x.|) - q) / (1 + q)) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((x `1) / |.x.|) - q) / (1 + q)) ^2))) * (sqrt (1 - (((((x `1) / |.x.|) - q) / (1 + q)) ^2))) is V28() real ext-real set
(|.x.| ^2) * ((sqrt (1 - (((((x `1) / |.x.|) - q) / (1 + q)) ^2))) ^2) is V28() real ext-real Element of REAL
(|.x.| ^2) * (1 - (((((x `1) / |.x.|) - q) / (1 + q)) ^2)) is V28() real ext-real Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
|.y.| ^2 is V28() real ext-real Element of REAL
|.y.| * |.y.| is V28() real ext-real non negative set
(y `1) ^2 is V28() real ext-real Element of REAL
(y `1) * (y `1) is V28() real ext-real set
((y `1) ^2) + ((y `2) ^2) is V28() real ext-real Element of REAL
sqrt (|.y.| ^2) is V28() real ext-real Element of REAL
|.(- x).| is V28() real ext-real non negative Element of REAL
- y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.(- y).| is V28() real ext-real non negative Element of REAL
(0. (TOP-REAL 2)) - y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K443((TOP-REAL 2),(0. (TOP-REAL 2)),(- y)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K230( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),(0. (TOP-REAL 2)),(- y)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.((0. (TOP-REAL 2)) - y).| is V28() real ext-real non negative Element of REAL
x is Element of the carrier of (Euclid 2)
dist (p1,x) is V28() real ext-real Element of REAL
x `2 is V28() real ext-real Element of REAL
x `1 is V28() real ext-real Element of REAL
|.x.| is V28() real ext-real non negative Element of REAL
(x `1) / |.x.| is V28() real ext-real Element of COMPLEX
cn ` is functional Element of K19( the carrier of (TOP-REAL 2))
K20( the carrier of ((TOP-REAL 2) | cn), the carrier of ((TOP-REAL 2) | cn)) is set
K19(K20( the carrier of ((TOP-REAL 2) | cn), the carrier of ((TOP-REAL 2) | cn))) is set
(q) | cn is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p1 is Relation-like the carrier of ((TOP-REAL 2) | cn) -defined the carrier of ((TOP-REAL 2) | cn) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of ((TOP-REAL 2) | cn), the carrier of ((TOP-REAL 2) | cn)))
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
q is set
p is set
(cn) . q is Relation-like Function-like set
(cn) . p is Relation-like Function-like set
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
1 - cn is V28() real ext-real Element of REAL
p2 `2 is V28() real ext-real Element of REAL
(cn) . p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 `2 is V28() real ext-real Element of REAL
p1 `1 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `2 is V28() real ext-real Element of REAL
|.p1.| ^2 is V28() real ext-real Element of REAL
|.p1.| * |.p1.| is V28() real ext-real non negative set
((p1 `1) / |.p1.|) - cn is V28() real ext-real Element of REAL
(p1 `1) ^2 is V28() real ext-real Element of REAL
(p1 `1) * (p1 `1) is V28() real ext-real set
(p1 `2) ^2 is V28() real ext-real Element of REAL
(p1 `2) * (p1 `2) is V28() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p1 `1) ^2) is V28() real ext-real Element of REAL
((p1 `1) ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
(|.p1.| ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
((p1 `1) / |.p1.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `1) / |.p1.|) * ((p1 `1) / |.p1.|) is V28() real ext-real set
- (1 - cn) is V28() real ext-real Element of REAL
- (((p1 `1) / |.p1.|) - cn) is V28() real ext-real Element of REAL
(- (1 - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
(- (((p1 `1) / |.p1.|) - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(((p1 `1) / |.p1.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p1 `1) / |.p1.|) - cn) / (1 - cn)) * ((((p1 `1) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2)))) is V28() real ext-real Element of REAL
|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn))),(|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2)))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((- (((p1 `1) / |.p1.|) - cn)) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((p1 `1) / |.p1.|) - cn)) / (1 - cn)) * ((- (((p1 `1) / |.p1.|) - cn)) / (1 - cn)) is V28() real ext-real set
1 - (((- (((p1 `1) / |.p1.|) - cn)) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((p1 `1) / |.p1.|) - cn)) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
(- (((p1 `1) / |.p1.|) - cn)) ^2 is V28() real ext-real Element of REAL
(- (((p1 `1) / |.p1.|) - cn)) * (- (((p1 `1) / |.p1.|) - cn)) is V28() real ext-real set
(1 - cn) ^2 is V28() real ext-real Element of REAL
(1 - cn) * (1 - cn) is V28() real ext-real set
((- (((p1 `1) / |.p1.|) - cn)) ^2) / ((1 - cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((- (((p1 `1) / |.p1.|) - cn)) ^2) / ((1 - cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((p1 `1) / |.p1.|) - cn)) ^2) / ((1 - cn) ^2))) is V28() real ext-real Element of REAL
(((p1 `1) / |.p1.|) - cn) ^2 is V28() real ext-real Element of REAL
(((p1 `1) / |.p1.|) - cn) * (((p1 `1) / |.p1.|) - cn) is V28() real ext-real set
((((p1 `1) / |.p1.|) - cn) ^2) / ((1 - cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((((p1 `1) / |.p1.|) - cn) ^2) / ((1 - cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `1) / |.p1.|) - cn) ^2) / ((1 - cn) ^2))) is V28() real ext-real Element of REAL
- ((((p1 `1) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real Element of COMPLEX
(- ((((p1 `1) / |.p1.|) - cn) / (1 - cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((p1 `1) / |.p1.|) - cn) / (1 - cn))) * (- ((((p1 `1) / |.p1.|) - cn) / (1 - cn))) is V28() real ext-real set
1 - ((- ((((p1 `1) / |.p1.|) - cn) / (1 - cn))) ^2) is V28() real ext-real Element of REAL
1 * (1 - cn) is V28() real ext-real Element of REAL
1 * |.p1.| is V28() real ext-real non negative Element of REAL
p1 `1 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `2 is V28() real ext-real Element of REAL
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((p1 `1) / |.p1.|) - cn is V28() real ext-real Element of REAL
1 + cn is V28() real ext-real Element of REAL
(((p1 `1) / |.p1.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p1 `1) / |.p1.|) - cn) / (1 + cn)) * ((((p1 `1) / |.p1.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2)))) is V28() real ext-real Element of REAL
|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn))),(|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2)))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.p1.| ^2 is V28() real ext-real Element of REAL
|.p1.| * |.p1.| is V28() real ext-real non negative set
(p1 `1) ^2 is V28() real ext-real Element of REAL
(p1 `1) * (p1 `1) is V28() real ext-real set
(p1 `2) ^2 is V28() real ext-real Element of REAL
(p1 `2) * (p1 `2) is V28() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V28() real ext-real Element of REAL
- (((p1 `1) / |.p1.|) - cn) is V28() real ext-real Element of REAL
(- (((p1 `1) / |.p1.|) - cn)) / (1 + cn) is V28() real ext-real Element of COMPLEX
0 + ((p1 `1) ^2) is V28() real ext-real Element of REAL
((p1 `1) ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
(|.p1.| ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
((p1 `1) / |.p1.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `1) / |.p1.|) * ((p1 `1) / |.p1.|) is V28() real ext-real set
- ((p1 `1) / |.p1.|) is V28() real ext-real Element of COMPLEX
(- ((p1 `1) / |.p1.|)) ^2 is V28() real ext-real Element of COMPLEX
(- ((p1 `1) / |.p1.|)) * (- ((p1 `1) / |.p1.|)) is V28() real ext-real set
(- ((p1 `1) / |.p1.|)) + cn is V28() real ext-real Element of REAL
((- (((p1 `1) / |.p1.|) - cn)) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((p1 `1) / |.p1.|) - cn)) / (1 + cn)) * ((- (((p1 `1) / |.p1.|) - cn)) / (1 + cn)) is V28() real ext-real set
1 - (((- (((p1 `1) / |.p1.|) - cn)) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((p1 `1) / |.p1.|) - cn)) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
(- (((p1 `1) / |.p1.|) - cn)) ^2 is V28() real ext-real Element of REAL
(- (((p1 `1) / |.p1.|) - cn)) * (- (((p1 `1) / |.p1.|) - cn)) is V28() real ext-real set
(1 + cn) ^2 is V28() real ext-real Element of REAL
(1 + cn) * (1 + cn) is V28() real ext-real set
((- (((p1 `1) / |.p1.|) - cn)) ^2) / ((1 + cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((- (((p1 `1) / |.p1.|) - cn)) ^2) / ((1 + cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((p1 `1) / |.p1.|) - cn)) ^2) / ((1 + cn) ^2))) is V28() real ext-real Element of REAL
(((p1 `1) / |.p1.|) - cn) ^2 is V28() real ext-real Element of REAL
(((p1 `1) / |.p1.|) - cn) * (((p1 `1) / |.p1.|) - cn) is V28() real ext-real set
((((p1 `1) / |.p1.|) - cn) ^2) / ((1 + cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((((p1 `1) / |.p1.|) - cn) ^2) / ((1 + cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `1) / |.p1.|) - cn) ^2) / ((1 + cn) ^2))) is V28() real ext-real Element of REAL
- ((((p1 `1) / |.p1.|) - cn) / (1 + cn)) is V28() real ext-real Element of COMPLEX
(- ((((p1 `1) / |.p1.|) - cn) / (1 + cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((p1 `1) / |.p1.|) - cn) / (1 + cn))) * (- ((((p1 `1) / |.p1.|) - cn) / (1 + cn))) is V28() real ext-real set
1 - ((- ((((p1 `1) / |.p1.|) - cn) / (1 + cn))) ^2) is V28() real ext-real Element of REAL
1 * (1 + cn) is V28() real ext-real Element of REAL
(1 + cn) - cn is V28() real ext-real Element of REAL
- (p1 `1) is V28() real ext-real Element of REAL
(- (p1 `1)) / |.p1.| is V28() real ext-real Element of COMPLEX
1 * |.p1.| is V28() real ext-real non negative Element of REAL
((p1 `1) ^2) - ((p1 `1) ^2) is V28() real ext-real Element of REAL
p1 `2 is V28() real ext-real Element of REAL
p1 `1 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
p2 `1 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `1) / |.p2.| is V28() real ext-real Element of COMPLEX
p2 `2 is V28() real ext-real Element of REAL
|.p2.| ^2 is V28() real ext-real Element of REAL
|.p2.| * |.p2.| is V28() real ext-real non negative set
((p2 `1) / |.p2.|) - cn is V28() real ext-real Element of REAL
(((p2 `1) / |.p2.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p2 `1) / |.p2.|) - cn) / (1 - cn)) * ((((p2 `1) / |.p2.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.p2.| * (- (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2)))) is V28() real ext-real Element of REAL
|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 - cn))),(|.p2.| * (- (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2)))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 - cn))),(|.p2.| * (- (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2)))))]| `1 is V28() real ext-real Element of REAL
(cn) . p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 `2 is V28() real ext-real Element of REAL
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(p2 `1) ^2 is V28() real ext-real Element of REAL
(p2 `1) * (p2 `1) is V28() real ext-real set
(p2 `2) ^2 is V28() real ext-real Element of REAL
(p2 `2) * (p2 `2) is V28() real ext-real set
((p2 `1) ^2) + ((p2 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p2 `1) ^2) is V28() real ext-real Element of REAL
((p2 `1) ^2) / (|.p2.| ^2) is V28() real ext-real Element of COMPLEX
(|.p2.| ^2) / (|.p2.| ^2) is V28() real ext-real Element of COMPLEX
((p2 `1) / |.p2.|) ^2 is V28() real ext-real Element of COMPLEX
((p2 `1) / |.p2.|) * ((p2 `1) / |.p2.|) is V28() real ext-real set
- (1 - cn) is V28() real ext-real Element of REAL
- (((p2 `1) / |.p2.|) - cn) is V28() real ext-real Element of REAL
(- (1 - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
(- (((p2 `1) / |.p2.|) - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
((- (((p2 `1) / |.p2.|) - cn)) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((p2 `1) / |.p2.|) - cn)) / (1 - cn)) * ((- (((p2 `1) / |.p2.|) - cn)) / (1 - cn)) is V28() real ext-real set
1 - (((- (((p2 `1) / |.p2.|) - cn)) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((p2 `1) / |.p2.|) - cn)) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
(- (((p2 `1) / |.p2.|) - cn)) ^2 is V28() real ext-real Element of REAL
(- (((p2 `1) / |.p2.|) - cn)) * (- (((p2 `1) / |.p2.|) - cn)) is V28() real ext-real set
(1 - cn) ^2 is V28() real ext-real Element of REAL
(1 - cn) * (1 - cn) is V28() real ext-real set
((- (((p2 `1) / |.p2.|) - cn)) ^2) / ((1 - cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((- (((p2 `1) / |.p2.|) - cn)) ^2) / ((1 - cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((p2 `1) / |.p2.|) - cn)) ^2) / ((1 - cn) ^2))) is V28() real ext-real Element of REAL
(((p2 `1) / |.p2.|) - cn) ^2 is V28() real ext-real Element of REAL
(((p2 `1) / |.p2.|) - cn) * (((p2 `1) / |.p2.|) - cn) is V28() real ext-real set
((((p2 `1) / |.p2.|) - cn) ^2) / ((1 - cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((((p2 `1) / |.p2.|) - cn) ^2) / ((1 - cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((((p2 `1) / |.p2.|) - cn) ^2) / ((1 - cn) ^2))) is V28() real ext-real Element of REAL
- ((((p2 `1) / |.p2.|) - cn) / (1 - cn)) is V28() real ext-real Element of COMPLEX
(- ((((p2 `1) / |.p2.|) - cn) / (1 - cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((p2 `1) / |.p2.|) - cn) / (1 - cn))) * (- ((((p2 `1) / |.p2.|) - cn) / (1 - cn))) is V28() real ext-real set
1 - ((- ((((p2 `1) / |.p2.|) - cn) / (1 - cn))) ^2) is V28() real ext-real Element of REAL
1 * (1 - cn) is V28() real ext-real Element of REAL
1 * |.p2.| is V28() real ext-real non negative Element of REAL
p1 `1 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `2 is V28() real ext-real Element of REAL
(p2 `2) ^2 is V28() real ext-real Element of REAL
(p2 `2) * (p2 `2) is V28() real ext-real set
(p2 `1) ^2 is V28() real ext-real Element of REAL
(p2 `1) * (p2 `1) is V28() real ext-real set
((p2 `1) ^2) + ((p2 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p2 `1) ^2) is V28() real ext-real Element of REAL
((p2 `1) ^2) / (|.p2.| ^2) is V28() real ext-real Element of COMPLEX
(|.p2.| ^2) / (|.p2.| ^2) is V28() real ext-real Element of COMPLEX
((p2 `1) / |.p2.|) ^2 is V28() real ext-real Element of COMPLEX
((p2 `1) / |.p2.|) * ((p2 `1) / |.p2.|) is V28() real ext-real set
- (1 - cn) is V28() real ext-real Element of REAL
- (((p2 `1) / |.p2.|) - cn) is V28() real ext-real Element of REAL
(- (1 - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
(- (((p2 `1) / |.p2.|) - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
((- (((p2 `1) / |.p2.|) - cn)) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((p2 `1) / |.p2.|) - cn)) / (1 - cn)) * ((- (((p2 `1) / |.p2.|) - cn)) / (1 - cn)) is V28() real ext-real set
1 - (((- (((p2 `1) / |.p2.|) - cn)) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
- ((((p2 `1) / |.p2.|) - cn) / (1 - cn)) is V28() real ext-real Element of COMPLEX
(- ((((p2 `1) / |.p2.|) - cn) / (1 - cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((p2 `1) / |.p2.|) - cn) / (1 - cn))) * (- ((((p2 `1) / |.p2.|) - cn) / (1 - cn))) is V28() real ext-real set
1 - ((- ((((p2 `1) / |.p2.|) - cn) / (1 - cn))) ^2) is V28() real ext-real Element of REAL
|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 - cn))),(|.p2.| * (- (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2)))))]| `2 is V28() real ext-real Element of REAL
(|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 - cn))),(|.p2.| * (- (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2)))))]| `2) ^2 is V28() real ext-real Element of REAL
(|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 - cn))),(|.p2.| * (- (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2)))))]| `2) * (|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 - cn))),(|.p2.| * (- (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2)))))]| `2) is V28() real ext-real set
(sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2))) * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real set
(|.p2.| ^2) * ((sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2))) ^2) is V28() real ext-real Element of REAL
(|.p2.| ^2) * (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 - cn))),(|.p2.| * (- (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2)))))]|.| is V28() real ext-real non negative Element of REAL
|.|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 - cn))),(|.p2.| * (- (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2)))))]|.| ^2 is V28() real ext-real Element of REAL
|.|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 - cn))),(|.p2.| * (- (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2)))))]|.| * |.|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 - cn))),(|.p2.| * (- (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2)))))]|.| is V28() real ext-real non negative set
(|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 - cn))),(|.p2.| * (- (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2)))))]| `1) ^2 is V28() real ext-real Element of REAL
(|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 - cn))),(|.p2.| * (- (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2)))))]| `1) * (|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 - cn))),(|.p2.| * (- (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2)))))]| `1) is V28() real ext-real set
((|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 - cn))),(|.p2.| * (- (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2)))))]| `1) ^2) + ((|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 - cn))),(|.p2.| * (- (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2)))))]| `2) ^2) is V28() real ext-real Element of REAL
sqrt (|.|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 - cn))),(|.p2.| * (- (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 - cn)) ^2)))))]|.| ^2) is V28() real ext-real Element of REAL
(p1 `2) ^2 is V28() real ext-real Element of REAL
(p1 `2) * (p1 `2) is V28() real ext-real set
|.p1.| ^2 is V28() real ext-real Element of REAL
|.p1.| * |.p1.| is V28() real ext-real non negative set
(p1 `1) ^2 is V28() real ext-real Element of REAL
(p1 `1) * (p1 `1) is V28() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p1 `1) ^2) is V28() real ext-real Element of REAL
((p1 `1) ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
(|.p1.| ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
((p1 `1) / |.p1.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `1) / |.p1.|) * ((p1 `1) / |.p1.|) is V28() real ext-real set
((p1 `1) / |.p1.|) - cn is V28() real ext-real Element of REAL
- (((p1 `1) / |.p1.|) - cn) is V28() real ext-real Element of REAL
(- (((p1 `1) / |.p1.|) - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
((- (((p1 `1) / |.p1.|) - cn)) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((p1 `1) / |.p1.|) - cn)) / (1 - cn)) * ((- (((p1 `1) / |.p1.|) - cn)) / (1 - cn)) is V28() real ext-real set
1 - (((- (((p1 `1) / |.p1.|) - cn)) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
(((p1 `1) / |.p1.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
- ((((p1 `1) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real Element of COMPLEX
(- ((((p1 `1) / |.p1.|) - cn) / (1 - cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((p1 `1) / |.p1.|) - cn) / (1 - cn))) * (- ((((p1 `1) / |.p1.|) - cn) / (1 - cn))) is V28() real ext-real set
1 - ((- ((((p1 `1) / |.p1.|) - cn) / (1 - cn))) ^2) is V28() real ext-real Element of REAL
|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p1 `1) / |.p1.|) - cn) / (1 - cn)) * ((((p1 `1) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2)))) is V28() real ext-real Element of REAL
|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn))),(|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2)))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn))),(|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2)))))]| `1 is V28() real ext-real Element of REAL
|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn))),(|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2)))))]| `2 is V28() real ext-real Element of REAL
(|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn))),(|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2)))))]| `2) ^2 is V28() real ext-real Element of REAL
(|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn))),(|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2)))))]| `2) * (|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn))),(|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2)))))]| `2) is V28() real ext-real set
(sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2))) * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real set
(|.p1.| ^2) * ((sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2))) ^2) is V28() real ext-real Element of REAL
(|.p1.| ^2) * (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn))),(|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2)))))]|.| is V28() real ext-real non negative Element of REAL
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn))),(|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2)))))]|.| ^2 is V28() real ext-real Element of REAL
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn))),(|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2)))))]|.| * |.|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn))),(|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2)))))]|.| is V28() real ext-real non negative set
(|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn))),(|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2)))))]| `1) ^2 is V28() real ext-real Element of REAL
(|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn))),(|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2)))))]| `1) * (|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn))),(|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2)))))]| `1) is V28() real ext-real set
((|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn))),(|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2)))))]| `1) ^2) + ((|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn))),(|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2)))))]| `2) ^2) is V28() real ext-real Element of REAL
sqrt (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn))),(|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2)))))]|.| ^2) is V28() real ext-real Element of REAL
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 - cn))) / |.p1.| is V28() real ext-real Element of COMPLEX
((((p1 `1) / |.p1.|) - cn) / (1 - cn)) * (1 - cn) is V28() real ext-real Element of REAL
((p1 `1) / |.p1.|) * |.p1.| is V28() real ext-real Element of REAL
- (p1 `2) is V28() real ext-real Element of REAL
(- (p1 `2)) ^2 is V28() real ext-real Element of REAL
(- (p1 `2)) * (- (p1 `2)) is V28() real ext-real set
- (p2 `2) is V28() real ext-real Element of REAL
(- (p2 `2)) ^2 is V28() real ext-real Element of REAL
(- (p2 `2)) * (- (p2 `2)) is V28() real ext-real set
sqrt ((- (p2 `2)) ^2) is V28() real ext-real Element of REAL
- (- (p1 `2)) is V28() real ext-real Element of REAL
- (- (p2 `2)) is V28() real ext-real Element of REAL
|[(p1 `1),(p1 `2)]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `2 is V28() real ext-real Element of REAL
((p1 `1) / |.p1.|) - cn is V28() real ext-real Element of REAL
1 + cn is V28() real ext-real Element of REAL
(((p1 `1) / |.p1.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p1 `1) / |.p1.|) - cn) / (1 + cn)) * ((((p1 `1) / |.p1.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2)))) is V28() real ext-real Element of REAL
|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn))),(|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2)))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn))),(|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2)))))]| `1 is V28() real ext-real Element of REAL
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 `2 is V28() real ext-real Element of REAL
p1 `1 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
p2 `1 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `1) / |.p2.| is V28() real ext-real Element of COMPLEX
p2 `2 is V28() real ext-real Element of REAL
|.p2.| ^2 is V28() real ext-real Element of REAL
|.p2.| * |.p2.| is V28() real ext-real non negative set
((p2 `1) / |.p2.|) - cn is V28() real ext-real Element of REAL
1 + cn is V28() real ext-real Element of REAL
(((p2 `1) / |.p2.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p2 `1) / |.p2.|) - cn) / (1 + cn)) * ((((p2 `1) / |.p2.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|.p2.| * (- (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2)))) is V28() real ext-real Element of REAL
|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 + cn))),(|.p2.| * (- (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2)))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 + cn))),(|.p2.| * (- (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2)))))]| `1 is V28() real ext-real Element of REAL
(cn) . p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 `2 is V28() real ext-real Element of REAL
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(p2 `1) ^2 is V28() real ext-real Element of REAL
(p2 `1) * (p2 `1) is V28() real ext-real set
(p2 `2) ^2 is V28() real ext-real Element of REAL
(p2 `2) * (p2 `2) is V28() real ext-real set
((p2 `1) ^2) + ((p2 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p2 `1) ^2) is V28() real ext-real Element of REAL
((p2 `1) ^2) / (|.p2.| ^2) is V28() real ext-real Element of COMPLEX
(|.p2.| ^2) / (|.p2.| ^2) is V28() real ext-real Element of COMPLEX
((p2 `1) / |.p2.|) ^2 is V28() real ext-real Element of COMPLEX
((p2 `1) / |.p2.|) * ((p2 `1) / |.p2.|) is V28() real ext-real set
- ((p2 `1) / |.p2.|) is V28() real ext-real Element of COMPLEX
(- ((p2 `1) / |.p2.|)) ^2 is V28() real ext-real Element of COMPLEX
(- ((p2 `1) / |.p2.|)) * (- ((p2 `1) / |.p2.|)) is V28() real ext-real set
(- ((p2 `1) / |.p2.|)) + cn is V28() real ext-real Element of REAL
- (((p2 `1) / |.p2.|) - cn) is V28() real ext-real Element of REAL
(- (((p2 `1) / |.p2.|) - cn)) / (1 + cn) is V28() real ext-real Element of COMPLEX
((- (((p2 `1) / |.p2.|) - cn)) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((p2 `1) / |.p2.|) - cn)) / (1 + cn)) * ((- (((p2 `1) / |.p2.|) - cn)) / (1 + cn)) is V28() real ext-real set
1 - (((- (((p2 `1) / |.p2.|) - cn)) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
- ((((p2 `1) / |.p2.|) - cn) / (1 + cn)) is V28() real ext-real Element of COMPLEX
(- ((((p2 `1) / |.p2.|) - cn) / (1 + cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((p2 `1) / |.p2.|) - cn) / (1 + cn))) * (- ((((p2 `1) / |.p2.|) - cn) / (1 + cn))) is V28() real ext-real set
1 - ((- ((((p2 `1) / |.p2.|) - cn) / (1 + cn))) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((p2 `1) / |.p2.|) - cn)) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
(- (((p2 `1) / |.p2.|) - cn)) ^2 is V28() real ext-real Element of REAL
(- (((p2 `1) / |.p2.|) - cn)) * (- (((p2 `1) / |.p2.|) - cn)) is V28() real ext-real set
(1 + cn) ^2 is V28() real ext-real Element of REAL
(1 + cn) * (1 + cn) is V28() real ext-real set
((- (((p2 `1) / |.p2.|) - cn)) ^2) / ((1 + cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((- (((p2 `1) / |.p2.|) - cn)) ^2) / ((1 + cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((p2 `1) / |.p2.|) - cn)) ^2) / ((1 + cn) ^2))) is V28() real ext-real Element of REAL
(((p2 `1) / |.p2.|) - cn) ^2 is V28() real ext-real Element of REAL
(((p2 `1) / |.p2.|) - cn) * (((p2 `1) / |.p2.|) - cn) is V28() real ext-real set
((((p2 `1) / |.p2.|) - cn) ^2) / ((1 + cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((((p2 `1) / |.p2.|) - cn) ^2) / ((1 + cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((((p2 `1) / |.p2.|) - cn) ^2) / ((1 + cn) ^2))) is V28() real ext-real Element of REAL
1 * (1 + cn) is V28() real ext-real Element of REAL
(1 + cn) - cn is V28() real ext-real Element of REAL
- (p2 `1) is V28() real ext-real Element of REAL
(- (p2 `1)) / |.p2.| is V28() real ext-real Element of COMPLEX
1 * |.p2.| is V28() real ext-real non negative Element of REAL
((p2 `1) ^2) - ((p2 `1) ^2) is V28() real ext-real Element of REAL
p1 `1 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `2 is V28() real ext-real Element of REAL
((p1 `1) / |.p1.|) - cn is V28() real ext-real Element of REAL
(((p1 `1) / |.p1.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p1 `1) / |.p1.|) - cn) / (1 - cn)) * ((((p1 `1) / |.p1.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2)))) is V28() real ext-real Element of REAL
|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn))),(|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2)))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 - cn))),(|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 - cn)) ^2)))))]| `1 is V28() real ext-real Element of REAL
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `2 is V28() real ext-real Element of REAL
(p1 `2) ^2 is V28() real ext-real Element of REAL
(p1 `2) * (p1 `2) is V28() real ext-real set
|.p1.| ^2 is V28() real ext-real Element of REAL
|.p1.| * |.p1.| is V28() real ext-real non negative set
(p1 `1) ^2 is V28() real ext-real Element of REAL
(p1 `1) * (p1 `1) is V28() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p1 `1) ^2) is V28() real ext-real Element of REAL
((p1 `1) ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
(|.p1.| ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
(p2 `2) ^2 is V28() real ext-real Element of REAL
(p2 `2) * (p2 `2) is V28() real ext-real set
(p2 `1) ^2 is V28() real ext-real Element of REAL
(p2 `1) * (p2 `1) is V28() real ext-real set
((p2 `1) ^2) + ((p2 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p2 `1) ^2) is V28() real ext-real Element of REAL
((p2 `1) ^2) / (|.p2.| ^2) is V28() real ext-real Element of COMPLEX
(|.p2.| ^2) / (|.p2.| ^2) is V28() real ext-real Element of COMPLEX
((p2 `1) / |.p2.|) ^2 is V28() real ext-real Element of COMPLEX
((p2 `1) / |.p2.|) * ((p2 `1) / |.p2.|) is V28() real ext-real set
(- 1) - cn is V28() real ext-real Element of REAL
- (((p2 `1) / |.p2.|) - cn) is V28() real ext-real Element of REAL
- ((- 1) - cn) is V28() real ext-real Element of REAL
(- (((p2 `1) / |.p2.|) - cn)) / (1 + cn) is V28() real ext-real Element of COMPLEX
((- (((p2 `1) / |.p2.|) - cn)) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((p2 `1) / |.p2.|) - cn)) / (1 + cn)) * ((- (((p2 `1) / |.p2.|) - cn)) / (1 + cn)) is V28() real ext-real set
1 - (((- (((p2 `1) / |.p2.|) - cn)) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
- ((((p2 `1) / |.p2.|) - cn) / (1 + cn)) is V28() real ext-real Element of COMPLEX
(- ((((p2 `1) / |.p2.|) - cn) / (1 + cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((p2 `1) / |.p2.|) - cn) / (1 + cn))) * (- ((((p2 `1) / |.p2.|) - cn) / (1 + cn))) is V28() real ext-real set
1 - ((- ((((p2 `1) / |.p2.|) - cn) / (1 + cn))) ^2) is V28() real ext-real Element of REAL
|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 + cn))),(|.p2.| * (- (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2)))))]| `2 is V28() real ext-real Element of REAL
(|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 + cn))),(|.p2.| * (- (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2)))))]| `2) ^2 is V28() real ext-real Element of REAL
(|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 + cn))),(|.p2.| * (- (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2)))))]| `2) * (|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 + cn))),(|.p2.| * (- (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2)))))]| `2) is V28() real ext-real set
(sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2))) * (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real set
(|.p2.| ^2) * ((sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2))) ^2) is V28() real ext-real Element of REAL
(|.p2.| ^2) * (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
((p1 `1) / |.p1.|) - cn is V28() real ext-real Element of REAL
(((p1 `1) / |.p1.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p1 `1) / |.p1.|) - cn) / (1 + cn)) * ((((p1 `1) / |.p1.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2)))) is V28() real ext-real Element of REAL
|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn))),(|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2)))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn))),(|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2)))))]| `1 is V28() real ext-real Element of REAL
((p1 `1) / |.p1.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `1) / |.p1.|) * ((p1 `1) / |.p1.|) is V28() real ext-real set
- (((p1 `1) / |.p1.|) - cn) is V28() real ext-real Element of REAL
(- (((p1 `1) / |.p1.|) - cn)) / (1 + cn) is V28() real ext-real Element of COMPLEX
((- (((p1 `1) / |.p1.|) - cn)) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((p1 `1) / |.p1.|) - cn)) / (1 + cn)) * ((- (((p1 `1) / |.p1.|) - cn)) / (1 + cn)) is V28() real ext-real set
1 - (((- (((p1 `1) / |.p1.|) - cn)) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
- ((((p1 `1) / |.p1.|) - cn) / (1 + cn)) is V28() real ext-real Element of COMPLEX
(- ((((p1 `1) / |.p1.|) - cn) / (1 + cn))) ^2 is V28() real ext-real Element of COMPLEX
(- ((((p1 `1) / |.p1.|) - cn) / (1 + cn))) * (- ((((p1 `1) / |.p1.|) - cn) / (1 + cn))) is V28() real ext-real set
1 - ((- ((((p1 `1) / |.p1.|) - cn) / (1 + cn))) ^2) is V28() real ext-real Element of REAL
|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn))),(|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2)))))]| `2 is V28() real ext-real Element of REAL
(|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn))),(|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2)))))]| `2) ^2 is V28() real ext-real Element of REAL
(|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn))),(|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2)))))]| `2) * (|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn))),(|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2)))))]| `2) is V28() real ext-real set
(sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2))) * (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real set
(|.p1.| ^2) * ((sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2))) ^2) is V28() real ext-real Element of REAL
(|.p1.| ^2) * (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn))),(|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2)))))]|.| is V28() real ext-real non negative Element of REAL
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn))),(|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2)))))]|.| ^2 is V28() real ext-real Element of REAL
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn))),(|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2)))))]|.| * |.|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn))),(|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2)))))]|.| is V28() real ext-real non negative set
(|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn))),(|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2)))))]| `1) ^2 is V28() real ext-real Element of REAL
(|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn))),(|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2)))))]| `1) * (|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn))),(|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2)))))]| `1) is V28() real ext-real set
((|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn))),(|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2)))))]| `1) ^2) + ((|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn))),(|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2)))))]| `2) ^2) is V28() real ext-real Element of REAL
sqrt (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) - cn) / (1 + cn))),(|.p1.| * (- (sqrt (1 - (((((p1 `1) / |.p1.|) - cn) / (1 + cn)) ^2)))))]|.| ^2) is V28() real ext-real Element of REAL
|.|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 + cn))),(|.p2.| * (- (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2)))))]|.| is V28() real ext-real non negative Element of REAL
|.|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 + cn))),(|.p2.| * (- (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2)))))]|.| ^2 is V28() real ext-real Element of REAL
|.|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 + cn))),(|.p2.| * (- (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2)))))]|.| * |.|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 + cn))),(|.p2.| * (- (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2)))))]|.| is V28() real ext-real non negative set
(|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 + cn))),(|.p2.| * (- (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2)))))]| `1) ^2 is V28() real ext-real Element of REAL
(|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 + cn))),(|.p2.| * (- (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2)))))]| `1) * (|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 + cn))),(|.p2.| * (- (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2)))))]| `1) is V28() real ext-real set
((|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 + cn))),(|.p2.| * (- (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2)))))]| `1) ^2) + ((|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 + cn))),(|.p2.| * (- (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2)))))]| `2) ^2) is V28() real ext-real Element of REAL
sqrt (|.|[(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 + cn))),(|.p2.| * (- (sqrt (1 - (((((p2 `1) / |.p2.|) - cn) / (1 + cn)) ^2)))))]|.| ^2) is V28() real ext-real Element of REAL
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(|.p2.| * ((((p2 `1) / |.p2.|) - cn) / (1 + cn))) / |.p1.| is V28() real ext-real Element of COMPLEX
((((p1 `1) / |.p1.|) - cn) / (1 + cn)) * (1 + cn) is V28() real ext-real Element of REAL
((p1 `1) / |.p1.|) * |.p1.| is V28() real ext-real Element of REAL
- (p1 `2) is V28() real ext-real Element of REAL
(- (p1 `2)) ^2 is V28() real ext-real Element of REAL
(- (p1 `2)) * (- (p1 `2)) is V28() real ext-real set
- (p2 `2) is V28() real ext-real Element of REAL
(- (p2 `2)) ^2 is V28() real ext-real Element of REAL
(- (p2 `2)) * (- (p2 `2)) is V28() real ext-real set
sqrt ((- (p2 `2)) ^2) is V28() real ext-real Element of REAL
- (- (p1 `2)) is V28() real ext-real Element of REAL
- (- (p2 `2)) is V28() real ext-real Element of REAL
|[(p1 `1),(p1 `2)]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 `2 is V28() real ext-real Element of REAL
p1 `1 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
p2 `2 is V28() real ext-real Element of REAL
p2 `1 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `1) / |.p2.| is V28() real ext-real Element of COMPLEX
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
rng (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
q is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
dom q is functional Element of K19( the carrier of (TOP-REAL 2))
rng q is functional Element of K19( the carrier of (TOP-REAL 2))
p is set
p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 `2 is V28() real ext-real Element of REAL
(cn) . p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
p1 `1 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `2 is V28() real ext-real Element of REAL
1 + cn is V28() real ext-real Element of REAL
- (1 + cn) is V28() real ext-real Element of REAL
- (- (1 + cn)) is V28() real ext-real Element of REAL
(- 1) - cn is V28() real ext-real Element of REAL
- ((- 1) - cn) is V28() real ext-real Element of REAL
1 - cn is V28() real ext-real Element of REAL
((p1 `1) / |.p1.|) * (1 - cn) is V28() real ext-real Element of REAL
((- 1) - cn) + cn is V28() real ext-real Element of REAL
(((p1 `1) / |.p1.|) * (1 - cn)) + cn is V28() real ext-real Element of REAL
|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn) is V28() real ext-real Element of REAL
((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2 is V28() real ext-real Element of REAL
((((p1 `1) / |.p1.|) * (1 - cn)) + cn) * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn) is V28() real ext-real set
1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)) is V28() real ext-real Element of REAL
|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))) is V28() real ext-real Element of REAL
- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))) is V28() real ext-real Element of REAL
|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]| `1 is V28() real ext-real Element of REAL
|.p1.| ^2 is V28() real ext-real Element of REAL
|.p1.| * |.p1.| is V28() real ext-real non negative set
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
(p1 `2) ^2 is V28() real ext-real Element of REAL
(p1 `2) * (p1 `2) is V28() real ext-real set
(p1 `1) ^2 is V28() real ext-real Element of REAL
(p1 `1) * (p1 `1) is V28() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p1 `1) ^2) is V28() real ext-real Element of REAL
((p1 `1) ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
(|.p1.| ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
((p1 `1) / |.p1.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `1) / |.p1.|) * ((p1 `1) / |.p1.|) is V28() real ext-real set
1 * (1 - cn) is V28() real ext-real Element of REAL
((((p1 `1) / |.p1.|) * (1 - cn)) + cn) - cn is V28() real ext-real Element of REAL
|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]| `2 is V28() real ext-real Element of REAL
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| is V28() real ext-real non negative Element of REAL
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| ^2 is V28() real ext-real Element of REAL
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| * |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| is V28() real ext-real non negative set
- |.p1.| is V28() real ext-real non positive Element of REAL
(- |.p1.|) * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))) is V28() real ext-real Element of REAL
((- |.p1.|) * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))) ^2 is V28() real ext-real Element of REAL
((- |.p1.|) * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))) * ((- |.p1.|) * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))) is V28() real ext-real set
(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)) ^2 is V28() real ext-real Element of REAL
(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)) * (|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)) is V28() real ext-real set
(((- |.p1.|) * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))) ^2) + ((|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)) ^2) is V28() real ext-real Element of REAL
(sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))) * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))) is V28() real ext-real set
(|.p1.| ^2) * ((sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))) ^2) is V28() real ext-real Element of REAL
(|.p1.| ^2) * (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2) is V28() real ext-real Element of REAL
((|.p1.| ^2) * ((sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))) ^2)) + ((|.p1.| ^2) * (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)) is V28() real ext-real Element of REAL
(|.p1.| ^2) * (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)) is V28() real ext-real Element of REAL
((|.p1.| ^2) * (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2))) + ((|.p1.| ^2) * (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)) is V28() real ext-real Element of REAL
sqrt (|.p1.| ^2) is V28() real ext-real Element of REAL
0 + cn is V28() real ext-real Element of REAL
(|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| is V28() real ext-real Element of COMPLEX
(cn) . |[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.|) - cn is V28() real ext-real Element of REAL
(((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| * ((((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
((((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.|) - cn) / (1 - cn)) * ((((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| * (- (sqrt (1 - (((((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.|) - cn) / (1 - cn)) ^2)))) is V28() real ext-real Element of REAL
|[(|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| * ((((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.|) - cn) / (1 - cn))),(|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| * (- (sqrt (1 - (((((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.|) - cn) / (1 - cn)) ^2)))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
- ((p1 `2) / |.p1.|) is V28() real ext-real Element of COMPLEX
(- ((p1 `2) / |.p1.|)) ^2 is V28() real ext-real Element of COMPLEX
(- ((p1 `2) / |.p1.|)) * (- ((p1 `2) / |.p1.|)) is V28() real ext-real set
sqrt ((- ((p1 `2) / |.p1.|)) ^2) is V28() real ext-real set
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| * (sqrt ((- ((p1 `2) / |.p1.|)) ^2)) is V28() real ext-real Element of REAL
|.p1.| * (- ((p1 `2) / |.p1.|)) is V28() real ext-real Element of REAL
- (p1 `2) is V28() real ext-real Element of REAL
(- (p1 `2)) / |.p1.| is V28() real ext-real Element of COMPLEX
((- (p1 `2)) / |.p1.|) * |.p1.| is V28() real ext-real Element of REAL
- (sqrt ((- ((p1 `2) / |.p1.|)) ^2)) is V28() real ext-real set
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| * (- (sqrt ((- ((p1 `2) / |.p1.|)) ^2))) is V28() real ext-real Element of REAL
(((((p1 `1) / |.p1.|) * (1 - cn)) + cn) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
|.p1.| * ((((((p1 `1) / |.p1.|) * (1 - cn)) + cn) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
|.p1.| * ((p1 `1) / |.p1.|) is V28() real ext-real Element of REAL
(p1 `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| is V28() real ext-real Element of COMPLEX
((p1 `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.|) * ((p1 `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.|) is V28() real ext-real set
1 - (((p1 `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.|) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((p1 `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.|) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((p1 `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.|) ^2))) is V28() real ext-real Element of REAL
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| * (- (sqrt (1 - (((p1 `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.|) ^2)))) is V28() real ext-real Element of REAL
((p1 `1) ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| ^2) is V28() real ext-real Element of COMPLEX
1 - (((p1 `1) ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((p1 `1) ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| ^2))) is V28() real ext-real Element of REAL
- (sqrt (1 - (((p1 `1) ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| ^2)))) is V28() real ext-real Element of REAL
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| * (- (sqrt (1 - (((p1 `1) ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| ^2))))) is V28() real ext-real Element of REAL
(|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| ^2) is V28() real ext-real Element of COMPLEX
((|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| ^2)) - (((p1 `1) ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| ^2)) is V28() real ext-real Element of COMPLEX
sqrt (((|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| ^2)) - (((p1 `1) ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| ^2))) is V28() real ext-real set
- (sqrt (((|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| ^2)) - (((p1 `1) ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| ^2)))) is V28() real ext-real set
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| * (- (sqrt (((|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| ^2)) - (((p1 `1) ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| ^2))))) is V28() real ext-real Element of REAL
(|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| ^2) - ((p1 `1) ^2) is V28() real ext-real Element of REAL
((|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| ^2) - ((p1 `1) ^2)) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| ^2) is V28() real ext-real Element of COMPLEX
sqrt (((|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| ^2) - ((p1 `1) ^2)) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| ^2)) is V28() real ext-real set
- (sqrt (((|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| ^2) - ((p1 `1) ^2)) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| ^2))) is V28() real ext-real set
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| * (- (sqrt (((|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| ^2) - ((p1 `1) ^2)) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| ^2)))) is V28() real ext-real Element of REAL
(((p1 `1) ^2) + ((p1 `2) ^2)) - ((p1 `1) ^2) is V28() real ext-real Element of REAL
((((p1 `1) ^2) + ((p1 `2) ^2)) - ((p1 `1) ^2)) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| ^2) is V28() real ext-real Element of COMPLEX
sqrt (((((p1 `1) ^2) + ((p1 `2) ^2)) - ((p1 `1) ^2)) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| ^2)) is V28() real ext-real set
- (sqrt (((((p1 `1) ^2) + ((p1 `2) ^2)) - ((p1 `1) ^2)) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| ^2))) is V28() real ext-real set
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| * (- (sqrt (((((p1 `1) ^2) + ((p1 `2) ^2)) - ((p1 `1) ^2)) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| ^2)))) is V28() real ext-real Element of REAL
((p1 `2) / |.p1.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `2) / |.p1.|) * ((p1 `2) / |.p1.|) is V28() real ext-real set
sqrt (((p1 `2) / |.p1.|) ^2) is V28() real ext-real set
- (sqrt (((p1 `2) / |.p1.|) ^2)) is V28() real ext-real set
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 - cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 - cn)) + cn) ^2)))))]|.| * (- (sqrt (((p1 `2) / |.p1.|) ^2))) is V28() real ext-real Element of REAL
p1 `1 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
p1 `2 is V28() real ext-real Element of REAL
1 + cn is V28() real ext-real Element of REAL
1 - cn is V28() real ext-real Element of REAL
((p1 `1) / |.p1.|) * (1 + cn) is V28() real ext-real Element of REAL
(((p1 `1) / |.p1.|) * (1 + cn)) + cn is V28() real ext-real Element of REAL
(1 - cn) + cn is V28() real ext-real Element of REAL
|.p1.| ^2 is V28() real ext-real Element of REAL
|.p1.| * |.p1.| is V28() real ext-real non negative set
(p1 `2) ^2 is V28() real ext-real Element of REAL
(p1 `2) * (p1 `2) is V28() real ext-real set
(p1 `1) ^2 is V28() real ext-real Element of REAL
(p1 `1) * (p1 `1) is V28() real ext-real set
((p1 `1) ^2) + ((p1 `2) ^2) is V28() real ext-real Element of REAL
0 + ((p1 `1) ^2) is V28() real ext-real Element of REAL
((p1 `1) ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
(|.p1.| ^2) / (|.p1.| ^2) is V28() real ext-real Element of COMPLEX
((p1 `1) / |.p1.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `1) / |.p1.|) * ((p1 `1) / |.p1.|) is V28() real ext-real set
(- 1) * (1 + cn) is V28() real ext-real Element of REAL
(- 1) - cn is V28() real ext-real Element of REAL
((((p1 `1) / |.p1.|) * (1 + cn)) + cn) - cn is V28() real ext-real Element of REAL
((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2 is V28() real ext-real Element of REAL
((((p1 `1) / |.p1.|) * (1 + cn)) + cn) * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn) is V28() real ext-real set
1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)) is V28() real ext-real Element of REAL
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn) is V28() real ext-real Element of REAL
|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))) is V28() real ext-real Element of REAL
- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))) is V28() real ext-real Element of REAL
|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]| `1 is V28() real ext-real Element of REAL
|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]| `2 is V28() real ext-real Element of REAL
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| is V28() real ext-real non negative Element of REAL
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| ^2 is V28() real ext-real Element of REAL
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| * |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| is V28() real ext-real non negative set
(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))) ^2 is V28() real ext-real Element of REAL
(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))) * (- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))) is V28() real ext-real set
(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)) ^2 is V28() real ext-real Element of REAL
(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)) * (|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)) is V28() real ext-real set
((- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))))) ^2) + ((|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)) ^2) is V28() real ext-real Element of REAL
(sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))) ^2 is V28() real ext-real Element of REAL
(sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))) * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))) is V28() real ext-real set
(|.p1.| ^2) * ((sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))) ^2) is V28() real ext-real Element of REAL
(|.p1.| ^2) * (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2) is V28() real ext-real Element of REAL
((|.p1.| ^2) * ((sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))) ^2)) + ((|.p1.| ^2) * (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)) is V28() real ext-real Element of REAL
(|.p1.| ^2) * (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)) is V28() real ext-real Element of REAL
((|.p1.| ^2) * (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2))) + ((|.p1.| ^2) * (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)) is V28() real ext-real Element of REAL
sqrt (|.p1.| ^2) is V28() real ext-real Element of REAL
0 + cn is V28() real ext-real Element of REAL
(|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| is V28() real ext-real Element of COMPLEX
(cn) . |[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.|) - cn is V28() real ext-real Element of REAL
(((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| * ((((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
((((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.|) - cn) / (1 + cn)) * ((((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| * (- (sqrt (1 - (((((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.|) - cn) / (1 + cn)) ^2)))) is V28() real ext-real Element of REAL
|[(|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| * ((((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.|) - cn) / (1 + cn))),(|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| * (- (sqrt (1 - (((((|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]| `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.|) - cn) / (1 + cn)) ^2)))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(p1 `2) / |.p1.| is V28() real ext-real Element of COMPLEX
((p1 `2) / |.p1.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `2) / |.p1.|) * ((p1 `2) / |.p1.|) is V28() real ext-real set
sqrt (((p1 `2) / |.p1.|) ^2) is V28() real ext-real set
- (sqrt (((p1 `2) / |.p1.|) ^2)) is V28() real ext-real set
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| * (- (sqrt (((p1 `2) / |.p1.|) ^2))) is V28() real ext-real Element of REAL
- ((p1 `2) / |.p1.|) is V28() real ext-real Element of COMPLEX
(- ((p1 `2) / |.p1.|)) ^2 is V28() real ext-real Element of COMPLEX
(- ((p1 `2) / |.p1.|)) * (- ((p1 `2) / |.p1.|)) is V28() real ext-real set
sqrt ((- ((p1 `2) / |.p1.|)) ^2) is V28() real ext-real set
- (sqrt ((- ((p1 `2) / |.p1.|)) ^2)) is V28() real ext-real set
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| * (- (sqrt ((- ((p1 `2) / |.p1.|)) ^2))) is V28() real ext-real Element of REAL
- (- ((p1 `2) / |.p1.|)) is V28() real ext-real Element of COMPLEX
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| * (- (- ((p1 `2) / |.p1.|))) is V28() real ext-real Element of REAL
(((((p1 `1) / |.p1.|) * (1 + cn)) + cn) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
|.p1.| * ((((((p1 `1) / |.p1.|) * (1 + cn)) + cn) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
|.p1.| * ((p1 `1) / |.p1.|) is V28() real ext-real Element of REAL
(p1 `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| is V28() real ext-real Element of COMPLEX
((p1 `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.|) ^2 is V28() real ext-real Element of COMPLEX
((p1 `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.|) * ((p1 `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.|) is V28() real ext-real set
1 - (((p1 `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.|) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((p1 `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.|) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((p1 `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.|) ^2))) is V28() real ext-real Element of REAL
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| * (- (sqrt (1 - (((p1 `1) / |.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.|) ^2)))) is V28() real ext-real Element of REAL
((p1 `1) ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| ^2) is V28() real ext-real Element of COMPLEX
1 - (((p1 `1) ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((p1 `1) ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| ^2))) is V28() real ext-real Element of REAL
- (sqrt (1 - (((p1 `1) ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| ^2)))) is V28() real ext-real Element of REAL
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| * (- (sqrt (1 - (((p1 `1) ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| ^2))))) is V28() real ext-real Element of REAL
(|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| ^2) is V28() real ext-real Element of COMPLEX
((|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| ^2)) - (((p1 `1) ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| ^2)) is V28() real ext-real Element of COMPLEX
sqrt (((|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| ^2)) - (((p1 `1) ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| ^2))) is V28() real ext-real set
- (sqrt (((|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| ^2)) - (((p1 `1) ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| ^2)))) is V28() real ext-real set
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| * (- (sqrt (((|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| ^2)) - (((p1 `1) ^2) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| ^2))))) is V28() real ext-real Element of REAL
(|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| ^2) - ((p1 `1) ^2) is V28() real ext-real Element of REAL
((|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| ^2) - ((p1 `1) ^2)) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| ^2) is V28() real ext-real Element of COMPLEX
sqrt (((|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| ^2) - ((p1 `1) ^2)) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| ^2)) is V28() real ext-real set
- (sqrt (((|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| ^2) - ((p1 `1) ^2)) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| ^2))) is V28() real ext-real set
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| * (- (sqrt (((|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| ^2) - ((p1 `1) ^2)) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| ^2)))) is V28() real ext-real Element of REAL
(((p1 `1) ^2) + ((p1 `2) ^2)) - ((p1 `1) ^2) is V28() real ext-real Element of REAL
((((p1 `1) ^2) + ((p1 `2) ^2)) - ((p1 `1) ^2)) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| ^2) is V28() real ext-real Element of COMPLEX
sqrt (((((p1 `1) ^2) + ((p1 `2) ^2)) - ((p1 `1) ^2)) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| ^2)) is V28() real ext-real set
- (sqrt (((((p1 `1) ^2) + ((p1 `2) ^2)) - ((p1 `1) ^2)) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| ^2))) is V28() real ext-real set
|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| * (- (sqrt (((((p1 `1) ^2) + ((p1 `2) ^2)) - ((p1 `1) ^2)) / (|.|[(|.p1.| * ((((p1 `1) / |.p1.|) * (1 + cn)) + cn)),(- (|.p1.| * (sqrt (1 - (((((p1 `1) / |.p1.|) * (1 + cn)) + cn) ^2)))))]|.| ^2)))) is V28() real ext-real Element of REAL
p1 `2 is V28() real ext-real Element of REAL
p1 `1 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
p1 `2 is V28() real ext-real Element of REAL
dom (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
p1 `1 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
q3 is set
(cn) . q3 is Relation-like Function-like set
VV0 is set
(cn) . VV0 is Relation-like Function-like set
u2 is set
(cn) . u2 is Relation-like Function-like set
q is V28() real ext-real Element of REAL
(q) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(q) . p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn is Element of the carrier of (Euclid 2)
|.p.| is V28() real ext-real non negative Element of REAL
|.p.| + 1 is non empty V28() real ext-real positive non negative Element of REAL
Ball (cn,(|.p.| + 1)) is bounded Element of K19( the carrier of (Euclid 2))
p1 is functional Element of K19( the carrier of (TOP-REAL 2))
cl_Ball (cn,(|.p.| + 1)) is Element of K19( the carrier of (Euclid 2))
the carrier of (TopSpaceMetr (Euclid 2)) is set
K19( the carrier of (TopSpaceMetr (Euclid 2))) is set
p2 is functional non empty closed compact bounded Element of K19( the carrier of (TOP-REAL 2))
(q) .: p2 is functional Element of K19( the carrier of (TOP-REAL 2))
y is set
dom (q) is functional Element of K19( the carrier of (TOP-REAL 2))
q4 is set
(q) . q4 is Relation-like Function-like set
y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
x is Element of the carrier of (Euclid 2)
dist (cn,x) is V28() real ext-real Element of REAL
(0. (TOP-REAL 2)) - y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
- y is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K443((TOP-REAL 2),(0. (TOP-REAL 2)),(- y)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is Relation-like K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)) -defined the carrier of (TOP-REAL 2) -valued Function-like total quasi_total Element of K19(K20(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)))
K20(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) is set
K19(K20(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2))) is set
K230( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),(0. (TOP-REAL 2)),(- y)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.((0. (TOP-REAL 2)) - y).| is V28() real ext-real non negative Element of REAL
|.(- y).| is V28() real ext-real non negative Element of REAL
|.y.| is V28() real ext-real non negative Element of REAL
rng (q) is functional Element of K19( the carrier of (TOP-REAL 2))
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.q.| is V28() real ext-real non negative Element of REAL
- q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.(- q).| is V28() real ext-real non negative Element of REAL
(0. (TOP-REAL 2)) - q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K443((TOP-REAL 2),(0. (TOP-REAL 2)),(- q)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K230( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),(0. (TOP-REAL 2)),(- q)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.((0. (TOP-REAL 2)) - q).| is V28() real ext-real non negative Element of REAL
x is Element of the carrier of (Euclid 2)
dist (cn,x) is V28() real ext-real Element of REAL
VV0 is Element of K19( the carrier of (TopSpaceMetr (Euclid 2)))
- p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.(- p).| is V28() real ext-real non negative Element of REAL
(0. (TOP-REAL 2)) - p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K443((TOP-REAL 2),(0. (TOP-REAL 2)),(- p)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is Relation-like K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)) -defined the carrier of (TOP-REAL 2) -valued Function-like total quasi_total Element of K19(K20(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)))
K20(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2)) is set
K19(K20(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)), the carrier of (TOP-REAL 2))) is set
K230( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),(0. (TOP-REAL 2)),(- p)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.((0. (TOP-REAL 2)) - p).| is V28() real ext-real non negative Element of REAL
u2 is Element of the carrier of (Euclid 2)
dist (cn,u2) is V28() real ext-real Element of REAL
|.((q) . p).| is V28() real ext-real non negative Element of REAL
- ((q) . p) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.(- ((q) . p)).| is V28() real ext-real non negative Element of REAL
(0. (TOP-REAL 2)) - ((q) . p) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K443((TOP-REAL 2),(0. (TOP-REAL 2)),(- ((q) . p))) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
K230( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),(0. (TOP-REAL 2)),(- ((q) . p))) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.((0. (TOP-REAL 2)) - ((q) . p)).| is V28() real ext-real non negative Element of REAL
u3 is Element of the carrier of (Euclid 2)
dist (cn,u3) is V28() real ext-real Element of REAL
y is set
rng (q) is functional Element of K19( the carrier of (TOP-REAL 2))
q4 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
dom (q) is functional Element of K19( the carrier of (TOP-REAL 2))
y is Element of the carrier of (Euclid 2)
x is set
(q) . x is Relation-like Function-like set
x is Element of the carrier of (Euclid 2)
|.q4.| is V28() real ext-real non negative Element of REAL
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.q.| is V28() real ext-real non negative Element of REAL
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(cn) . p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
rng (cn) is functional Element of K19( the carrier of (TOP-REAL 2))
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q `2 is V28() real ext-real Element of REAL
q `1 is V28() real ext-real Element of REAL
|.q.| is V28() real ext-real non negative Element of REAL
(q `1) / |.q.| is V28() real ext-real Element of COMPLEX
(cn) . q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
1 - cn is V28() real ext-real Element of REAL
p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p `2 is V28() real ext-real Element of REAL
p `1 is V28() real ext-real Element of REAL
((q `1) / |.q.|) - cn is V28() real ext-real Element of REAL
(((q `1) / |.q.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
|.q.| * ((((q `1) / |.q.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
((((q `1) / |.q.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((q `1) / |.q.|) - cn) / (1 - cn)) * ((((q `1) / |.q.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.q.| * (- (sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2)))) is V28() real ext-real Element of REAL
|[(|.q.| * ((((q `1) / |.q.|) - cn) / (1 - cn))),(|.q.| * (- (sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2)))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
|.q.| ^2 is V28() real ext-real Element of REAL
|.q.| * |.q.| is V28() real ext-real non negative set
(q `1) ^2 is V28() real ext-real Element of REAL
(q `1) * (q `1) is V28() real ext-real set
(q `2) ^2 is V28() real ext-real Element of REAL
(q `2) * (q `2) is V28() real ext-real set
((q `1) ^2) + ((q `2) ^2) is V28() real ext-real Element of REAL
0 + ((q `1) ^2) is V28() real ext-real Element of REAL
(|.q.| ^2) / (|.q.| ^2) is V28() real ext-real Element of COMPLEX
((q `1) ^2) / (|.q.| ^2) is V28() real ext-real Element of COMPLEX
((q `1) / |.q.|) ^2 is V28() real ext-real Element of COMPLEX
((q `1) / |.q.|) * ((q `1) / |.q.|) is V28() real ext-real set
- (((q `1) / |.q.|) - cn) is V28() real ext-real Element of REAL
- (1 - cn) is V28() real ext-real Element of REAL
(- (((q `1) / |.q.|) - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
(- (1 - cn)) / (1 - cn) is V28() real ext-real Element of COMPLEX
((- (((q `1) / |.q.|) - cn)) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((q `1) / |.q.|) - cn)) / (1 - cn)) * ((- (((q `1) / |.q.|) - cn)) / (1 - cn)) is V28() real ext-real set
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q `2 is V28() real ext-real Element of REAL
q `1 is V28() real ext-real Element of REAL
|.q.| is V28() real ext-real non negative Element of REAL
(q `1) / |.q.| is V28() real ext-real Element of COMPLEX
(cn) . q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
1 + cn is V28() real ext-real Element of REAL
((q `1) / |.q.|) - cn is V28() real ext-real Element of REAL
- (((q `1) / |.q.|) - cn) is V28() real ext-real Element of REAL
(- (((q `1) / |.q.|) - cn)) / (1 + cn) is V28() real ext-real Element of COMPLEX
- (1 + cn) is V28() real ext-real Element of REAL
(- (1 + cn)) / (1 + cn) is V28() real ext-real Element of COMPLEX
|.q.| ^2 is V28() real ext-real Element of REAL
|.q.| * |.q.| is V28() real ext-real non negative set
(q `1) ^2 is V28() real ext-real Element of REAL
(q `1) * (q `1) is V28() real ext-real set
(q `2) ^2 is V28() real ext-real Element of REAL
(q `2) * (q `2) is V28() real ext-real set
((q `1) ^2) + ((q `2) ^2) is V28() real ext-real Element of REAL
0 + ((q `1) ^2) is V28() real ext-real Element of REAL
(|.q.| ^2) / (|.q.| ^2) is V28() real ext-real Element of COMPLEX
((q `1) ^2) / (|.q.| ^2) is V28() real ext-real Element of COMPLEX
((q `1) / |.q.|) ^2 is V28() real ext-real Element of COMPLEX
((q `1) / |.q.|) * ((q `1) / |.q.|) is V28() real ext-real set
(- 1) - cn is V28() real ext-real Element of REAL
- (- (1 + cn)) is V28() real ext-real Element of REAL
((- (((q `1) / |.q.|) - cn)) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((- (((q `1) / |.q.|) - cn)) / (1 + cn)) * ((- (((q `1) / |.q.|) - cn)) / (1 + cn)) is V28() real ext-real set
1 - (((- (((q `1) / |.q.|) - cn)) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((q `1) / |.q.|) - cn)) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
(- (((q `1) / |.q.|) - cn)) ^2 is V28() real ext-real Element of REAL
(- (((q `1) / |.q.|) - cn)) * (- (((q `1) / |.q.|) - cn)) is V28() real ext-real set
(1 + cn) ^2 is V28() real ext-real Element of REAL
(1 + cn) * (1 + cn) is V28() real ext-real set
((- (((q `1) / |.q.|) - cn)) ^2) / ((1 + cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((- (((q `1) / |.q.|) - cn)) ^2) / ((1 + cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((- (((q `1) / |.q.|) - cn)) ^2) / ((1 + cn) ^2))) is V28() real ext-real Element of REAL
(((q `1) / |.q.|) - cn) ^2 is V28() real ext-real Element of REAL
(((q `1) / |.q.|) - cn) * (((q `1) / |.q.|) - cn) is V28() real ext-real set
((((q `1) / |.q.|) - cn) ^2) / ((1 + cn) ^2) is V28() real ext-real Element of COMPLEX
1 - (((((q `1) / |.q.|) - cn) ^2) / ((1 + cn) ^2)) is V28() real ext-real Element of REAL
sqrt (1 - (((((q `1) / |.q.|) - cn) ^2) / ((1 + cn) ^2))) is V28() real ext-real Element of REAL
(((q `1) / |.q.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
((((q `1) / |.q.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((q `1) / |.q.|) - cn) / (1 + cn)) * ((((q `1) / |.q.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((q `1) / |.q.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
- (- (sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 + cn)) ^2)))) is V28() real ext-real Element of REAL
p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p `2 is V28() real ext-real Element of REAL
p `1 is V28() real ext-real Element of REAL
|.q.| * ((((q `1) / |.q.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
|.q.| * (- (sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 + cn)) ^2)))) is V28() real ext-real Element of REAL
|[(|.q.| * ((((q `1) / |.q.|) - cn) / (1 + cn))),(|.q.| * (- (sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 + cn)) ^2)))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q `2 is V28() real ext-real Element of REAL
q `1 is V28() real ext-real Element of REAL
|.q.| is V28() real ext-real non negative Element of REAL
(q `1) / |.q.| is V28() real ext-real Element of COMPLEX
p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p `2 is V28() real ext-real Element of REAL
p `1 is V28() real ext-real Element of REAL
|.p.| is V28() real ext-real non negative Element of REAL
(p `1) / |.p.| is V28() real ext-real Element of COMPLEX
(cn) . q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(cn) . p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((p `1) / |.p.|) - cn is V28() real ext-real Element of REAL
((q `1) / |.q.|) - cn is V28() real ext-real Element of REAL
1 - cn is V28() real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `1 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `1) / |.p2.| is V28() real ext-real Element of COMPLEX
p1 `1 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
(((p `1) / |.p.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
|.p.| * ((((p `1) / |.p.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
((((p `1) / |.p.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p `1) / |.p.|) - cn) / (1 - cn)) * ((((p `1) / |.p.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((p `1) / |.p.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p `1) / |.p.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((p `1) / |.p.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.p.| * (- (sqrt (1 - (((((p `1) / |.p.|) - cn) / (1 - cn)) ^2)))) is V28() real ext-real Element of REAL
|[(|.p.| * ((((p `1) / |.p.|) - cn) / (1 - cn))),(|.p.| * (- (sqrt (1 - (((((p `1) / |.p.|) - cn) / (1 - cn)) ^2)))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(((q `1) / |.q.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
|.q.| * ((((q `1) / |.q.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
((((q `1) / |.q.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((q `1) / |.q.|) - cn) / (1 - cn)) * ((((q `1) / |.q.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.q.| * (- (sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2)))) is V28() real ext-real Element of REAL
|[(|.q.| * ((((q `1) / |.q.|) - cn) / (1 - cn))),(|.q.| * (- (sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2)))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q `2 is V28() real ext-real Element of REAL
q `1 is V28() real ext-real Element of REAL
|.q.| is V28() real ext-real non negative Element of REAL
(q `1) / |.q.| is V28() real ext-real Element of COMPLEX
p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p `2 is V28() real ext-real Element of REAL
p `1 is V28() real ext-real Element of REAL
|.p.| is V28() real ext-real non negative Element of REAL
(p `1) / |.p.| is V28() real ext-real Element of COMPLEX
(cn) . q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(cn) . p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
((p `1) / |.p.|) - cn is V28() real ext-real Element of REAL
((q `1) / |.q.|) - cn is V28() real ext-real Element of REAL
1 + cn is V28() real ext-real Element of REAL
p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `1 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `1) / |.p2.| is V28() real ext-real Element of COMPLEX
p1 `1 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
(((p `1) / |.p.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
|.p.| * ((((p `1) / |.p.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
((((p `1) / |.p.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((p `1) / |.p.|) - cn) / (1 + cn)) * ((((p `1) / |.p.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((p `1) / |.p.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((p `1) / |.p.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((p `1) / |.p.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|.p.| * (- (sqrt (1 - (((((p `1) / |.p.|) - cn) / (1 + cn)) ^2)))) is V28() real ext-real Element of REAL
|[(|.p.| * ((((p `1) / |.p.|) - cn) / (1 + cn))),(|.p.| * (- (sqrt (1 - (((((p `1) / |.p.|) - cn) / (1 + cn)) ^2)))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(((q `1) / |.q.|) - cn) / (1 + cn) is V28() real ext-real Element of COMPLEX
|.q.| * ((((q `1) / |.q.|) - cn) / (1 + cn)) is V28() real ext-real Element of REAL
((((q `1) / |.q.|) - cn) / (1 + cn)) ^2 is V28() real ext-real Element of COMPLEX
((((q `1) / |.q.|) - cn) / (1 + cn)) * ((((q `1) / |.q.|) - cn) / (1 + cn)) is V28() real ext-real set
1 - (((((q `1) / |.q.|) - cn) / (1 + cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 + cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 + cn)) ^2))) is V28() real ext-real Element of REAL
|.q.| * (- (sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 + cn)) ^2)))) is V28() real ext-real Element of REAL
|[(|.q.| * ((((q `1) / |.q.|) - cn) / (1 + cn))),(|.q.| * (- (sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 + cn)) ^2)))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q `2 is V28() real ext-real Element of REAL
p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p `2 is V28() real ext-real Element of REAL
p `1 is V28() real ext-real Element of REAL
|.p.| is V28() real ext-real non negative Element of REAL
(p `1) / |.p.| is V28() real ext-real Element of COMPLEX
q `1 is V28() real ext-real Element of REAL
|.q.| is V28() real ext-real non negative Element of REAL
(q `1) / |.q.| is V28() real ext-real Element of COMPLEX
(cn) . q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
(cn) . p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p1 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p2 `1 is V28() real ext-real Element of REAL
|.p2.| is V28() real ext-real non negative Element of REAL
(p2 `1) / |.p2.| is V28() real ext-real Element of COMPLEX
p1 `1 is V28() real ext-real Element of REAL
|.p1.| is V28() real ext-real non negative Element of REAL
(p1 `1) / |.p1.| is V28() real ext-real Element of COMPLEX
cn is V28() real ext-real Element of REAL
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
q `2 is V28() real ext-real Element of REAL
q `1 is V28() real ext-real Element of REAL
|.q.| is V28() real ext-real non negative Element of REAL
(q `1) / |.q.| is V28() real ext-real Element of COMPLEX
(cn) . q is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
p `2 is V28() real ext-real Element of REAL
p `1 is V28() real ext-real Element of REAL
((q `1) / |.q.|) - cn is V28() real ext-real Element of REAL
1 - cn is V28() real ext-real Element of REAL
(((q `1) / |.q.|) - cn) / (1 - cn) is V28() real ext-real Element of COMPLEX
|.q.| * ((((q `1) / |.q.|) - cn) / (1 - cn)) is V28() real ext-real Element of REAL
((((q `1) / |.q.|) - cn) / (1 - cn)) ^2 is V28() real ext-real Element of COMPLEX
((((q `1) / |.q.|) - cn) / (1 - cn)) * ((((q `1) / |.q.|) - cn) / (1 - cn)) is V28() real ext-real set
1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2) is V28() real ext-real Element of REAL
sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2)) is V28() real ext-real Element of REAL
- (sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2))) is V28() real ext-real Element of REAL
|.q.| * (- (sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2)))) is V28() real ext-real Element of REAL
|[(|.q.| * ((((q `1) / |.q.|) - cn) / (1 - cn))),(|.q.| * (- (sqrt (1 - (((((q `1) / |.q.|) - cn) / (1 - cn)) ^2)))))]| is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)
cn is V28() real ext-real set
(cn) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(cn) . (0. (TOP-REAL 2)) is Relation-like Function-like V42(2) V118() V137() Element of the carrier of (TOP-REAL 2)